id	sid	tid	token	lemma	pos
ejpam-4553	1	1	european	european	PROPN
ejpam-4553	1	2	journal	journal	PROPN
ejpam-4553	1	3	of	of	ADP
ejpam-4553	1	4	pure	pure	ADJ
ejpam-4553	1	5	and	and	CCONJ
ejpam-4553	1	6	applied	apply	VERB
ejpam-4553	1	7	mathematics	mathematic	NOUN
ejpam-4553	1	8	vol	vol	NOUN
ejpam-4553	1	9	.	.	PROPN
ejpam-4553	2	1	15	15	NUM
ejpam-4553	2	2	,	,	PUNCT
ejpam-4553	2	3	no	no	INTJ
ejpam-4553	2	4	.	.	NOUN
ejpam-4553	2	5	4	4	NUM
ejpam-4553	2	6	,	,	PUNCT
ejpam-4553	2	7	2022	2022	NUM
ejpam-4553	2	8	,	,	PUNCT
ejpam-4553	2	9	1716	1716	NUM
ejpam-4553	2	10	-	-	SYM
ejpam-4553	2	11	1737	1737	NUM
ejpam-4553	2	12	issn	issn	PROPN
ejpam-4553	2	13	1307	1307	NUM
ejpam-4553	2	14	-	-	SYM
ejpam-4553	2	15	5543	5543	NUM
ejpam-4553	2	16	–	–	PUNCT
ejpam-4553	2	17	ejpam.com	ejpam.com	X
ejpam-4553	2	18	published	publish	VERB
ejpam-4553	2	19	by	by	ADP
ejpam-4553	2	20	new	new	PROPN
ejpam-4553	2	21	york	york	PROPN
ejpam-4553	2	22	business	business	PROPN
ejpam-4553	2	23	global	global	PROPN
ejpam-4553	2	24	boundedness	boundedness	NOUN
ejpam-4553	2	25	of	of	ADP
ejpam-4553	2	26	non	non	ADJ
ejpam-4553	2	27	regular	regular	ADJ
ejpam-4553	2	28	pseudo	pseudo	NOUN
ejpam-4553	2	29	-	-	ADJ
ejpam-4553	2	30	differential	differential	ADJ
ejpam-4553	2	31	operators	operator	NOUN
ejpam-4553	2	32	and	and	CCONJ
ejpam-4553	2	33	their	their	PRON
ejpam-4553	2	34	adjoints	adjoint	NOUN
ejpam-4553	2	35	on	on	ADP
ejpam-4553	2	36	variable	variable	ADJ
ejpam-4553	2	37	exponent	exponent	NOUN
ejpam-4553	2	38	besov	besov	NOUN
ejpam-4553	2	39	-	-	PUNCT
ejpam-4553	2	40	morrey	morrey	PROPN
ejpam-4553	2	41	spaces	space	NOUN
ejpam-4553	2	42	mohamed	mohamed	PROPN
ejpam-4553	2	43	congo1,∗	congo1,∗	PROPN
ejpam-4553	2	44	,	,	PUNCT
ejpam-4553	2	45	marie	marie	PROPN
ejpam-4553	2	46	françoise	françoise	PROPN
ejpam-4553	2	47	ouedraogo1	ouedraogo1	PROPN
ejpam-4553	2	48	1	1	NUM
ejpam-4553	2	49	département	département	PROPN
ejpam-4553	2	50	de	de	X
ejpam-4553	2	51	mathematiques	mathematique	NOUN
ejpam-4553	2	52	.	.	PUNCT
ejpam-4553	3	1	ufr	ufr	PROPN
ejpam-4553	3	2	sciences	sciences	PROPN
ejpam-4553	3	3	exactes	exact	VERB
ejpam-4553	3	4	et	et	NOUN
ejpam-4553	3	5	appliquées/	appliquées/	PROPN
ejpam-4553	3	6	université	université	NOUN
ejpam-4553	3	7	joseph	joseph	PROPN
ejpam-4553	3	8	ki	ki	PROPN
ejpam-4553	3	9	-	-	PUNCT
ejpam-4553	3	10	zerbo	zerbo	PROPN
ejpam-4553	3	11	,	,	PUNCT
ejpam-4553	3	12	03	03	NUM
ejpam-4553	3	13	bp	bp	PROPN
ejpam-4553	3	14	7021	7021	NUM
ejpam-4553	3	15	ouaga	ouaga	NOUN
ejpam-4553	3	16	03	03	NUM
ejpam-4553	3	17	,	,	PUNCT
ejpam-4553	3	18	ouagadougou	ouagadougou	PROPN
ejpam-4553	3	19	,	,	PUNCT
ejpam-4553	3	20	burkina	burkina	PROPN
ejpam-4553	3	21	faso	faso	PROPN
ejpam-4553	3	22	abstract	abstract	PROPN
ejpam-4553	3	23	.	.	PUNCT
ejpam-4553	4	1	this	this	DET
ejpam-4553	4	2	paper	paper	NOUN
ejpam-4553	4	3	deal	deal	NOUN
ejpam-4553	4	4	with	with	ADP
ejpam-4553	4	5	the	the	DET
ejpam-4553	4	6	boundedness	boundedness	NOUN
ejpam-4553	4	7	property	property	NOUN
ejpam-4553	4	8	of	of	ADP
ejpam-4553	4	9	non	non	ADJ
ejpam-4553	4	10	regular	regular	ADJ
ejpam-4553	4	11	pseudo	pseudo	NOUN
ejpam-4553	4	12	-	-	NOUN
ejpam-4553	4	13	differential	differential	ADJ
ejpam-4553	4	14	operators	operator	NOUN
ejpam-4553	4	15	a(x	a(x	NOUN
ejpam-4553	4	16	,	,	PUNCT
ejpam-4553	4	17	d	d	NOUN
ejpam-4553	4	18	)	)	PUNCT
ejpam-4553	4	19	and	and	CCONJ
ejpam-4553	4	20	their	their	PRON
ejpam-4553	4	21	adjoints	adjoint	NOUN
ejpam-4553	4	22	a(x	a(x	NOUN
ejpam-4553	4	23	,	,	PUNCT
ejpam-4553	4	24	d)∗	d)∗	PROPN
ejpam-4553	4	25	on	on	ADP
ejpam-4553	4	26	variable	variable	ADJ
ejpam-4553	4	27	exponent	exponent	NOUN
ejpam-4553	4	28	bm	bm	PROPN
ejpam-4553	4	29	spaces	space	VERB
ejpam-4553	4	30	.	.	PUNCT
ejpam-4553	5	1	for	for	ADP
ejpam-4553	5	2	this	this	DET
ejpam-4553	5	3	purpose	purpose	NOUN
ejpam-4553	5	4	,	,	PUNCT
ejpam-4553	5	5	given	give	VERB
ejpam-4553	5	6	such	such	DET
ejpam-4553	5	7	an	an	DET
ejpam-4553	5	8	operator	operator	NOUN
ejpam-4553	5	9	,	,	PUNCT
ejpam-4553	5	10	we	we	PRON
ejpam-4553	5	11	use	use	VERB
ejpam-4553	5	12	the	the	DET
ejpam-4553	5	13	technique	technique	NOUN
ejpam-4553	5	14	of	of	ADP
ejpam-4553	5	15	decomposition	decomposition	NOUN
ejpam-4553	5	16	of	of	ADP
ejpam-4553	5	17	its	its	PRON
ejpam-4553	5	18	symbol	symbol	NOUN
ejpam-4553	5	19	into	into	ADP
ejpam-4553	5	20	elementary	elementary	ADJ
ejpam-4553	5	21	symbols	symbol	NOUN
ejpam-4553	5	22	already	already	ADV
ejpam-4553	5	23	used	use	VERB
ejpam-4553	5	24	in	in	ADP
ejpam-4553	5	25	other	other	ADJ
ejpam-4553	5	26	spaces	space	NOUN
ejpam-4553	5	27	.	.	PUNCT
ejpam-4553	6	1	2020	2020	NUM
ejpam-4553	6	2	mathematics	mathematic	NOUN
ejpam-4553	6	3	subject	subject	NOUN
ejpam-4553	6	4	classifications	classification	NOUN
ejpam-4553	6	5	:	:	PUNCT
ejpam-4553	6	6	42b37	42b37	NUM
ejpam-4553	6	7	,	,	PUNCT
ejpam-4553	6	8	46e30	46e30	NUM
ejpam-4553	6	9	,	,	PUNCT
ejpam-4553	6	10	35s05	35s05	NUM
ejpam-4553	6	11	key	key	ADJ
ejpam-4553	6	12	words	word	NOUN
ejpam-4553	6	13	and	and	CCONJ
ejpam-4553	6	14	phrases	phrase	NOUN
ejpam-4553	6	15	:	:	PUNCT
ejpam-4553	6	16	pseudo	pseudo	NOUN
ejpam-4553	6	17	-	-	NOUN
ejpam-4553	6	18	differential	differential	ADJ
ejpam-4553	6	19	operators	operator	NOUN
ejpam-4553	6	20	,	,	PUNCT
ejpam-4553	6	21	adjoints	adjoint	NOUN
ejpam-4553	6	22	,	,	PUNCT
ejpam-4553	6	23	non	non	X
ejpam-4553	6	24	regular	regular	ADJ
ejpam-4553	6	25	symbols	symbol	NOUN
ejpam-4553	6	26	,	,	PUNCT
ejpam-4553	6	27	elementary	elementary	ADJ
ejpam-4553	6	28	symbol	symbol	NOUN
ejpam-4553	6	29	,	,	PUNCT
ejpam-4553	6	30	variable	variable	ADJ
ejpam-4553	6	31	exponent	exponent	NOUN
ejpam-4553	6	32	besov	besov	NOUN
ejpam-4553	6	33	-	-	PUNCT
ejpam-4553	6	34	morrey	morrey	NOUN
ejpam-4553	6	35	spaces	space	NOUN
ejpam-4553	6	36	.	.	PUNCT
ejpam-4553	7	1	1	1	X
ejpam-4553	7	2	.	.	X
ejpam-4553	7	3	introduction	introduction	NOUN
ejpam-4553	7	4	besov	besov	NOUN
ejpam-4553	7	5	-	-	PUNCT
ejpam-4553	7	6	morrey	morrey	NOUN
ejpam-4553	7	7	spaces	space	NOUN
ejpam-4553	7	8	denoted	denote	VERB
ejpam-4553	7	9	n	n	PROPN
ejpam-4553	7	10	s	s	PROPN
ejpam-4553	7	11	p	p	X
ejpam-4553	7	12	,	,	PUNCT
ejpam-4553	7	13	u	u	NOUN
ejpam-4553	7	14	,	,	PUNCT
ejpam-4553	7	15	q	q	PUNCT
ejpam-4553	7	16	were	be	AUX
ejpam-4553	7	17	initially	initially	ADV
ejpam-4553	7	18	investigated	investigate	VERB
ejpam-4553	7	19	by	by	ADP
ejpam-4553	7	20	kozono	kozono	PROPN
ejpam-4553	7	21	and	and	CCONJ
ejpam-4553	7	22	yamazaki	yamazaki	PROPN
ejpam-4553	7	23	in	in	ADP
ejpam-4553	7	24	[	[	X
ejpam-4553	7	25	8	8	NUM
ejpam-4553	7	26	]	]	PUNCT
ejpam-4553	7	27	to	to	PART
ejpam-4553	7	28	study	study	VERB
ejpam-4553	7	29	the	the	DET
ejpam-4553	7	30	solutions	solution	NOUN
ejpam-4553	7	31	of	of	ADP
ejpam-4553	7	32	the	the	DET
ejpam-4553	7	33	navier	navier	NOUN
ejpam-4553	7	34	-	-	PUNCT
ejpam-4553	7	35	stokes	stoke	NOUN
ejpam-4553	7	36	equations	equation	NOUN
ejpam-4553	7	37	with	with	ADP
ejpam-4553	7	38	critical	critical	ADJ
ejpam-4553	7	39	regularity	regularity	NOUN
ejpam-4553	7	40	.	.	PUNCT
ejpam-4553	8	1	the	the	DET
ejpam-4553	8	2	theory	theory	NOUN
ejpam-4553	8	3	of	of	ADP
ejpam-4553	8	4	besov	besov	NOUN
ejpam-4553	8	5	-	-	PUNCT
ejpam-4553	8	6	morrey	morrey	NOUN
ejpam-4553	8	7	spaces	space	NOUN
ejpam-4553	8	8	and	and	CCONJ
ejpam-4553	8	9	their	their	PRON
ejpam-4553	8	10	applications	application	NOUN
ejpam-4553	8	11	to	to	ADP
ejpam-4553	8	12	non	non	ADJ
ejpam-4553	8	13	-	-	ADJ
ejpam-4553	8	14	linear	linear	ADJ
ejpam-4553	8	15	pdes	pde	NOUN
ejpam-4553	8	16	were	be	AUX
ejpam-4553	8	17	further	far	ADV
ejpam-4553	8	18	studied	study	VERB
ejpam-4553	8	19	by	by	ADP
ejpam-4553	8	20	mazzucato	mazzucato	PROPN
ejpam-4553	9	1	[	[	X
ejpam-4553	9	2	13	13	NUM
ejpam-4553	9	3	]	]	PUNCT
ejpam-4553	9	4	.	.	PUNCT
ejpam-4553	10	1	they	they	PRON
ejpam-4553	10	2	are	be	AUX
ejpam-4553	10	3	modified	modify	VERB
ejpam-4553	10	4	besov	besov	NOUN
ejpam-4553	10	5	spaces	space	NOUN
ejpam-4553	10	6	where	where	SCONJ
ejpam-4553	10	7	the	the	DET
ejpam-4553	10	8	base	base	NOUN
ejpam-4553	10	9	norm	norm	NOUN
ejpam-4553	10	10	is	be	AUX
ejpam-4553	10	11	of	of	ADP
ejpam-4553	10	12	morrey	morrey	NOUN
ejpam-4553	10	13	-	-	PUNCT
ejpam-4553	10	14	type	type	NOUN
ejpam-4553	10	15	.	.	PUNCT
ejpam-4553	11	1	a	a	DET
ejpam-4553	11	2	first	first	ADJ
ejpam-4553	11	3	generalisation	generalisation	NOUN
ejpam-4553	11	4	of	of	ADP
ejpam-4553	11	5	the	the	DET
ejpam-4553	11	6	besov	besov	NOUN
ejpam-4553	11	7	-	-	PUNCT
ejpam-4553	11	8	morrey	morrey	NOUN
ejpam-4553	11	9	spaces	space	VERB
ejpam-4553	11	10	n	n	PROPN
ejpam-4553	11	11	s	s	PROPN
ejpam-4553	11	12	p	p	X
ejpam-4553	11	13	,	,	PUNCT
ejpam-4553	11	14	u	u	NOUN
ejpam-4553	11	15	,	,	PUNCT
ejpam-4553	11	16	q	q	PUNCT
ejpam-4553	11	17	into	into	ADP
ejpam-4553	11	18	n	n	DET
ejpam-4553	11	19	s	s	NOUN
ejpam-4553	11	20	p(·),u(·),q	p(·),u(·),q	NUM
ejpam-4553	11	21	where	where	SCONJ
ejpam-4553	11	22	only	only	ADV
ejpam-4553	11	23	the	the	DET
ejpam-4553	11	24	exponents	exponent	NOUN
ejpam-4553	11	25	p	p	NOUN
ejpam-4553	11	26	and	and	CCONJ
ejpam-4553	11	27	u	u	NOUN
ejpam-4553	11	28	varied	varied	ADJ
ejpam-4553	11	29	was	be	AUX
ejpam-4553	11	30	introduced	introduce	VERB
ejpam-4553	11	31	by	by	ADP
ejpam-4553	11	32	fu	fu	NOUN
ejpam-4553	11	33	and	and	CCONJ
ejpam-4553	11	34	xu	xu	VERB
ejpam-4553	11	35	in	in	ADP
ejpam-4553	11	36	[	[	X
ejpam-4553	11	37	6	6	NUM
ejpam-4553	11	38	]	]	PUNCT
ejpam-4553	11	39	and	and	CCONJ
ejpam-4553	11	40	a	a	DET
ejpam-4553	11	41	full	full	ADJ
ejpam-4553	11	42	generalisation	generalisation	NOUN
ejpam-4553	11	43	to	to	ADP
ejpam-4553	11	44	variable	variable	ADJ
ejpam-4553	11	45	exponent	exponent	NOUN
ejpam-4553	11	46	besov	besov	NOUN
ejpam-4553	11	47	-	-	PUNCT
ejpam-4553	11	48	morrey	morrey	NOUN
ejpam-4553	11	49	spaces	space	NOUN
ejpam-4553	11	50	denoted	denote	VERB
ejpam-4553	11	51	n	n	PROPN
ejpam-4553	11	52	s	s	PROPN
ejpam-4553	11	53	(	(	PUNCT
ejpam-4553	11	54	·	·	PUNCT
ejpam-4553	11	55	)	)	PUNCT
ejpam-4553	11	56	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	11	57	(	(	PUNCT
ejpam-4553	11	58	·	·	PUNCT
ejpam-4553	11	59	)	)	PUNCT
ejpam-4553	11	60	with	with	SCONJ
ejpam-4553	11	61	all	all	DET
ejpam-4553	11	62	exponents	exponent	NOUN
ejpam-4553	11	63	variable	variable	ADJ
ejpam-4553	11	64	is	be	AUX
ejpam-4553	11	65	due	due	ADJ
ejpam-4553	11	66	to	to	ADP
ejpam-4553	11	67	almeida	almeida	PROPN
ejpam-4553	11	68	and	and	CCONJ
ejpam-4553	11	69	caetano	caetano	PROPN
ejpam-4553	12	1	[	[	X
ejpam-4553	12	2	1	1	NUM
ejpam-4553	12	3	]	]	PUNCT
ejpam-4553	12	4	.	.	PUNCT
ejpam-4553	13	1	now	now	ADV
ejpam-4553	13	2	the	the	DET
ejpam-4553	13	3	boundedness	boundedness	NOUN
ejpam-4553	13	4	of	of	ADP
ejpam-4553	13	5	an	an	DET
ejpam-4553	13	6	operator	operator	NOUN
ejpam-4553	13	7	is	be	AUX
ejpam-4553	13	8	a	a	DET
ejpam-4553	13	9	fundamental	fundamental	ADJ
ejpam-4553	13	10	property	property	NOUN
ejpam-4553	13	11	for	for	ADP
ejpam-4553	13	12	it	it	PRON
ejpam-4553	13	13	’s	’	VERB
ejpam-4553	13	14	use	use	NOUN
ejpam-4553	13	15	.	.	PUNCT
ejpam-4553	14	1	one	one	PRON
ejpam-4553	14	2	can	can	AUX
ejpam-4553	14	3	find	find	VERB
ejpam-4553	14	4	in	in	ADP
ejpam-4553	14	5	several	several	ADJ
ejpam-4553	14	6	works	work	NOUN
ejpam-4553	14	7	the	the	DET
ejpam-4553	14	8	study	study	NOUN
ejpam-4553	14	9	of	of	ADP
ejpam-4553	14	10	boundedness	boundedness	NOUN
ejpam-4553	14	11	of	of	ADP
ejpam-4553	14	12	pseudo	pseudo	NOUN
ejpam-4553	14	13	-	-	NOUN
ejpam-4553	14	14	differential	differential	ADJ
ejpam-4553	14	15	operators	operator	NOUN
ejpam-4553	14	16	:	:	PUNCT
ejpam-4553	14	17	on	on	ADP
ejpam-4553	14	18	lebesgue	lebesgue	NOUN
ejpam-4553	14	19	spaces	space	NOUN
ejpam-4553	14	20	,	,	PUNCT
ejpam-4553	14	21	besov	besov	NOUN
ejpam-4553	14	22	spaces	space	NOUN
ejpam-4553	14	23	,	,	PUNCT
ejpam-4553	14	24	triebel	triebel	NOUN
ejpam-4553	14	25	-	-	PUNCT
ejpam-4553	14	26	lizorkin	lizorkin	NOUN
ejpam-4553	14	27	spaces	space	NOUN
ejpam-4553	14	28	and	and	CCONJ
ejpam-4553	14	29	sobolev	sobolev	NOUN
ejpam-4553	14	30	spaces	space	NOUN
ejpam-4553	14	31	(	(	PUNCT
ejpam-4553	14	32	see	see	VERB
ejpam-4553	14	33	[	[	X
ejpam-4553	14	34	2	2	NUM
ejpam-4553	14	35	]	]	PUNCT
ejpam-4553	14	36	,	,	PUNCT
ejpam-4553	14	37	[	[	X
ejpam-4553	14	38	3	3	NUM
ejpam-4553	14	39	]	]	PUNCT
ejpam-4553	14	40	,	,	PUNCT
ejpam-4553	14	41	[	[	X
ejpam-4553	14	42	11	11	NUM
ejpam-4553	14	43	]	]	PUNCT
ejpam-4553	14	44	and	and	CCONJ
ejpam-4553	15	1	[	[	X
ejpam-4553	15	2	12	12	NUM
ejpam-4553	15	3	]	]	PUNCT
ejpam-4553	15	4	)	)	PUNCT
ejpam-4553	15	5	.	.	PUNCT
ejpam-4553	16	1	in	in	ADP
ejpam-4553	16	2	particular	particular	ADJ
ejpam-4553	16	3	,	,	PUNCT
ejpam-4553	16	4	the	the	DET
ejpam-4553	16	5	boundedness	boundedness	NOUN
ejpam-4553	16	6	of	of	ADP
ejpam-4553	16	7	pseudo	pseudo	NOUN
ejpam-4553	16	8	-	-	NOUN
ejpam-4553	16	9	differential	differential	ADJ
ejpam-4553	16	10	operators	operator	NOUN
ejpam-4553	16	11	on	on	ADP
ejpam-4553	16	12	besov	besov	NOUN
ejpam-4553	16	13	-	-	PUNCT
ejpam-4553	16	14	morrey	morrey	NOUN
ejpam-4553	16	15	(	(	PUNCT
ejpam-4553	16	16	bm	bm	NOUN
ejpam-4553	16	17	)	)	PUNCT
ejpam-4553	16	18	spaces	space	VERB
ejpam-4553	16	19	with	with	ADP
ejpam-4553	16	20	constant	constant	ADJ
ejpam-4553	16	21	exponents	exponent	NOUN
ejpam-4553	16	22	denoted	denote	VERB
ejpam-4553	16	23	n	n	PROPN
ejpam-4553	16	24	s	s	PROPN
ejpam-4553	16	25	p	p	X
ejpam-4553	16	26	,	,	PUNCT
ejpam-4553	16	27	u	u	NOUN
ejpam-4553	16	28	,	,	PUNCT
ejpam-4553	16	29	q	q	PUNCT
ejpam-4553	16	30	was	be	AUX
ejpam-4553	16	31	studied	study	VERB
ejpam-4553	16	32	by	by	ADP
ejpam-4553	16	33	mazzucato	mazzucato	NOUN
ejpam-4553	16	34	in	in	ADP
ejpam-4553	16	35	[	[	X
ejpam-4553	16	36	13	13	NUM
ejpam-4553	16	37	]	]	PUNCT
ejpam-4553	16	38	.	.	PUNCT
ejpam-4553	17	1	we	we	PRON
ejpam-4553	17	2	are	be	AUX
ejpam-4553	17	3	concerned	concerned	ADJ
ejpam-4553	17	4	in	in	ADP
ejpam-4553	17	5	this	this	DET
ejpam-4553	17	6	paper	paper	NOUN
ejpam-4553	17	7	with	with	ADP
ejpam-4553	17	8	the	the	DET
ejpam-4553	17	9	boundedness	boundedness	NOUN
ejpam-4553	17	10	of	of	ADP
ejpam-4553	17	11	pseudo	pseudo	NOUN
ejpam-4553	17	12	-	-	ADJ
ejpam-4553	17	13	differential	differential	ADJ
ejpam-4553	17	14	operators	operator	NOUN
ejpam-4553	17	15	on	on	ADP
ejpam-4553	17	16	∗corresponding	∗corresponde	VERB
ejpam-4553	17	17	author	author	NOUN
ejpam-4553	17	18	.	.	PUNCT
ejpam-4553	18	1	doi	doi	NOUN
ejpam-4553	18	2	:	:	PUNCT
ejpam-4553	18	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4553	https://doi.org/10.29020/nybg.ejpam.v15i4.4553	PROPN
ejpam-4553	18	4	email	email	NOUN
ejpam-4553	18	5	addresses	address	NOUN
ejpam-4553	18	6	:	:	PUNCT
ejpam-4553	18	7	mohamed.congo@yahoo.fr	mohamed.congo@yahoo.fr	PROPN
ejpam-4553	18	8	(	(	PUNCT
ejpam-4553	18	9	m.	m.	NOUN
ejpam-4553	18	10	congo	congo	PROPN
ejpam-4553	18	11	)	)	PUNCT
ejpam-4553	18	12	,	,	PUNCT
ejpam-4553	18	13	omfrancoise@yahoo.fr	omfrancoise@yahoo.fr	PROPN
ejpam-4553	18	14	(	(	PUNCT
ejpam-4553	18	15	m.	m.	PROPN
ejpam-4553	18	16	f.	f.	PROPN
ejpam-4553	18	17	ouedraogo	ouedraogo	PROPN
ejpam-4553	18	18	)	)	PUNCT
ejpam-4553	18	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4553	18	20	1716	1716	NUM
ejpam-4553	18	21	©	©	PROPN
ejpam-4553	18	22	2022	2022	NUM
ejpam-4553	18	23	ejpam	ejpam	VERB
ejpam-4553	18	24	all	all	DET
ejpam-4553	18	25	rights	right	NOUN
ejpam-4553	18	26	reserved	reserve	VERB
ejpam-4553	18	27	.	.	PUNCT
ejpam-4553	19	1	mohamed	mohamed	PROPN
ejpam-4553	19	2	congo	congo	PROPN
ejpam-4553	19	3	,	,	PUNCT
ejpam-4553	19	4	m.	m.	PROPN
ejpam-4553	19	5	f.	f.	PROPN
ejpam-4553	19	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	19	7	/	/	SYM
ejpam-4553	19	8	eur	eur	PROPN
ejpam-4553	19	9	.	.	PUNCT
ejpam-4553	20	1	j.	j.	PROPN
ejpam-4553	20	2	pure	pure	PROPN
ejpam-4553	20	3	appl	appl	PROPN
ejpam-4553	20	4	.	.	PROPN
ejpam-4553	20	5	math	math	PROPN
ejpam-4553	20	6	,	,	PUNCT
ejpam-4553	20	7	15	15	NUM
ejpam-4553	20	8	(	(	PUNCT
ejpam-4553	20	9	4	4	NUM
ejpam-4553	20	10	)	)	PUNCT
ejpam-4553	20	11	(	(	PUNCT
ejpam-4553	20	12	2022	2022	NUM
ejpam-4553	20	13	)	)	PUNCT
ejpam-4553	20	14	,	,	PUNCT
ejpam-4553	20	15	1716	1716	NUM
ejpam-4553	20	16	-	-	SYM
ejpam-4553	20	17	1737	1737	NUM
ejpam-4553	20	18	1717	1717	NUM
ejpam-4553	20	19	besov	besov	NOUN
ejpam-4553	20	20	-	-	PUNCT
ejpam-4553	20	21	morrey	morrey	NOUN
ejpam-4553	20	22	spaces	space	NOUN
ejpam-4553	20	23	with	with	ADP
ejpam-4553	20	24	variable	variable	ADJ
ejpam-4553	20	25	exponents	exponent	NOUN
ejpam-4553	20	26	denoted	denote	VERB
ejpam-4553	20	27	n	n	PROPN
ejpam-4553	20	28	s	s	PROPN
ejpam-4553	20	29	(	(	PUNCT
ejpam-4553	20	30	·	·	PUNCT
ejpam-4553	20	31	)	)	PUNCT
ejpam-4553	20	32	p(·),u(·),q(·)(see	p(·),u(·),q(·)(see	PUNCT
ejpam-4553	21	1	[	[	X
ejpam-4553	21	2	1	1	NUM
ejpam-4553	21	3	]	]	NUM
ejpam-4553	21	4	)	)	PUNCT
ejpam-4553	21	5	.	.	PUNCT
ejpam-4553	22	1	since	since	SCONJ
ejpam-4553	22	2	the	the	DET
ejpam-4553	22	3	symbol	symbol	NOUN
ejpam-4553	22	4	class	class	NOUN
ejpam-4553	22	5	sm	sm	PROPN
ejpam-4553	22	6	1,δ	1,δ	PROPN
ejpam-4553	22	7	is	be	AUX
ejpam-4553	22	8	too	too	ADV
ejpam-4553	22	9	restrictive	restrictive	ADJ
ejpam-4553	22	10	for	for	ADP
ejpam-4553	22	11	applications	application	NOUN
ejpam-4553	22	12	to	to	ADP
ejpam-4553	22	13	non	non	ADJ
ejpam-4553	22	14	-	-	ADJ
ejpam-4553	22	15	linear	linear	ADJ
ejpam-4553	22	16	equations	equation	NOUN
ejpam-4553	22	17	,	,	PUNCT
ejpam-4553	22	18	we	we	PRON
ejpam-4553	22	19	use	use	VERB
ejpam-4553	22	20	symbols	symbol	NOUN
ejpam-4553	22	21	in	in	ADP
ejpam-4553	22	22	the	the	DET
ejpam-4553	22	23	class	class	NOUN
ejpam-4553	22	24	cℓ	cℓ	ADP
ejpam-4553	22	25	∗s	∗s	PROPN
ejpam-4553	22	26	m	m	PROPN
ejpam-4553	22	27	1,δ	1,δ	NUM
ejpam-4553	22	28	where	where	SCONJ
ejpam-4553	22	29	the	the	DET
ejpam-4553	22	30	x	x	PROPN
ejpam-4553	22	31	regularity	regularity	NOUN
ejpam-4553	22	32	is	be	AUX
ejpam-4553	22	33	measured	measure	VERB
ejpam-4553	22	34	in	in	ADP
ejpam-4553	22	35	hölder	hölder	NOUN
ejpam-4553	22	36	-	-	PUNCT
ejpam-4553	22	37	zygmund	zygmund	NOUN
ejpam-4553	22	38	spaces	space	NOUN
ejpam-4553	22	39	.	.	PUNCT
ejpam-4553	23	1	the	the	DET
ejpam-4553	23	2	results	result	NOUN
ejpam-4553	23	3	of	of	ADP
ejpam-4553	23	4	this	this	DET
ejpam-4553	23	5	paper	paper	NOUN
ejpam-4553	23	6	generalize	generalize	VERB
ejpam-4553	23	7	those	those	PRON
ejpam-4553	23	8	of	of	ADP
ejpam-4553	23	9	[	[	X
ejpam-4553	23	10	13	13	NUM
ejpam-4553	23	11	]	]	PUNCT
ejpam-4553	23	12	and	and	CCONJ
ejpam-4553	23	13	complement	complement	VERB
ejpam-4553	23	14	the	the	DET
ejpam-4553	23	15	studies	study	NOUN
ejpam-4553	23	16	done	do	VERB
ejpam-4553	23	17	on	on	ADP
ejpam-4553	23	18	triebellizorkin	triebellizorkin	NOUN
ejpam-4553	23	19	-	-	PUNCT
ejpam-4553	23	20	morrey	morrey	NOUN
ejpam-4553	23	21	spaces	space	NOUN
ejpam-4553	23	22	(	(	PUNCT
ejpam-4553	23	23	see	see	VERB
ejpam-4553	23	24	[	[	X
ejpam-4553	23	25	4	4	NUM
ejpam-4553	23	26	]	]	NUM
ejpam-4553	23	27	)	)	PUNCT
ejpam-4553	23	28	.	.	PUNCT
ejpam-4553	24	1	we	we	PRON
ejpam-4553	24	2	further	far	ADV
ejpam-4553	24	3	extended	extend	VERB
ejpam-4553	24	4	the	the	DET
ejpam-4553	24	5	study	study	NOUN
ejpam-4553	24	6	of	of	ADP
ejpam-4553	24	7	the	the	DET
ejpam-4553	24	8	boundedness	boundedness	NOUN
ejpam-4553	24	9	of	of	ADP
ejpam-4553	24	10	such	such	ADJ
ejpam-4553	24	11	pseudo	pseudo	NOUN
ejpam-4553	24	12	-	-	ADJ
ejpam-4553	24	13	differential	differential	ADJ
ejpam-4553	24	14	operators	operator	NOUN
ejpam-4553	24	15	to	to	ADP
ejpam-4553	24	16	their	their	PRON
ejpam-4553	24	17	adjoints	adjoint	NOUN
ejpam-4553	24	18	.	.	PUNCT
ejpam-4553	25	1	our	our	PRON
ejpam-4553	25	2	approach	approach	NOUN
ejpam-4553	25	3	is	be	AUX
ejpam-4553	25	4	as	as	SCONJ
ejpam-4553	25	5	follows	follow	VERB
ejpam-4553	25	6	:	:	PUNCT
ejpam-4553	25	7	we	we	PRON
ejpam-4553	25	8	consider	consider	VERB
ejpam-4553	25	9	pseudo	pseudo	NOUN
ejpam-4553	25	10	-	-	NOUN
ejpam-4553	25	11	differential	differential	ADJ
ejpam-4553	25	12	operators	operator	NOUN
ejpam-4553	25	13	in	in	ADP
ejpam-4553	25	14	n	n	PRON
ejpam-4553	25	15	s	s	PROPN
ejpam-4553	25	16	(	(	PUNCT
ejpam-4553	25	17	·	·	PUNCT
ejpam-4553	25	18	)	)	PUNCT
ejpam-4553	25	19	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	25	20	(	(	PUNCT
ejpam-4553	25	21	·	·	PUNCT
ejpam-4553	25	22	)	)	PUNCT
ejpam-4553	25	23	whose	whose	DET
ejpam-4553	25	24	symbols	symbol	NOUN
ejpam-4553	25	25	belong	belong	VERB
ejpam-4553	25	26	to	to	ADP
ejpam-4553	25	27	the	the	DET
ejpam-4553	25	28	class	class	NOUN
ejpam-4553	25	29	cℓ	cℓ	ADP
ejpam-4553	25	30	∗s	∗s	PROPN
ejpam-4553	25	31	m	m	NOUN
ejpam-4553	25	32	1,δ	1,δ	NUM
ejpam-4553	25	33	.	.	PUNCT
ejpam-4553	26	1	we	we	PRON
ejpam-4553	26	2	use	use	VERB
ejpam-4553	26	3	the	the	DET
ejpam-4553	26	4	decomposition	decomposition	NOUN
ejpam-4553	26	5	of	of	ADP
ejpam-4553	26	6	these	these	DET
ejpam-4553	26	7	symbols	symbol	NOUN
ejpam-4553	26	8	into	into	ADP
ejpam-4553	26	9	elementary	elementary	ADJ
ejpam-4553	26	10	symbols	symbol	NOUN
ejpam-4553	26	11	following	follow	VERB
ejpam-4553	26	12	the	the	DET
ejpam-4553	26	13	method	method	NOUN
ejpam-4553	26	14	of	of	ADP
ejpam-4553	26	15	[	[	X
ejpam-4553	26	16	2	2	NUM
ejpam-4553	26	17	]	]	PUNCT
ejpam-4553	26	18	,	,	PUNCT
ejpam-4553	26	19	[	[	X
ejpam-4553	26	20	11	11	NUM
ejpam-4553	26	21	]	]	PUNCT
ejpam-4553	26	22	and	and	CCONJ
ejpam-4553	26	23	[	[	X
ejpam-4553	26	24	13	13	NUM
ejpam-4553	26	25	]	]	PUNCT
ejpam-4553	26	26	.	.	PUNCT
ejpam-4553	27	1	we	we	PRON
ejpam-4553	27	2	then	then	ADV
ejpam-4553	27	3	set	set	VERB
ejpam-4553	27	4	up	up	ADP
ejpam-4553	27	5	intermediary	intermediary	ADJ
ejpam-4553	27	6	results	result	NOUN
ejpam-4553	27	7	useful	useful	ADJ
ejpam-4553	27	8	to	to	PART
ejpam-4553	27	9	prove	prove	VERB
ejpam-4553	27	10	the	the	DET
ejpam-4553	27	11	main	main	ADJ
ejpam-4553	27	12	results	result	NOUN
ejpam-4553	27	13	in	in	ADP
ejpam-4553	27	14	theorem	theorem	NOUN
ejpam-4553	27	15	[	[	X
ejpam-4553	27	16	2	2	NUM
ejpam-4553	27	17	]	]	PUNCT
ejpam-4553	27	18	and	and	CCONJ
ejpam-4553	27	19	theorem	theorem	VERB
ejpam-4553	27	20	[	[	X
ejpam-4553	27	21	3	3	NUM
ejpam-4553	27	22	]	]	PUNCT
ejpam-4553	27	23	.	.	PUNCT
ejpam-4553	28	1	this	this	DET
ejpam-4553	28	2	paper	paper	NOUN
ejpam-4553	28	3	is	be	AUX
ejpam-4553	28	4	structured	structure	VERB
ejpam-4553	28	5	in	in	ADP
ejpam-4553	28	6	4	4	NUM
ejpam-4553	28	7	sections	section	NOUN
ejpam-4553	28	8	:	:	PUNCT
ejpam-4553	28	9	the	the	DET
ejpam-4553	28	10	section	section	NOUN
ejpam-4553	28	11	2	2	NUM
ejpam-4553	28	12	concerns	concern	NOUN
ejpam-4553	28	13	preliminaries	preliminary	NOUN
ejpam-4553	28	14	and	and	CCONJ
ejpam-4553	28	15	set	set	VERB
ejpam-4553	28	16	up	up	ADP
ejpam-4553	28	17	notations	notation	NOUN
ejpam-4553	28	18	as	as	ADV
ejpam-4553	28	19	well	well	ADV
ejpam-4553	28	20	as	as	ADP
ejpam-4553	28	21	definitions	definition	NOUN
ejpam-4553	28	22	and	and	CCONJ
ejpam-4553	28	23	properties	property	NOUN
ejpam-4553	28	24	of	of	ADP
ejpam-4553	28	25	morrey	morrey	PROPN
ejpam-4553	28	26	spaces	space	NOUN
ejpam-4553	28	27	and	and	CCONJ
ejpam-4553	28	28	besov	besov	NOUN
ejpam-4553	28	29	-	-	PUNCT
ejpam-4553	28	30	morrey	morrey	NOUN
ejpam-4553	28	31	spaces	space	NOUN
ejpam-4553	28	32	with	with	ADP
ejpam-4553	28	33	variable	variable	ADJ
ejpam-4553	28	34	smoothness	smoothness	NOUN
ejpam-4553	28	35	and	and	CCONJ
ejpam-4553	28	36	integrability	integrability	NOUN
ejpam-4553	28	37	.	.	PUNCT
ejpam-4553	29	1	in	in	ADP
ejpam-4553	29	2	section	section	NOUN
ejpam-4553	29	3	3	3	NUM
ejpam-4553	29	4	,	,	PUNCT
ejpam-4553	29	5	we	we	PRON
ejpam-4553	29	6	recall	recall	VERB
ejpam-4553	29	7	tools	tool	NOUN
ejpam-4553	29	8	that	that	PRON
ejpam-4553	29	9	are	be	AUX
ejpam-4553	29	10	necessary	necessary	ADJ
ejpam-4553	29	11	to	to	PART
ejpam-4553	29	12	establish	establish	VERB
ejpam-4553	29	13	lemmas	lemmas	PROPN
ejpam-4553	29	14	and	and	CCONJ
ejpam-4553	29	15	the	the	DET
ejpam-4553	29	16	main	main	ADJ
ejpam-4553	29	17	theorems	theorem	NOUN
ejpam-4553	29	18	of	of	ADP
ejpam-4553	29	19	the	the	DET
ejpam-4553	29	20	next	next	ADJ
ejpam-4553	29	21	section	section	NOUN
ejpam-4553	29	22	.	.	PUNCT
ejpam-4553	30	1	the	the	DET
ejpam-4553	30	2	section	section	NOUN
ejpam-4553	30	3	4	4	NUM
ejpam-4553	30	4	contains	contain	VERB
ejpam-4553	30	5	the	the	DET
ejpam-4553	30	6	results	result	NOUN
ejpam-4553	30	7	and	and	CCONJ
ejpam-4553	30	8	the	the	DET
ejpam-4553	30	9	proof	proof	NOUN
ejpam-4553	30	10	of	of	ADP
ejpam-4553	30	11	the	the	DET
ejpam-4553	30	12	main	main	ADJ
ejpam-4553	30	13	theorem	theorem	NOUN
ejpam-4553	30	14	of	of	ADP
ejpam-4553	30	15	the	the	DET
ejpam-4553	30	16	boundedness	boundedness	NOUN
ejpam-4553	30	17	of	of	ADP
ejpam-4553	30	18	non	non	ADJ
ejpam-4553	30	19	regular	regular	ADJ
ejpam-4553	30	20	pseudo	pseudo	NOUN
ejpam-4553	30	21	-	-	ADJ
ejpam-4553	30	22	differential	differential	ADJ
ejpam-4553	30	23	operators	operator	NOUN
ejpam-4553	30	24	in	in	ADP
ejpam-4553	30	25	the	the	DET
ejpam-4553	30	26	space	space	NOUN
ejpam-4553	30	27	n	n	X
ejpam-4553	30	28	s	s	PROPN
ejpam-4553	30	29	(	(	PUNCT
ejpam-4553	30	30	·	·	PUNCT
ejpam-4553	30	31	)	)	PUNCT
ejpam-4553	30	32	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	30	33	(	(	PUNCT
ejpam-4553	30	34	·	·	PUNCT
ejpam-4553	30	35	)	)	PUNCT
ejpam-4553	30	36	as	as	ADV
ejpam-4553	30	37	well	well	ADV
ejpam-4553	30	38	as	as	ADP
ejpam-4553	30	39	the	the	DET
ejpam-4553	30	40	adjoint	adjoint	PROPN
ejpam-4553	30	41	estimate	estimate	NOUN
ejpam-4553	30	42	.	.	PUNCT
ejpam-4553	31	1	2	2	X
ejpam-4553	31	2	.	.	NUM
ejpam-4553	31	3	preliminaries	preliminary	NOUN
ejpam-4553	31	4	2.1	2.1	NUM
ejpam-4553	31	5	.	.	PUNCT
ejpam-4553	32	1	general	general	ADJ
ejpam-4553	32	2	notation	notation	NOUN
ejpam-4553	32	3	we	we	PRON
ejpam-4553	32	4	denote	denote	VERB
ejpam-4553	32	5	by	by	ADP
ejpam-4553	32	6	rn	rn	PROPN
ejpam-4553	32	7	the	the	DET
ejpam-4553	32	8	n	n	ADV
ejpam-4553	32	9	-	-	PUNCT
ejpam-4553	32	10	dimensional	dimensional	ADJ
ejpam-4553	32	11	real	real	ADJ
ejpam-4553	32	12	euclidean	euclidean	ADJ
ejpam-4553	32	13	space	space	NOUN
ejpam-4553	32	14	,	,	PUNCT
ejpam-4553	32	15	n	n	CCONJ
ejpam-4553	32	16	the	the	DET
ejpam-4553	32	17	collection	collection	NOUN
ejpam-4553	32	18	of	of	ADP
ejpam-4553	32	19	all	all	DET
ejpam-4553	32	20	natural	natural	ADJ
ejpam-4553	32	21	numbers	number	NOUN
ejpam-4553	32	22	and	and	CCONJ
ejpam-4553	32	23	n0	n0	NOUN
ejpam-4553	32	24	=	=	SYM
ejpam-4553	32	25	n	n	PRON
ejpam-4553	32	26	∪	∪	X
ejpam-4553	32	27	{	{	PUNCT
ejpam-4553	32	28	0	0	NUM
ejpam-4553	32	29	}	}	PUNCT
ejpam-4553	32	30	.	.	PUNCT
ejpam-4553	33	1	we	we	PRON
ejpam-4553	33	2	write	write	VERB
ejpam-4553	33	3	b(x	b(x	NOUN
ejpam-4553	33	4	,	,	PUNCT
ejpam-4553	33	5	r	r	NOUN
ejpam-4553	33	6	)	)	PUNCT
ejpam-4553	33	7	for	for	ADP
ejpam-4553	33	8	the	the	DET
ejpam-4553	33	9	open	open	ADJ
ejpam-4553	33	10	ball	ball	NOUN
ejpam-4553	33	11	in	in	ADP
ejpam-4553	33	12	rn	rn	PROPN
ejpam-4553	33	13	centered	center	VERB
ejpam-4553	33	14	at	at	ADP
ejpam-4553	33	15	x	x	PROPN
ejpam-4553	33	16	∈	∈	PROPN
ejpam-4553	33	17	rn	rn	PROPN
ejpam-4553	33	18	with	with	ADP
ejpam-4553	33	19	radius	radius	NOUN
ejpam-4553	33	20	r	r	NOUN
ejpam-4553	33	21	>	>	X
ejpam-4553	33	22	0	0	NUM
ejpam-4553	33	23	.	.	PUNCT
ejpam-4553	34	1	we	we	PRON
ejpam-4553	34	2	use	use	VERB
ejpam-4553	34	3	c	c	PROPN
ejpam-4553	34	4	as	as	ADP
ejpam-4553	34	5	a	a	DET
ejpam-4553	34	6	generic	generic	ADJ
ejpam-4553	34	7	positive	positive	ADJ
ejpam-4553	34	8	constant	constant	ADJ
ejpam-4553	34	9	,	,	PUNCT
ejpam-4553	34	10	i.e.	i.e.	X
ejpam-4553	34	11	a	a	DET
ejpam-4553	34	12	constant	constant	ADJ
ejpam-4553	34	13	whose	whose	DET
ejpam-4553	34	14	value	value	NOUN
ejpam-4553	34	15	may	may	AUX
ejpam-4553	34	16	change	change	VERB
ejpam-4553	34	17	with	with	ADP
ejpam-4553	34	18	each	each	DET
ejpam-4553	34	19	appearance	appearance	NOUN
ejpam-4553	34	20	.	.	PUNCT
ejpam-4553	35	1	if	if	SCONJ
ejpam-4553	35	2	ξ	ξ	PROPN
ejpam-4553	35	3	belongs	belong	VERB
ejpam-4553	35	4	to	to	ADP
ejpam-4553	35	5	rn	rn	PROPN
ejpam-4553	35	6	and	and	CCONJ
ejpam-4553	35	7	r	r	VERB
ejpam-4553	35	8	to	to	ADP
ejpam-4553	35	9	r	r	NOUN
ejpam-4553	35	10	,	,	PUNCT
ejpam-4553	35	11	the	the	DET
ejpam-4553	35	12	expression	expression	NOUN
ejpam-4553	35	13	|ξ|	|ξ|	NOUN
ejpam-4553	35	14	∼	∼	NOUN
ejpam-4553	35	15	r	r	NOUN
ejpam-4553	35	16	means	mean	VERB
ejpam-4553	35	17	that	that	SCONJ
ejpam-4553	35	18	there	there	PRON
ejpam-4553	35	19	exists	exist	VERB
ejpam-4553	35	20	two	two	NUM
ejpam-4553	35	21	constants	constant	NOUN
ejpam-4553	35	22	c1	c1	NOUN
ejpam-4553	35	23	,	,	PUNCT
ejpam-4553	35	24	c2	c2	PROPN
ejpam-4553	35	25	>	>	X
ejpam-4553	35	26	0	0	NUM
ejpam-4553	36	1	such	such	ADJ
ejpam-4553	36	2	that	that	DET
ejpam-4553	36	3	c1r	c1r	NOUN
ejpam-4553	36	4	≤	≤	X
ejpam-4553	36	5	|ξ|	|ξ|	PROPN
ejpam-4553	36	6	≤	≤	PROPN
ejpam-4553	36	7	c2r	c2r	NOUN
ejpam-4553	36	8	.	.	PUNCT
ejpam-4553	37	1	the	the	DET
ejpam-4553	37	2	expression	expression	NOUN
ejpam-4553	37	3	f	f	PROPN
ejpam-4553	37	4	≲	≲	PROPN
ejpam-4553	37	5	g	g	PROPN
ejpam-4553	37	6	means	mean	VERB
ejpam-4553	37	7	that	that	SCONJ
ejpam-4553	37	8	f	f	PROPN
ejpam-4553	37	9	≤	≤	X
ejpam-4553	37	10	cg	cg	NOUN
ejpam-4553	37	11	for	for	ADP
ejpam-4553	37	12	some	some	DET
ejpam-4553	37	13	independent	independent	ADJ
ejpam-4553	37	14	constant	constant	ADJ
ejpam-4553	37	15	c	c	NOUN
ejpam-4553	37	16	,	,	PUNCT
ejpam-4553	37	17	and	and	CCONJ
ejpam-4553	37	18	f	f	X
ejpam-4553	37	19	≈	≈	PROPN
ejpam-4553	37	20	g	g	PROPN
ejpam-4553	37	21	means	mean	VERB
ejpam-4553	37	22	f	f	PROPN
ejpam-4553	37	23	≲	≲	PROPN
ejpam-4553	37	24	g	g	PROPN
ejpam-4553	37	25	≲	≲	PROPN
ejpam-4553	37	26	f	f	PROPN
ejpam-4553	37	27	.	.	PUNCT
ejpam-4553	38	1	throughout	throughout	ADP
ejpam-4553	38	2	the	the	DET
ejpam-4553	38	3	paper	paper	NOUN
ejpam-4553	38	4	we	we	PRON
ejpam-4553	38	5	denote	denote	VERB
ejpam-4553	38	6	by	by	ADP
ejpam-4553	38	7	m(rn	m(rn	PROPN
ejpam-4553	38	8	)	)	PUNCT
ejpam-4553	38	9	the	the	DET
ejpam-4553	38	10	family	family	NOUN
ejpam-4553	38	11	of	of	ADP
ejpam-4553	38	12	all	all	DET
ejpam-4553	38	13	complex	complex	ADJ
ejpam-4553	38	14	or	or	CCONJ
ejpam-4553	38	15	extended	extended	ADJ
ejpam-4553	38	16	realvalued	realvalue	VERB
ejpam-4553	38	17	measurable	measurable	ADJ
ejpam-4553	38	18	functions	function	NOUN
ejpam-4553	38	19	on	on	ADP
ejpam-4553	38	20	rn	rn	PROPN
ejpam-4553	38	21	.	.	PUNCT
ejpam-4553	39	1	by	by	ADP
ejpam-4553	39	2	suppf	suppf	NOUN
ejpam-4553	39	3	we	we	PRON
ejpam-4553	39	4	denote	denote	VERB
ejpam-4553	39	5	the	the	DET
ejpam-4553	39	6	support	support	NOUN
ejpam-4553	39	7	of	of	ADP
ejpam-4553	39	8	the	the	DET
ejpam-4553	39	9	function	function	NOUN
ejpam-4553	39	10	f	f	PROPN
ejpam-4553	39	11	,	,	PUNCT
ejpam-4553	39	12	i.e.	i.e.	X
ejpam-4553	39	13	the	the	DET
ejpam-4553	39	14	closure	closure	NOUN
ejpam-4553	39	15	of	of	ADP
ejpam-4553	39	16	its	its	PRON
ejpam-4553	39	17	non	non	ADJ
ejpam-4553	39	18	-	-	ADJ
ejpam-4553	39	19	zero	zero	NUM
ejpam-4553	39	20	set	set	NOUN
ejpam-4553	39	21	.	.	PUNCT
ejpam-4553	40	1	if	if	SCONJ
ejpam-4553	40	2	e	e	PROPN
ejpam-4553	40	3	⊂	⊂	PROPN
ejpam-4553	40	4	rn	rn	PROPN
ejpam-4553	40	5	is	be	AUX
ejpam-4553	40	6	a	a	DET
ejpam-4553	40	7	measurable	measurable	ADJ
ejpam-4553	40	8	set	set	NOUN
ejpam-4553	40	9	,	,	PUNCT
ejpam-4553	40	10	then	then	ADV
ejpam-4553	40	11	χe	χe	PROPN
ejpam-4553	40	12	denotes	denote	VERB
ejpam-4553	40	13	its	its	PRON
ejpam-4553	40	14	characteristic	characteristic	ADJ
ejpam-4553	40	15	function	function	NOUN
ejpam-4553	40	16	.	.	PUNCT
ejpam-4553	41	1	we	we	PRON
ejpam-4553	41	2	denote	denote	VERB
ejpam-4553	41	3	by	by	ADP
ejpam-4553	41	4	s	s	PROPN
ejpam-4553	41	5	=	=	SYM
ejpam-4553	41	6	s(rn	s(rn	PROPN
ejpam-4553	41	7	)	)	PUNCT
ejpam-4553	41	8	the	the	DET
ejpam-4553	41	9	set	set	NOUN
ejpam-4553	41	10	of	of	ADP
ejpam-4553	41	11	all	all	DET
ejpam-4553	41	12	schwartz	schwartz	PROPN
ejpam-4553	41	13	functions	function	NOUN
ejpam-4553	41	14	on	on	ADP
ejpam-4553	41	15	rn	rn	PROPN
ejpam-4553	41	16	.	.	PUNCT
ejpam-4553	42	1	we	we	PRON
ejpam-4553	42	2	denote	denote	VERB
ejpam-4553	42	3	by	by	ADP
ejpam-4553	42	4	s	s	PRON
ejpam-4553	42	5	′	′	NUM
ejpam-4553	42	6	=	=	SYM
ejpam-4553	42	7	s	s	PART
ejpam-4553	42	8	′(rn	′(rn	PROPN
ejpam-4553	42	9	)	)	PUNCT
ejpam-4553	42	10	the	the	DET
ejpam-4553	42	11	dual	dual	ADJ
ejpam-4553	42	12	space	space	NOUN
ejpam-4553	42	13	of	of	ADP
ejpam-4553	42	14	all	all	DET
ejpam-4553	42	15	tempered	temper	VERB
ejpam-4553	42	16	distributions	distribution	NOUN
ejpam-4553	42	17	on	on	ADP
ejpam-4553	42	18	rn	rn	PROPN
ejpam-4553	42	19	.	.	PUNCT
ejpam-4553	43	1	the	the	DET
ejpam-4553	43	2	fourier	fourier	NOUN
ejpam-4553	43	3	transform	transform	NOUN
ejpam-4553	43	4	denoted	denote	VERB
ejpam-4553	43	5	ff(ξ	ff(ξ	NOUN
ejpam-4553	43	6	)	)	PUNCT
ejpam-4553	43	7	or	or	CCONJ
ejpam-4553	43	8	f̂	f̂	NUM
ejpam-4553	43	9	is	be	AUX
ejpam-4553	43	10	defined	define	VERB
ejpam-4553	43	11	on	on	ADP
ejpam-4553	43	12	s	s	PRON
ejpam-4553	43	13	by	by	ADP
ejpam-4553	43	14	f̂(ξ	f̂(ξ	NOUN
ejpam-4553	43	15	)	)	PUNCT
ejpam-4553	43	16	:	:	PUNCT
ejpam-4553	44	1	=	=	SYM
ejpam-4553	44	2	∫	∫	PROPN
ejpam-4553	44	3	rn	rn	PROPN
ejpam-4553	44	4	e−ix·ξf(x)dx	e−ix·ξf(x)dx	ADJ
ejpam-4553	44	5	and	and	CCONJ
ejpam-4553	44	6	extended	extend	VERB
ejpam-4553	44	7	to	to	ADP
ejpam-4553	44	8	s	s	NOUN
ejpam-4553	44	9	′	′	VERB
ejpam-4553	44	10	by	by	ADP
ejpam-4553	44	11	duality	duality	NOUN
ejpam-4553	44	12	.	.	PUNCT
ejpam-4553	45	1	the	the	DET
ejpam-4553	45	2	inverse	inverse	ADJ
ejpam-4553	45	3	fourier	fourier	NOUN
ejpam-4553	45	4	transform	transform	NOUN
ejpam-4553	45	5	denoted	denote	VERB
ejpam-4553	45	6	f−1f(x	f−1f(x	NOUN
ejpam-4553	45	7	)	)	PUNCT
ejpam-4553	45	8	or	or	CCONJ
ejpam-4553	45	9	f̌	f̌	PROPN
ejpam-4553	45	10	is	be	AUX
ejpam-4553	45	11	defined	define	VERB
ejpam-4553	45	12	by	by	ADP
ejpam-4553	45	13	f̌(x	f̌(x	PROPN
ejpam-4553	45	14	)	)	PUNCT
ejpam-4553	45	15	:	:	PUNCT
ejpam-4553	45	16	=	=	SYM
ejpam-4553	45	17	1	1	NUM
ejpam-4553	45	18	(	(	PUNCT
ejpam-4553	45	19	2π)n	2π)n	NUM
ejpam-4553	45	20	∫	∫	PROPN
ejpam-4553	45	21	rn	rn	PROPN
ejpam-4553	45	22	eix·ξf(ξ)dξ	eix·ξf(ξ)dξ	PROPN
ejpam-4553	45	23	.	.	PUNCT
ejpam-4553	46	1	mohamed	mohamed	PROPN
ejpam-4553	46	2	congo	congo	PROPN
ejpam-4553	46	3	,	,	PUNCT
ejpam-4553	46	4	m.	m.	PROPN
ejpam-4553	46	5	f.	f.	PROPN
ejpam-4553	46	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	46	7	/	/	SYM
ejpam-4553	46	8	eur	eur	PROPN
ejpam-4553	46	9	.	.	PUNCT
ejpam-4553	47	1	j.	j.	PROPN
ejpam-4553	47	2	pure	pure	PROPN
ejpam-4553	47	3	appl	appl	PROPN
ejpam-4553	47	4	.	.	PROPN
ejpam-4553	47	5	math	math	PROPN
ejpam-4553	47	6	,	,	PUNCT
ejpam-4553	47	7	15	15	NUM
ejpam-4553	47	8	(	(	PUNCT
ejpam-4553	47	9	4	4	NUM
ejpam-4553	47	10	)	)	PUNCT
ejpam-4553	47	11	(	(	PUNCT
ejpam-4553	47	12	2022	2022	NUM
ejpam-4553	47	13	)	)	PUNCT
ejpam-4553	47	14	,	,	PUNCT
ejpam-4553	47	15	1716	1716	NUM
ejpam-4553	47	16	-	-	SYM
ejpam-4553	47	17	1737	1737	NUM
ejpam-4553	47	18	1718	1718	NUM
ejpam-4553	47	19	for	for	ADP
ejpam-4553	47	20	two	two	NUM
ejpam-4553	47	21	complex	complex	ADJ
ejpam-4553	47	22	or	or	CCONJ
ejpam-4553	47	23	extended	extended	ADJ
ejpam-4553	47	24	real	real	ADV
ejpam-4553	47	25	-	-	PUNCT
ejpam-4553	47	26	valued	value	VERB
ejpam-4553	47	27	measurable	measurable	ADJ
ejpam-4553	47	28	functions	function	NOUN
ejpam-4553	47	29	f	f	NOUN
ejpam-4553	47	30	,	,	PUNCT
ejpam-4553	47	31	g	g	PROPN
ejpam-4553	47	32	on	on	ADP
ejpam-4553	47	33	rn	rn	PROPN
ejpam-4553	47	34	the	the	DET
ejpam-4553	47	35	convolution	convolution	NOUN
ejpam-4553	48	1	f	f	PROPN
ejpam-4553	48	2	∗	∗	NOUN
ejpam-4553	48	3	g	g	PROPN
ejpam-4553	48	4	is	be	AUX
ejpam-4553	48	5	given	give	VERB
ejpam-4553	48	6	,	,	PUNCT
ejpam-4553	48	7	in	in	ADP
ejpam-4553	48	8	the	the	DET
ejpam-4553	48	9	usual	usual	ADJ
ejpam-4553	48	10	way	way	NOUN
ejpam-4553	48	11	,	,	PUNCT
ejpam-4553	48	12	by	by	ADP
ejpam-4553	48	13	(	(	PUNCT
ejpam-4553	48	14	f	f	PROPN
ejpam-4553	48	15	∗	∗	PROPN
ejpam-4553	48	16	g)(x	g)(x	PROPN
ejpam-4553	48	17	)	)	PUNCT
ejpam-4553	48	18	:	:	PUNCT
ejpam-4553	49	1	=	=	SYM
ejpam-4553	49	2	∫	∫	PROPN
ejpam-4553	49	3	rn	rn	PROPN
ejpam-4553	49	4	f(x−	f(x−	PROPN
ejpam-4553	49	5	y)g(y)dy	y)g(y)dy	NOUN
ejpam-4553	49	6	,	,	PUNCT
ejpam-4553	49	7	x	x	PROPN
ejpam-4553	49	8	∈	∈	PROPN
ejpam-4553	49	9	rn	rn	PROPN
ejpam-4553	49	10	and	and	CCONJ
ejpam-4553	49	11	supp(f	supp(f	PROPN
ejpam-4553	49	12	∗	∗	VERB
ejpam-4553	49	13	g	g	NOUN
ejpam-4553	49	14	)	)	PUNCT
ejpam-4553	50	1	⊂	⊂	PROPN
ejpam-4553	50	2	suppf	suppf	PROPN
ejpam-4553	50	3	+	+	CCONJ
ejpam-4553	50	4	suppg	suppg	ADJ
ejpam-4553	50	5	.	.	PUNCT
ejpam-4553	51	1	2.2	2.2	NUM
ejpam-4553	51	2	.	.	PUNCT
ejpam-4553	52	1	variable	variable	ADJ
ejpam-4553	52	2	exponents	exponent	NOUN
ejpam-4553	52	3	in	in	ADP
ejpam-4553	52	4	this	this	DET
ejpam-4553	52	5	sub	sub	NOUN
ejpam-4553	52	6	-	-	NOUN
ejpam-4553	52	7	section	section	NOUN
ejpam-4553	52	8	we	we	PRON
ejpam-4553	52	9	recall	recall	VERB
ejpam-4553	52	10	the	the	DET
ejpam-4553	52	11	definition	definition	NOUN
ejpam-4553	52	12	and	and	CCONJ
ejpam-4553	52	13	some	some	DET
ejpam-4553	52	14	properties	property	NOUN
ejpam-4553	52	15	of	of	ADP
ejpam-4553	52	16	variable	variable	ADJ
ejpam-4553	52	17	exponents	exponent	NOUN
ejpam-4553	52	18	.	.	PUNCT
ejpam-4553	53	1	for	for	SCONJ
ejpam-4553	53	2	more	more	ADJ
ejpam-4553	53	3	details	detail	NOUN
ejpam-4553	53	4	see	see	VERB
ejpam-4553	53	5	[	[	X
ejpam-4553	53	6	10	10	NUM
ejpam-4553	53	7	]	]	PUNCT
ejpam-4553	53	8	and	and	CCONJ
ejpam-4553	53	9	[	[	X
ejpam-4553	53	10	5	5	NUM
ejpam-4553	53	11	]	]	PUNCT
ejpam-4553	53	12	.	.	PUNCT
ejpam-4553	54	1	•	•	INTJ
ejpam-4553	54	2	we	we	PRON
ejpam-4553	54	3	denote	denote	VERB
ejpam-4553	54	4	by	by	ADP
ejpam-4553	54	5	p(rn	p(rn	PROPN
ejpam-4553	54	6	)	)	PUNCT
ejpam-4553	55	1	the	the	DET
ejpam-4553	55	2	set	set	NOUN
ejpam-4553	55	3	of	of	ADP
ejpam-4553	55	4	all	all	DET
ejpam-4553	55	5	measurable	measurable	ADJ
ejpam-4553	55	6	functions	function	NOUN
ejpam-4553	55	7	p	p	X
ejpam-4553	55	8	:	:	PUNCT
ejpam-4553	55	9	rn	rn	PROPN
ejpam-4553	55	10	→	→	PROPN
ejpam-4553	55	11	(	(	PUNCT
ejpam-4553	55	12	0,∞	0,∞	NUM
ejpam-4553	55	13	]	]	PUNCT
ejpam-4553	55	14	(	(	PUNCT
ejpam-4553	55	15	called	call	VERB
ejpam-4553	55	16	variable	variable	ADJ
ejpam-4553	55	17	exponents	exponent	NOUN
ejpam-4553	55	18	)	)	PUNCT
ejpam-4553	55	19	which	which	PRON
ejpam-4553	55	20	are	be	AUX
ejpam-4553	55	21	essentially	essentially	ADV
ejpam-4553	55	22	bounded	bound	VERB
ejpam-4553	55	23	away	away	ADV
ejpam-4553	55	24	from	from	ADP
ejpam-4553	55	25	zero	zero	NUM
ejpam-4553	55	26	.	.	PUNCT
ejpam-4553	56	1	we	we	PRON
ejpam-4553	56	2	denote	denote	VERB
ejpam-4553	56	3	p+rn	p+rn	PROPN
ejpam-4553	56	4	:	:	PUNCT
ejpam-4553	56	5	=	=	PUNCT
ejpam-4553	56	6	ess	ess	PROPN
ejpam-4553	56	7	suprnp(x	suprnp(x	PROPN
ejpam-4553	56	8	)	)	PUNCT
ejpam-4553	56	9	and	and	CCONJ
ejpam-4553	56	10	p−rn	p−rn	NOUN
ejpam-4553	56	11	:	:	PUNCT
ejpam-4553	56	12	=	=	PUNCT
ejpam-4553	56	13	ess	ess	PROPN
ejpam-4553	56	14	infrnp(x	infrnp(x	PROPN
ejpam-4553	56	15	)	)	PUNCT
ejpam-4553	56	16	;	;	PUNCT
ejpam-4553	56	17	we	we	PRON
ejpam-4553	56	18	abbreviate	abbreviate	VERB
ejpam-4553	56	19	p+	p+	VERB
ejpam-4553	56	20	=	=	SYM
ejpam-4553	56	21	p+rn	p+rn	NOUN
ejpam-4553	56	22	and	and	CCONJ
ejpam-4553	56	23	p−	p−	NOUN
ejpam-4553	56	24	=	=	NOUN
ejpam-4553	56	25	p−rn	p−rn	NOUN
ejpam-4553	56	26	.	.	PUNCT
ejpam-4553	57	1	•	•	NUM
ejpam-4553	57	2	the	the	DET
ejpam-4553	57	3	function	function	NOUN
ejpam-4553	57	4	ϕp	ϕp	INTJ
ejpam-4553	57	5	is	be	AUX
ejpam-4553	57	6	defined	define	VERB
ejpam-4553	57	7	as	as	SCONJ
ejpam-4553	57	8	follows	follow	VERB
ejpam-4553	57	9	:	:	PUNCT
ejpam-4553	57	10	ϕp(x)(t	ϕp(x)(t	NUM
ejpam-4553	57	11	)	)	PUNCT
ejpam-4553	57	12	=	=	PUNCT
ejpam-4553	58	1			PROPN
ejpam-4553	58	2	tp(x	tp(x	NOUN
ejpam-4553	58	3	)	)	PUNCT
ejpam-4553	58	4	if	if	SCONJ
ejpam-4553	58	5	p(x	p(x	NOUN
ejpam-4553	58	6	)	)	PUNCT
ejpam-4553	58	7	∈	∈	PROPN
ejpam-4553	58	8	(	(	PUNCT
ejpam-4553	58	9	0,∞	0,∞	NOUN
ejpam-4553	58	10	)	)	PUNCT
ejpam-4553	58	11	,	,	PUNCT
ejpam-4553	58	12	0	0	NUM
ejpam-4553	58	13	if	if	SCONJ
ejpam-4553	58	14	p(x	p(x	NOUN
ejpam-4553	58	15	)	)	PUNCT
ejpam-4553	58	16	=	=	SYM
ejpam-4553	59	1	∞	∞	PROPN
ejpam-4553	59	2	and	and	CCONJ
ejpam-4553	59	3	t	t	NOUN
ejpam-4553	59	4	∈	∈	PROPN
ejpam-4553	60	1	[	[	X
ejpam-4553	60	2	0	0	NUM
ejpam-4553	60	3	,	,	PUNCT
ejpam-4553	60	4	1	1	NUM
ejpam-4553	60	5	]	]	PUNCT
ejpam-4553	60	6	,	,	PUNCT
ejpam-4553	60	7	∞	∞	PROPN
ejpam-4553	60	8	if	if	SCONJ
ejpam-4553	60	9	p(x	p(x	VERB
ejpam-4553	60	10	)	)	PUNCT
ejpam-4553	60	11	=	=	SYM
ejpam-4553	60	12	∞	∞	PROPN
ejpam-4553	60	13	and	and	CCONJ
ejpam-4553	60	14	t	t	PROPN
ejpam-4553	60	15	∈	∈	PROPN
ejpam-4553	60	16	(	(	PUNCT
ejpam-4553	60	17	1,∞	1,∞	NUM
ejpam-4553	60	18	]	]	PUNCT
ejpam-4553	60	19	.	.	PUNCT
ejpam-4553	61	1	the	the	DET
ejpam-4553	61	2	variable	variable	ADJ
ejpam-4553	61	3	exponent	exponent	NOUN
ejpam-4553	61	4	modular	modular	NOUN
ejpam-4553	61	5	associated	associate	VERB
ejpam-4553	61	6	to	to	ADP
ejpam-4553	61	7	p	p	X
ejpam-4553	61	8	(	(	PUNCT
ejpam-4553	61	9	·	·	PUNCT
ejpam-4553	61	10	)	)	PUNCT
ejpam-4553	61	11	is	be	AUX
ejpam-4553	61	12	defined	define	VERB
ejpam-4553	61	13	by	by	ADP
ejpam-4553	61	14	ϱp(·)(f	ϱp(·)(f	PROPN
ejpam-4553	61	15	)	)	PUNCT
ejpam-4553	62	1	:	:	PUNCT
ejpam-4553	62	2	=	=	SYM
ejpam-4553	62	3	∫	∫	PROPN
ejpam-4553	62	4	rn	rn	PROPN
ejpam-4553	62	5	ϕp(x)(|f(x)|)dx	ϕp(x)(|f(x)|)dx	PROPN
ejpam-4553	62	6	.	.	PUNCT
ejpam-4553	63	1	the	the	DET
ejpam-4553	63	2	variable	variable	ADJ
ejpam-4553	63	3	exponent	exponent	NOUN
ejpam-4553	63	4	lebesgue	lebesgue	PROPN
ejpam-4553	63	5	space	space	PROPN
ejpam-4553	63	6	lp	lp	PROPN
ejpam-4553	63	7	(	(	PUNCT
ejpam-4553	63	8	·	·	PUNCT
ejpam-4553	63	9	)	)	PUNCT
ejpam-4553	63	10	:	:	PUNCT
ejpam-4553	63	11	=	=	SYM
ejpam-4553	63	12	lp(·)(rn	lp(·)(rn	X
ejpam-4553	63	13	)	)	PUNCT
ejpam-4553	63	14	is	be	AUX
ejpam-4553	63	15	the	the	DET
ejpam-4553	63	16	family	family	NOUN
ejpam-4553	63	17	of	of	ADP
ejpam-4553	63	18	(	(	PUNCT
ejpam-4553	63	19	equivalence	equivalence	NOUN
ejpam-4553	63	20	classes	class	NOUN
ejpam-4553	63	21	of	of	ADP
ejpam-4553	63	22	)	)	PUNCT
ejpam-4553	63	23	functions	function	NOUN
ejpam-4553	63	24	f	f	PROPN
ejpam-4553	63	25	∈	∈	PROPN
ejpam-4553	63	26	m(rn	m(rn	PROPN
ejpam-4553	63	27	)	)	PUNCT
ejpam-4553	63	28	such	such	ADJ
ejpam-4553	63	29	that	that	SCONJ
ejpam-4553	63	30	ϱp(·)(f	ϱp(·)(f	PROPN
ejpam-4553	63	31	/	/	SYM
ejpam-4553	63	32	λ	λ	PROPN
ejpam-4553	63	33	)	)	PUNCT
ejpam-4553	63	34	is	be	AUX
ejpam-4553	63	35	finite	finite	ADJ
ejpam-4553	63	36	for	for	ADP
ejpam-4553	63	37	some	some	DET
ejpam-4553	63	38	λ	λ	PROPN
ejpam-4553	63	39	>	>	X
ejpam-4553	63	40	0	0	NUM
ejpam-4553	63	41	.	.	PUNCT
ejpam-4553	64	1	lp	lp	ADJ
ejpam-4553	64	2	(	(	PUNCT
ejpam-4553	64	3	·	·	PUNCT
ejpam-4553	64	4	)	)	PUNCT
ejpam-4553	64	5	is	be	AUX
ejpam-4553	64	6	a	a	DET
ejpam-4553	64	7	quasi	quasi	ADJ
ejpam-4553	64	8	-	-	ADJ
ejpam-4553	64	9	banach	banach	ADJ
ejpam-4553	64	10	space	space	NOUN
ejpam-4553	64	11	equipped	equip	VERB
ejpam-4553	64	12	with	with	ADP
ejpam-4553	64	13	the	the	DET
ejpam-4553	64	14	quasinorm	quasinorm	NOUN
ejpam-4553	64	15	∥f∥p	∥f∥p	NOUN
ejpam-4553	64	16	(	(	PUNCT
ejpam-4553	64	17	·	·	PUNCT
ejpam-4553	64	18	)	)	PUNCT
ejpam-4553	64	19	:	:	PUNCT
ejpam-4553	65	1	=	=	SYM
ejpam-4553	65	2	inf	inf	PROPN
ejpam-4553	65	3	{	{	PUNCT
ejpam-4553	65	4	µ	µ	X
ejpam-4553	65	5	>	>	X
ejpam-4553	65	6	0	0	NUM
ejpam-4553	65	7	:	:	PUNCT
ejpam-4553	65	8	ϱp	ϱp	ADJ
ejpam-4553	65	9	(	(	PUNCT
ejpam-4553	65	10	·	·	PUNCT
ejpam-4553	65	11	)	)	PUNCT
ejpam-4553	65	12	(	(	PUNCT
ejpam-4553	65	13	1	1	NUM
ejpam-4553	65	14	µ	µ	PROPN
ejpam-4553	65	15	f	f	NOUN
ejpam-4553	65	16	)	)	PUNCT
ejpam-4553	65	17	≤	≤	NUM
ejpam-4553	65	18	1	1	NUM
ejpam-4553	65	19	}	}	PUNCT
ejpam-4553	65	20	.	.	PUNCT
ejpam-4553	66	1	•	•	INTJ
ejpam-4553	66	2	we	we	PRON
ejpam-4553	66	3	say	say	VERB
ejpam-4553	66	4	that	that	SCONJ
ejpam-4553	66	5	a	a	DET
ejpam-4553	66	6	continuous	continuous	ADJ
ejpam-4553	66	7	function	function	NOUN
ejpam-4553	66	8	g	g	NOUN
ejpam-4553	66	9	:	:	PUNCT
ejpam-4553	66	10	rn	rn	PROPN
ejpam-4553	66	11	→	→	SYM
ejpam-4553	66	12	r	r	NOUN
ejpam-4553	66	13	is	be	AUX
ejpam-4553	66	14	locally	locally	ADV
ejpam-4553	66	15	log	log	NOUN
ejpam-4553	66	16	-	-	PUNCT
ejpam-4553	66	17	hölder	hölder	NOUN
ejpam-4553	66	18	continuous	continuous	ADJ
ejpam-4553	66	19	,	,	PUNCT
ejpam-4553	66	20	abbreviated	abbreviate	VERB
ejpam-4553	66	21	g	g	PROPN
ejpam-4553	66	22	∈	∈	PROPN
ejpam-4553	66	23	c	c	PROPN
ejpam-4553	66	24	log	log	PROPN
ejpam-4553	66	25	loc	loc	X
ejpam-4553	66	26	(	(	PUNCT
ejpam-4553	66	27	r	r	NOUN
ejpam-4553	66	28	n	n	CCONJ
ejpam-4553	66	29	)	)	PUNCT
ejpam-4553	66	30	,	,	PUNCT
ejpam-4553	66	31	if	if	SCONJ
ejpam-4553	66	32	there	there	PRON
ejpam-4553	66	33	exists	exist	VERB
ejpam-4553	66	34	clog(g	clog(g	NOUN
ejpam-4553	66	35	)	)	PUNCT
ejpam-4553	66	36	≥	≥	NOUN
ejpam-4553	66	37	0	0	NUM
ejpam-4553	66	38	such	such	ADJ
ejpam-4553	66	39	that	that	DET
ejpam-4553	66	40	|g(x)−	|g(x)−	NOUN
ejpam-4553	66	41	g(y)|	g(y)|	PROPN
ejpam-4553	66	42	≤	≤	NUM
ejpam-4553	66	43	clog(g	clog(g	NOUN
ejpam-4553	66	44	)	)	PUNCT
ejpam-4553	67	1	log(e	log(e	PROPN
ejpam-4553	68	1	+	+	NUM
ejpam-4553	68	2	1/|x−	1/|x−	PROPN
ejpam-4553	68	3	y|	y|	NOUN
ejpam-4553	68	4	)	)	PUNCT
ejpam-4553	68	5	for	for	ADP
ejpam-4553	68	6	all	all	DET
ejpam-4553	68	7	x	x	NOUN
ejpam-4553	68	8	,	,	PUNCT
ejpam-4553	68	9	y	y	PROPN
ejpam-4553	68	10	∈	∈	PROPN
ejpam-4553	68	11	rn	rn	PROPN
ejpam-4553	68	12	.	.	PROPN
ejpam-4553	69	1	(	(	PUNCT
ejpam-4553	69	2	1	1	X
ejpam-4553	69	3	)	)	PUNCT
ejpam-4553	69	4	the	the	DET
ejpam-4553	69	5	function	function	NOUN
ejpam-4553	69	6	g	g	NOUN
ejpam-4553	69	7	:	:	PUNCT
ejpam-4553	69	8	rn	rn	PROPN
ejpam-4553	69	9	→	→	SYM
ejpam-4553	69	10	r	r	NOUN
ejpam-4553	69	11	is	be	AUX
ejpam-4553	69	12	said	say	VERB
ejpam-4553	69	13	to	to	PART
ejpam-4553	69	14	be	be	AUX
ejpam-4553	69	15	globally	globally	ADV
ejpam-4553	69	16	log	log	NOUN
ejpam-4553	69	17	-	-	PUNCT
ejpam-4553	69	18	hölder	hölder	NOUN
ejpam-4553	69	19	continuous	continuous	ADJ
ejpam-4553	69	20	,	,	PUNCT
ejpam-4553	69	21	abbreviated	abbreviate	VERB
ejpam-4553	69	22	g	g	PROPN
ejpam-4553	69	23	∈	∈	PROPN
ejpam-4553	69	24	c	c	X
ejpam-4553	69	25	log(rn	log(rn	PROPN
ejpam-4553	69	26	)	)	PUNCT
ejpam-4553	69	27	,	,	PUNCT
ejpam-4553	69	28	if	if	SCONJ
ejpam-4553	69	29	it	it	PRON
ejpam-4553	69	30	is	be	AUX
ejpam-4553	69	31	locally	locally	ADV
ejpam-4553	69	32	log	log	NOUN
ejpam-4553	69	33	-	-	PUNCT
ejpam-4553	69	34	hölder	hölder	NOUN
ejpam-4553	69	35	continuous	continuous	ADJ
ejpam-4553	69	36	and	and	CCONJ
ejpam-4553	69	37	there	there	PRON
ejpam-4553	69	38	exists	exist	VERB
ejpam-4553	69	39	g∞	g∞	PROPN
ejpam-4553	69	40	∈	∈	PROPN
ejpam-4553	69	41	r	r	NOUN
ejpam-4553	69	42	and	and	CCONJ
ejpam-4553	69	43	c∞(g	c∞(g	PROPN
ejpam-4553	69	44	)	)	PUNCT
ejpam-4553	69	45	≥	≥	NOUN
ejpam-4553	69	46	0	0	NUM
ejpam-4553	69	47	such	such	ADJ
ejpam-4553	69	48	that	that	PRON
ejpam-4553	69	49	|g(x)−	|g(x)−	NOUN
ejpam-4553	69	50	g∞|	g∞|	VERB
ejpam-4553	69	51	≤	≤	NUM
ejpam-4553	69	52	c∞(g	c∞(g	PROPN
ejpam-4553	69	53	)	)	PUNCT
ejpam-4553	70	1	log(e	log(e	PROPN
ejpam-4553	71	1	+	+	CCONJ
ejpam-4553	71	2	|x|	|x|	PROPN
ejpam-4553	71	3	)	)	PUNCT
ejpam-4553	71	4	for	for	ADP
ejpam-4553	71	5	all	all	DET
ejpam-4553	71	6	x	x	PROPN
ejpam-4553	71	7	∈	∈	PROPN
ejpam-4553	71	8	rn	rn	PROPN
ejpam-4553	71	9	.	.	PUNCT
ejpam-4553	72	1	we	we	PRON
ejpam-4553	72	2	define	define	VERB
ejpam-4553	72	3	the	the	DET
ejpam-4553	72	4	following	follow	VERB
ejpam-4553	72	5	class	class	NOUN
ejpam-4553	72	6	of	of	ADP
ejpam-4553	72	7	variable	variable	ADJ
ejpam-4553	72	8	exponents	exponent	NOUN
ejpam-4553	72	9	p	p	NOUN
ejpam-4553	72	10	log(rn	log(rn	PROPN
ejpam-4553	72	11	)	)	PUNCT
ejpam-4553	72	12	:	:	PUNCT
ejpam-4553	73	1	=	=	X
ejpam-4553	73	2	{	{	PUNCT
ejpam-4553	73	3	p	p	X
ejpam-4553	73	4	∈	∈	PROPN
ejpam-4553	73	5	p	p	X
ejpam-4553	73	6	:	:	PUNCT
ejpam-4553	73	7	1	1	NUM
ejpam-4553	73	8	p	p	NOUN
ejpam-4553	73	9	∈	∈	PROPN
ejpam-4553	73	10	c	c	X
ejpam-4553	73	11	log(rn	log(rn	X
ejpam-4553	73	12	)	)	PUNCT
ejpam-4553	73	13	}	}	PUNCT
ejpam-4553	73	14	.	.	PUNCT
ejpam-4553	74	1	we	we	PRON
ejpam-4553	74	2	define	define	VERB
ejpam-4553	74	3	1	1	NUM
ejpam-4553	74	4	p∞	p∞	PROPN
ejpam-4553	74	5	:	:	PUNCT
ejpam-4553	74	6	=	=	SYM
ejpam-4553	74	7	lim	lim	NOUN
ejpam-4553	74	8	|x|→∞	|x|→∞	NOUN
ejpam-4553	74	9	1	1	NUM
ejpam-4553	74	10	p(x	p(x	NOUN
ejpam-4553	74	11	)	)	PUNCT
ejpam-4553	74	12	and	and	CCONJ
ejpam-4553	74	13	we	we	PRON
ejpam-4553	74	14	use	use	VERB
ejpam-4553	74	15	the	the	DET
ejpam-4553	74	16	convention	convention	NOUN
ejpam-4553	74	17	1	1	NUM
ejpam-4553	74	18	∞	∞	NUM
ejpam-4553	74	19	=	=	SYM
ejpam-4553	74	20	0	0	X
ejpam-4553	74	21	.	.	PUNCT
ejpam-4553	74	22	mohamed	mohamed	PROPN
ejpam-4553	74	23	congo	congo	PROPN
ejpam-4553	74	24	,	,	PUNCT
ejpam-4553	74	25	m.	m.	PROPN
ejpam-4553	74	26	f.	f.	PROPN
ejpam-4553	74	27	ouedraogo	ouedraogo	PROPN
ejpam-4553	74	28	/	/	SYM
ejpam-4553	74	29	eur	eur	PROPN
ejpam-4553	74	30	.	.	PUNCT
ejpam-4553	75	1	j.	j.	PROPN
ejpam-4553	75	2	pure	pure	PROPN
ejpam-4553	75	3	appl	appl	PROPN
ejpam-4553	75	4	.	.	PROPN
ejpam-4553	75	5	math	math	PROPN
ejpam-4553	75	6	,	,	PUNCT
ejpam-4553	75	7	15	15	NUM
ejpam-4553	75	8	(	(	PUNCT
ejpam-4553	75	9	4	4	NUM
ejpam-4553	75	10	)	)	PUNCT
ejpam-4553	75	11	(	(	PUNCT
ejpam-4553	75	12	2022	2022	NUM
ejpam-4553	75	13	)	)	PUNCT
ejpam-4553	75	14	,	,	PUNCT
ejpam-4553	75	15	1716	1716	NUM
ejpam-4553	75	16	-	-	SYM
ejpam-4553	75	17	1737	1737	NUM
ejpam-4553	75	18	1719	1719	NUM
ejpam-4553	75	19	2.3	2.3	NUM
ejpam-4553	75	20	.	.	PUNCT
ejpam-4553	76	1	variable	variable	ADJ
ejpam-4553	76	2	exponent	exponent	PROPN
ejpam-4553	76	3	besov	besov	PROPN
ejpam-4553	76	4	-	-	PUNCT
ejpam-4553	76	5	morrey	morrey	NOUN
ejpam-4553	76	6	spaces	space	NOUN
ejpam-4553	76	7	we	we	PRON
ejpam-4553	76	8	recall	recall	VERB
ejpam-4553	76	9	the	the	DET
ejpam-4553	76	10	definition	definition	NOUN
ejpam-4553	76	11	of	of	ADP
ejpam-4553	76	12	variable	variable	ADJ
ejpam-4553	76	13	exponent	exponent	NOUN
ejpam-4553	76	14	besov	besov	NOUN
ejpam-4553	76	15	-	-	PUNCT
ejpam-4553	76	16	morrey	morrey	NOUN
ejpam-4553	76	17	spaces	space	NOUN
ejpam-4553	76	18	.	.	PUNCT
ejpam-4553	77	1	we	we	PRON
ejpam-4553	77	2	refer	refer	VERB
ejpam-4553	77	3	to	to	ADP
ejpam-4553	77	4	the	the	DET
ejpam-4553	77	5	papers	paper	NOUN
ejpam-4553	77	6	[	[	X
ejpam-4553	77	7	1	1	NUM
ejpam-4553	77	8	]	]	PUNCT
ejpam-4553	77	9	,	,	PUNCT
ejpam-4553	77	10	[	[	X
ejpam-4553	77	11	18	18	NUM
ejpam-4553	77	12	]	]	PUNCT
ejpam-4553	77	13	,	,	PUNCT
ejpam-4553	77	14	[	[	X
ejpam-4553	77	15	17	17	NUM
ejpam-4553	77	16	]	]	PUNCT
ejpam-4553	77	17	and	and	CCONJ
ejpam-4553	77	18	[	[	X
ejpam-4553	77	19	8	8	NUM
ejpam-4553	77	20	]	]	PUNCT
ejpam-4553	77	21	,	,	PUNCT
ejpam-4553	77	22	for	for	ADP
ejpam-4553	77	23	further	further	ADJ
ejpam-4553	77	24	results	result	NOUN
ejpam-4553	77	25	on	on	ADP
ejpam-4553	77	26	these	these	DET
ejpam-4553	77	27	spaces	space	NOUN
ejpam-4553	77	28	.	.	PUNCT
ejpam-4553	78	1	definition	definition	NOUN
ejpam-4553	78	2	1	1	NUM
ejpam-4553	78	3	.	.	PUNCT
ejpam-4553	79	1	for	for	ADP
ejpam-4553	79	2	p	p	NOUN
ejpam-4553	79	3	,	,	PUNCT
ejpam-4553	79	4	u	u	PROPN
ejpam-4553	79	5	∈	∈	PROPN
ejpam-4553	79	6	p(rn	p(rn	PROPN
ejpam-4553	79	7	)	)	PUNCT
ejpam-4553	79	8	with	with	ADP
ejpam-4553	79	9	0	0	NUM
ejpam-4553	79	10	<	<	X
ejpam-4553	79	11	p−	p−	NOUN
ejpam-4553	79	12	≤	≤	NUM
ejpam-4553	79	13	p(x	p(x	PROPN
ejpam-4553	79	14	)	)	PUNCT
ejpam-4553	79	15	≤	≤	NUM
ejpam-4553	79	16	u(x	u(x	NOUN
ejpam-4553	79	17	)	)	PUNCT
ejpam-4553	79	18	≤	≤	NUM
ejpam-4553	79	19	∞	∞	PROPN
ejpam-4553	79	20	,	,	PUNCT
ejpam-4553	79	21	the	the	DET
ejpam-4553	79	22	variable	variable	ADJ
ejpam-4553	79	23	exponent	exponent	NOUN
ejpam-4553	79	24	morrey	morrey	PROPN
ejpam-4553	79	25	space	space	PROPN
ejpam-4553	79	26	mp(·),u	mp(·),u	PROPN
ejpam-4553	79	27	(	(	PUNCT
ejpam-4553	79	28	·	·	PUNCT
ejpam-4553	79	29	)	)	PUNCT
ejpam-4553	79	30	:	:	PUNCT
ejpam-4553	79	31	=	=	SYM
ejpam-4553	79	32	mp(·),u(·)(rn	mp(·),u(·)(rn	PROPN
ejpam-4553	79	33	)	)	PUNCT
ejpam-4553	79	34	consists	consist	VERB
ejpam-4553	79	35	of	of	ADP
ejpam-4553	79	36	all	all	DET
ejpam-4553	79	37	functions	function	NOUN
ejpam-4553	79	38	f	f	PROPN
ejpam-4553	79	39	∈	∈	PROPN
ejpam-4553	79	40	m(rn	m(rn	PROPN
ejpam-4553	79	41	)	)	PUNCT
ejpam-4553	79	42	with	with	ADP
ejpam-4553	79	43	finite	finite	ADJ
ejpam-4553	79	44	quasinorm	quasinorm	NOUN
ejpam-4553	79	45	∥f∥mp(·),u	∥f∥mp(·),u	PROPN
ejpam-4553	79	46	(	(	PUNCT
ejpam-4553	79	47	·	·	PUNCT
ejpam-4553	79	48	)	)	PUNCT
ejpam-4553	79	49	:	:	PUNCT
ejpam-4553	80	1	=	=	SYM
ejpam-4553	80	2	sup	sup	NOUN
ejpam-4553	80	3	x∈rn	x∈rn	PROPN
ejpam-4553	80	4	,	,	PUNCT
ejpam-4553	80	5	r>0	r>0	PROPN
ejpam-4553	80	6	r	r	NOUN
ejpam-4553	80	7	n	n	CCONJ
ejpam-4553	80	8	u(x	u(x	NOUN
ejpam-4553	80	9	)	)	PUNCT
ejpam-4553	80	10	−	−	PROPN
ejpam-4553	80	11	n	n	SYM
ejpam-4553	80	12	p(x	p(x	NOUN
ejpam-4553	80	13	)	)	PUNCT
ejpam-4553	80	14	∥∥fχb(x.r	∥∥fχb(x.r	ADV
ejpam-4553	80	15	)	)	PUNCT
ejpam-4553	80	16	∥∥	∥∥	X
ejpam-4553	80	17	lp	lp	ADJ
ejpam-4553	80	18	(	(	PUNCT
ejpam-4553	80	19	·	·	PUNCT
ejpam-4553	80	20	)	)	PUNCT
ejpam-4553	80	21	.	.	PUNCT
ejpam-4553	81	1	(	(	PUNCT
ejpam-4553	81	2	2	2	X
ejpam-4553	81	3	)	)	PUNCT
ejpam-4553	81	4	definition	definition	NOUN
ejpam-4553	81	5	2	2	NUM
ejpam-4553	81	6	.	.	PUNCT
ejpam-4553	82	1	let	let	VERB
ejpam-4553	82	2	p	p	PRON
ejpam-4553	82	3	,	,	PUNCT
ejpam-4553	82	4	q	q	ADJ
ejpam-4553	82	5	,	,	PUNCT
ejpam-4553	82	6	u	u	PROPN
ejpam-4553	82	7	∈	∈	PROPN
ejpam-4553	82	8	p(rn	p(rn	PROPN
ejpam-4553	82	9	)	)	PUNCT
ejpam-4553	82	10	with	with	ADP
ejpam-4553	82	11	p(x	p(x	NOUN
ejpam-4553	82	12	)	)	PUNCT
ejpam-4553	82	13	≤	≤	NUM
ejpam-4553	82	14	u(x	u(x	NOUN
ejpam-4553	82	15	)	)	PUNCT
ejpam-4553	82	16	.	.	PUNCT
ejpam-4553	83	1	given	give	VERB
ejpam-4553	83	2	a	a	DET
ejpam-4553	83	3	sequence	sequence	NOUN
ejpam-4553	83	4	(	(	PUNCT
ejpam-4553	83	5	fν)ν	fν)ν	PROPN
ejpam-4553	83	6	⊂	⊂	ADJ
ejpam-4553	83	7	m(rn	m(rn	PROPN
ejpam-4553	83	8	)	)	PUNCT
ejpam-4553	83	9	,	,	PUNCT
ejpam-4553	83	10	we	we	PRON
ejpam-4553	83	11	set	set	VERB
ejpam-4553	83	12	ϱℓq(·)(mp(·),u	ϱℓq(·)(mp(·),u	PROPN
ejpam-4553	83	13	(	(	PUNCT
ejpam-4553	83	14	·	·	PUNCT
ejpam-4553	83	15	)	)	PUNCT
ejpam-4553	83	16	)	)	PUNCT
ejpam-4553	84	1	(	(	PUNCT
ejpam-4553	84	2	(	(	PUNCT
ejpam-4553	84	3	fν)ν	fν)ν	NOUN
ejpam-4553	84	4	)	)	PUNCT
ejpam-4553	84	5	:	:	PUNCT
ejpam-4553	84	6	=	=	PUNCT
ejpam-4553	84	7	∑	∑	PUNCT
ejpam-4553	84	8	ν≥0	ν≥0	NOUN
ejpam-4553	84	9	sup	sup	NOUN
ejpam-4553	84	10	x∈rn	x∈rn	PROPN
ejpam-4553	84	11	,	,	PUNCT
ejpam-4553	84	12	r>0	r>0	PROPN
ejpam-4553	84	13	inf	inf	PROPN
ejpam-4553	84	14	{	{	PUNCT
ejpam-4553	84	15	λ	λ	X
ejpam-4553	84	16	>	>	X
ejpam-4553	84	17	0	0	NUM
ejpam-4553	84	18	:	:	PUNCT
ejpam-4553	84	19	ϱp	ϱp	ADJ
ejpam-4553	84	20	(	(	PUNCT
ejpam-4553	84	21	·	·	PUNCT
ejpam-4553	84	22	)	)	PUNCT
ejpam-4553	84	23	(	(	PUNCT
ejpam-4553	84	24	r	r	NOUN
ejpam-4553	84	25	n	n	X
ejpam-4553	84	26	u(x	u(x	NOUN
ejpam-4553	84	27	)	)	PUNCT
ejpam-4553	84	28	−	−	PROPN
ejpam-4553	84	29	n	n	SYM
ejpam-4553	84	30	p(x	p(x	PROPN
ejpam-4553	84	31	)	)	PUNCT
ejpam-4553	84	32	fνχb(x.r)/λ	fνχb(x.r)/λ	NOUN
ejpam-4553	85	1	1	1	NUM
ejpam-4553	85	2	q	q	NOUN
ejpam-4553	85	3	(	(	PUNCT
ejpam-4553	85	4	·	·	PUNCT
ejpam-4553	85	5	)	)	PUNCT
ejpam-4553	85	6	)	)	PUNCT
ejpam-4553	85	7	≤	≤	ADV
ejpam-4553	85	8	1	1	NUM
ejpam-4553	85	9	}	}	PUNCT
ejpam-4553	85	10	.	.	PUNCT
ejpam-4553	86	1	(	(	PUNCT
ejpam-4553	86	2	3	3	X
ejpam-4553	86	3	)	)	PUNCT
ejpam-4553	86	4	remark	remark	NOUN
ejpam-4553	86	5	1	1	NUM
ejpam-4553	86	6	.	.	PUNCT
ejpam-4553	87	1	when	when	SCONJ
ejpam-4553	87	2	q+	q+	ADV
ejpam-4553	87	3	<	<	X
ejpam-4553	87	4	∞	∞	NUM
ejpam-4553	87	5	or	or	CCONJ
ejpam-4553	87	6	q+	q+	ADP
ejpam-4553	87	7	=	=	SYM
ejpam-4553	87	8	∞	∞	PROPN
ejpam-4553	87	9	and	and	CCONJ
ejpam-4553	87	10	p(x	p(x	PROPN
ejpam-4553	87	11	)	)	PUNCT
ejpam-4553	87	12	≥	≥	NUM
ejpam-4553	87	13	q(x	q(x	NOUN
ejpam-4553	87	14	)	)	PUNCT
ejpam-4553	87	15	we	we	PRON
ejpam-4553	87	16	can	can	AUX
ejpam-4553	87	17	simplify	simplify	VERB
ejpam-4553	87	18	(	(	PUNCT
ejpam-4553	87	19	3	3	NUM
ejpam-4553	87	20	)	)	PUNCT
ejpam-4553	87	21	to	to	PART
ejpam-4553	87	22	obtain	obtain	VERB
ejpam-4553	87	23	ϱℓq(·)(mp(·),u	ϱℓq(·)(mp(·),u	PROPN
ejpam-4553	87	24	(	(	PUNCT
ejpam-4553	87	25	·	·	PUNCT
ejpam-4553	87	26	)	)	PUNCT
ejpam-4553	87	27	)	)	PUNCT
ejpam-4553	88	1	(	(	PUNCT
ejpam-4553	88	2	(	(	PUNCT
ejpam-4553	88	3	fν)ν	fν)ν	NOUN
ejpam-4553	88	4	)	)	PUNCT
ejpam-4553	88	5	:	:	PUNCT
ejpam-4553	88	6	=	=	PUNCT
ejpam-4553	88	7	∑	∑	PUNCT
ejpam-4553	88	8	ν≥0	ν≥0	NOUN
ejpam-4553	88	9	sup	sup	NOUN
ejpam-4553	88	10	x∈rn	x∈rn	PROPN
ejpam-4553	88	11	,	,	PUNCT
ejpam-4553	88	12	r>0	r>0	PROPN
ejpam-4553	88	13	∥∥∥ϕq	∥∥∥ϕq	PROPN
ejpam-4553	88	14	(	(	PUNCT
ejpam-4553	88	15	·	·	PUNCT
ejpam-4553	88	16	)	)	PUNCT
ejpam-4553	88	17	(	(	PUNCT
ejpam-4553	88	18	r	r	NOUN
ejpam-4553	88	19	n	n	X
ejpam-4553	88	20	u(x	u(x	NOUN
ejpam-4553	88	21	)	)	PUNCT
ejpam-4553	88	22	−	−	PROPN
ejpam-4553	88	23	n	n	SYM
ejpam-4553	88	24	p(x	p(x	PROPN
ejpam-4553	88	25	)	)	PUNCT
ejpam-4553	88	26	|fν	|fν	NUM
ejpam-4553	88	27	|χb(x.r	|χb(x.r	ADJ
ejpam-4553	88	28	)	)	PUNCT
ejpam-4553	88	29	)	)	PUNCT
ejpam-4553	89	1	∥∥∥	∥∥∥	NOUN
ejpam-4553	89	2	l	l	NOUN
ejpam-4553	90	1	p	p	X
ejpam-4553	90	2	(	(	PUNCT
ejpam-4553	90	3	·	·	PUNCT
ejpam-4553	90	4	)	)	PUNCT
ejpam-4553	90	5	q	q	NOUN
ejpam-4553	90	6	(	(	PUNCT
ejpam-4553	90	7	·	·	PUNCT
ejpam-4553	90	8	)	)	PUNCT
ejpam-4553	90	9	definition	definition	NOUN
ejpam-4553	90	10	3	3	X
ejpam-4553	90	11	.	.	PUNCT
ejpam-4553	90	12	let	let	VERB
ejpam-4553	90	13	p	p	PRON
ejpam-4553	90	14	,	,	PUNCT
ejpam-4553	90	15	q	q	ADJ
ejpam-4553	90	16	,	,	PUNCT
ejpam-4553	90	17	u	u	PROPN
ejpam-4553	90	18	∈	∈	PROPN
ejpam-4553	90	19	p(rn	p(rn	PROPN
ejpam-4553	90	20	)	)	PUNCT
ejpam-4553	90	21	with	with	ADP
ejpam-4553	90	22	p(x	p(x	NOUN
ejpam-4553	90	23	)	)	PUNCT
ejpam-4553	90	24	≤	≤	NUM
ejpam-4553	90	25	u(x).the	u(x).the	DET
ejpam-4553	90	26	mixed	mix	VERB
ejpam-4553	90	27	morrey	morrey	NOUN
ejpam-4553	90	28	-	-	PUNCT
ejpam-4553	90	29	sequence	sequence	NOUN
ejpam-4553	90	30	space	space	NOUN
ejpam-4553	90	31	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	NOUN
ejpam-4553	90	32	(	(	PUNCT
ejpam-4553	90	33	·	·	PUNCT
ejpam-4553	90	34	)	)	PUNCT
ejpam-4553	90	35	)	)	PUNCT
ejpam-4553	91	1	consists	consist	VERB
ejpam-4553	91	2	of	of	ADP
ejpam-4553	91	3	all	all	DET
ejpam-4553	91	4	sequences	sequence	NOUN
ejpam-4553	91	5	(	(	PUNCT
ejpam-4553	91	6	fν)ν	fν)ν	PROPN
ejpam-4553	91	7	⊂	⊂	ADJ
ejpam-4553	91	8	m(rn	m(rn	PROPN
ejpam-4553	91	9	)	)	PUNCT
ejpam-4553	91	10	such	such	ADJ
ejpam-4553	91	11	that	that	SCONJ
ejpam-4553	91	12	,	,	PUNCT
ejpam-4553	91	13	ϱℓq(·)(mp(·),u	ϱℓq(·)(mp(·),u	PROPN
ejpam-4553	91	14	(	(	PUNCT
ejpam-4553	91	15	·	·	PUNCT
ejpam-4553	91	16	)	)	PUNCT
ejpam-4553	91	17	)	)	PUNCT
ejpam-4553	91	18	(	(	PUNCT
ejpam-4553	91	19	µ(fν	µ(fν	NOUN
ejpam-4553	91	20	)	)	PUNCT
ejpam-4553	91	21	)	)	PUNCT
ejpam-4553	91	22	<	<	X
ejpam-4553	92	1	∞	∞	NUM
ejpam-4553	92	2	for	for	ADP
ejpam-4553	92	3	some	some	DET
ejpam-4553	92	4	µ	µ	NOUN
ejpam-4553	92	5	>	>	X
ejpam-4553	92	6	0	0	NUM
ejpam-4553	92	7	.	.	PUNCT
ejpam-4553	93	1	for	for	ADP
ejpam-4553	93	2	(	(	PUNCT
ejpam-4553	93	3	fν)ν	fν)ν	PROPN
ejpam-4553	93	4	∈	∈	PROPN
ejpam-4553	93	5	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	NOUN
ejpam-4553	93	6	(	(	PUNCT
ejpam-4553	93	7	·	·	PUNCT
ejpam-4553	93	8	)	)	PUNCT
ejpam-4553	93	9	)	)	PUNCT
ejpam-4553	93	10	we	we	PRON
ejpam-4553	93	11	define	define	VERB
ejpam-4553	93	12	∥(fν)ν∥ℓq(·)(mp(·),u	∥(fν)ν∥ℓq(·)(mp(·),u	ADJ
ejpam-4553	93	13	(	(	PUNCT
ejpam-4553	93	14	·	·	PUNCT
ejpam-4553	93	15	)	)	PUNCT
ejpam-4553	93	16	)	)	PUNCT
ejpam-4553	94	1	:	:	PUNCT
ejpam-4553	94	2	=	=	SYM
ejpam-4553	94	3	inf	inf	PROPN
ejpam-4553	94	4	{	{	PUNCT
ejpam-4553	94	5	µ	µ	X
ejpam-4553	94	6	>	>	X
ejpam-4553	94	7	0	0	NUM
ejpam-4553	94	8	:	:	PUNCT
ejpam-4553	94	9	ϱℓq(·)(mp(·),u	ϱℓq(·)(mp(·),u	PROPN
ejpam-4553	94	10	(	(	PUNCT
ejpam-4553	94	11	·	·	PUNCT
ejpam-4553	94	12	)	)	PUNCT
ejpam-4553	94	13	)	)	PUNCT
ejpam-4553	95	1	(	(	PUNCT
ejpam-4553	95	2	1	1	NUM
ejpam-4553	95	3	µ	µ	X
ejpam-4553	95	4	(	(	PUNCT
ejpam-4553	95	5	fν	fν	NOUN
ejpam-4553	95	6	)	)	PUNCT
ejpam-4553	95	7	)	)	PUNCT
ejpam-4553	95	8	≤	≤	ADV
ejpam-4553	95	9	1	1	NUM
ejpam-4553	95	10	}	}	PUNCT
ejpam-4553	95	11	.	.	PUNCT
ejpam-4553	96	1	(	(	PUNCT
ejpam-4553	96	2	4	4	X
ejpam-4553	96	3	)	)	PUNCT
ejpam-4553	96	4	proposition	proposition	NOUN
ejpam-4553	96	5	1	1	NUM
ejpam-4553	96	6	.	.	PUNCT
ejpam-4553	97	1	let	let	VERB
ejpam-4553	97	2	p	p	PRON
ejpam-4553	97	3	,	,	PUNCT
ejpam-4553	97	4	q	q	ADJ
ejpam-4553	97	5	,	,	PUNCT
ejpam-4553	97	6	u	u	PROPN
ejpam-4553	97	7	∈	∈	PROPN
ejpam-4553	97	8	p(rn	p(rn	PROPN
ejpam-4553	97	9	)	)	PUNCT
ejpam-4553	97	10	with	with	ADP
ejpam-4553	97	11	p(x	p(x	NOUN
ejpam-4553	97	12	)	)	PUNCT
ejpam-4553	97	13	≤	≤	NUM
ejpam-4553	97	14	u(x	u(x	NOUN
ejpam-4553	97	15	)	)	PUNCT
ejpam-4553	97	16	.	.	PUNCT
ejpam-4553	98	1	let	let	VERB
ejpam-4553	98	2	(	(	PUNCT
ejpam-4553	98	3	fν)ν	fν)ν	NOUN
ejpam-4553	98	4	∈	∈	PROPN
ejpam-4553	98	5	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	NOUN
ejpam-4553	98	6	(	(	PUNCT
ejpam-4553	98	7	·	·	PUNCT
ejpam-4553	98	8	)	)	PUNCT
ejpam-4553	98	9	)	)	PUNCT
ejpam-4553	99	1	(	(	PUNCT
ejpam-4553	99	2	i	i	NOUN
ejpam-4553	99	3	)	)	PUNCT
ejpam-4553	99	4	the	the	DET
ejpam-4553	99	5	functional	functional	ADJ
ejpam-4553	99	6	∥·∥ℓq(·)(mp(·),u	∥·∥ℓq(·)(mp(·),u	NOUN
ejpam-4553	99	7	(	(	PUNCT
ejpam-4553	99	8	·	·	PUNCT
ejpam-4553	99	9	)	)	PUNCT
ejpam-4553	99	10	)	)	PUNCT
ejpam-4553	99	11	is	be	AUX
ejpam-4553	99	12	a	a	DET
ejpam-4553	99	13	quasinorm	quasinorm	NOUN
ejpam-4553	99	14	in	in	ADP
ejpam-4553	99	15	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	99	16	(	(	PUNCT
ejpam-4553	99	17	·	·	PUNCT
ejpam-4553	99	18	)	)	PUNCT
ejpam-4553	99	19	)	)	PUNCT
ejpam-4553	99	20	and	and	CCONJ
ejpam-4553	99	21	∥(fν)ν∥tℓq(·)(mp(·),u	∥(fν)ν∥tℓq(·)(mp(·),u	PROPN
ejpam-4553	99	22	(	(	PUNCT
ejpam-4553	99	23	·	·	PUNCT
ejpam-4553	99	24	)	)	PUNCT
ejpam-4553	99	25	)	)	PUNCT
ejpam-4553	100	1	=	=	PUNCT
ejpam-4553	100	2	∥∥(|fν	∥∥(|fν	X
ejpam-4553	100	3	|t)ν∥∥ℓq(·)/t(mp(·)/t	|t)ν∥∥ℓq(·)/t(mp(·)/t	NUM
ejpam-4553	100	4	,	,	PUNCT
ejpam-4553	100	5	u(·)/t	u(·)/t	NOUN
ejpam-4553	100	6	)	)	PUNCT
ejpam-4553	100	7	,	,	PUNCT
ejpam-4553	100	8	∀t	∀t	PROPN
ejpam-4553	100	9	>	>	X
ejpam-4553	100	10	0	0	NUM
ejpam-4553	100	11	.	.	PUNCT
ejpam-4553	100	12	(	(	PUNCT
ejpam-4553	100	13	ii	ii	NOUN
ejpam-4553	100	14	)	)	PUNCT
ejpam-4553	100	15	if	if	SCONJ
ejpam-4553	100	16	fν0	fν0	NOUN
ejpam-4553	100	17	=	=	SYM
ejpam-4553	100	18	f	f	PROPN
ejpam-4553	100	19	for	for	ADP
ejpam-4553	100	20	some	some	DET
ejpam-4553	100	21	f	f	PROPN
ejpam-4553	100	22	∈mp(·),u(·)(rn	∈mp(·),u(·)(rn	PROPN
ejpam-4553	100	23	)	)	PUNCT
ejpam-4553	100	24	and	and	CCONJ
ejpam-4553	100	25	ν0	ν0	PROPN
ejpam-4553	100	26	∈	∈	PROPN
ejpam-4553	100	27	n0	n0	PROPN
ejpam-4553	100	28	,	,	PUNCT
ejpam-4553	100	29	and	and	CCONJ
ejpam-4553	100	30	fν	fν	NOUN
ejpam-4553	100	31	=	=	NOUN
ejpam-4553	100	32	0	0	NUM
ejpam-4553	100	33	for	for	ADP
ejpam-4553	100	34	all	all	PRON
ejpam-4553	100	35	ν	ν	DET
ejpam-4553	100	36	̸=	̸=	PROPN
ejpam-4553	100	37	ν0	ν0	PROPN
ejpam-4553	100	38	,	,	PUNCT
ejpam-4553	100	39	then	then	ADV
ejpam-4553	100	40	∥(fν)ν∥ℓq(·)(mp(·),u	∥(fν)ν∥ℓq(·)(mp(·),u	PROPN
ejpam-4553	100	41	(	(	PUNCT
ejpam-4553	100	42	·	·	PUNCT
ejpam-4553	100	43	)	)	PUNCT
ejpam-4553	100	44	)	)	PUNCT
ejpam-4553	101	1	=	=	SYM
ejpam-4553	101	2	∥f∥mp(·),u	∥f∥mp(·),u	PROPN
ejpam-4553	101	3	(	(	PUNCT
ejpam-4553	101	4	·	·	PUNCT
ejpam-4553	101	5	)	)	PUNCT
ejpam-4553	101	6	.	.	PUNCT
ejpam-4553	102	1	theorem	theorem	NOUN
ejpam-4553	102	2	1	1	NUM
ejpam-4553	102	3	.	.	PUNCT
ejpam-4553	103	1	the	the	DET
ejpam-4553	103	2	functional	functional	ADJ
ejpam-4553	103	3	(	(	PUNCT
ejpam-4553	103	4	4	4	NUM
ejpam-4553	103	5	)	)	PUNCT
ejpam-4553	103	6	defines	define	VERB
ejpam-4553	103	7	a	a	DET
ejpam-4553	103	8	quasinorm	quasinorm	NOUN
ejpam-4553	103	9	in	in	ADP
ejpam-4553	103	10	the	the	DET
ejpam-4553	103	11	vector	vector	NOUN
ejpam-4553	103	12	space	space	NOUN
ejpam-4553	103	13	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	103	14	(	(	PUNCT
ejpam-4553	103	15	·	·	PUNCT
ejpam-4553	103	16	)	)	PUNCT
ejpam-4553	103	17	)	)	PUNCT
ejpam-4553	104	1	for	for	ADP
ejpam-4553	104	2	any	any	DET
ejpam-4553	104	3	p	p	X
ejpam-4553	104	4	,	,	PUNCT
ejpam-4553	104	5	q	q	ADJ
ejpam-4553	104	6	,	,	PUNCT
ejpam-4553	104	7	u	u	PROPN
ejpam-4553	104	8	∈	∈	PROPN
ejpam-4553	104	9	p(rn	p(rn	PROPN
ejpam-4553	104	10	)	)	PUNCT
ejpam-4553	104	11	with	with	ADP
ejpam-4553	104	12	p(x	p(x	NOUN
ejpam-4553	104	13	)	)	PUNCT
ejpam-4553	104	14	≤	≤	NUM
ejpam-4553	104	15	u(x	u(x	NOUN
ejpam-4553	104	16	)	)	PUNCT
ejpam-4553	104	17	.	.	PUNCT
ejpam-4553	105	1	moreover	moreover	ADV
ejpam-4553	105	2	,	,	PUNCT
ejpam-4553	105	3	it	it	PRON
ejpam-4553	105	4	induces	induce	VERB
ejpam-4553	105	5	a	a	DET
ejpam-4553	105	6	norm	norm	NOUN
ejpam-4553	105	7	in	in	ADP
ejpam-4553	105	8	the	the	DET
ejpam-4553	105	9	following	follow	VERB
ejpam-4553	105	10	cases	case	NOUN
ejpam-4553	105	11	(	(	PUNCT
ejpam-4553	105	12	each	each	DET
ejpam-4553	105	13	one	one	NOUN
ejpam-4553	105	14	understood	understand	VERB
ejpam-4553	105	15	for	for	ADP
ejpam-4553	105	16	almost	almost	ADV
ejpam-4553	105	17	every	every	PRON
ejpam-4553	105	18	x	x	PROPN
ejpam-4553	105	19	∈	∈	PROPN
ejpam-4553	105	20	rn	rn	PROPN
ejpam-4553	105	21	):	):	PUNCT
ejpam-4553	105	22	(	(	PUNCT
ejpam-4553	105	23	i	i	NOUN
ejpam-4553	105	24	)	)	PUNCT
ejpam-4553	105	25	p(x	p(x	PROPN
ejpam-4553	105	26	)	)	PUNCT
ejpam-4553	105	27	≥	≥	NOUN
ejpam-4553	105	28	1	1	NUM
ejpam-4553	105	29	and	and	CCONJ
ejpam-4553	105	30	q	q	ADJ
ejpam-4553	105	31	∈	∈	PROPN
ejpam-4553	106	1	[	[	X
ejpam-4553	106	2	1,∞	1,∞	NUM
ejpam-4553	106	3	]	]	PUNCT
ejpam-4553	106	4	is	be	AUX
ejpam-4553	106	5	constant	constant	ADJ
ejpam-4553	106	6	;	;	PUNCT
ejpam-4553	106	7	(	(	PUNCT
ejpam-4553	106	8	ii	ii	NOUN
ejpam-4553	106	9	)	)	PUNCT
ejpam-4553	106	10	1	1	NUM
ejpam-4553	106	11	≤	≤	NUM
ejpam-4553	106	12	q(x	q(x	NOUN
ejpam-4553	106	13	)	)	PUNCT
ejpam-4553	106	14	≤	≤	NUM
ejpam-4553	106	15	p(x	p(x	PROPN
ejpam-4553	106	16	)	)	PUNCT
ejpam-4553	106	17	≤	≤	NUM
ejpam-4553	106	18	u(x	u(x	NOUN
ejpam-4553	106	19	)	)	PUNCT
ejpam-4553	106	20	≤	≤	NUM
ejpam-4553	106	21	∞	∞	PROPN
ejpam-4553	106	22	;	;	PUNCT
ejpam-4553	106	23	mohamed	mohamed	PROPN
ejpam-4553	106	24	congo	congo	PROPN
ejpam-4553	106	25	,	,	PUNCT
ejpam-4553	106	26	m.	m.	PROPN
ejpam-4553	106	27	f.	f.	PROPN
ejpam-4553	106	28	ouedraogo	ouedraogo	PROPN
ejpam-4553	106	29	/	/	SYM
ejpam-4553	106	30	eur	eur	PROPN
ejpam-4553	106	31	.	.	PUNCT
ejpam-4553	107	1	j.	j.	PROPN
ejpam-4553	107	2	pure	pure	PROPN
ejpam-4553	107	3	appl	appl	PROPN
ejpam-4553	107	4	.	.	PROPN
ejpam-4553	107	5	math	math	PROPN
ejpam-4553	107	6	,	,	PUNCT
ejpam-4553	107	7	15	15	NUM
ejpam-4553	107	8	(	(	PUNCT
ejpam-4553	107	9	4	4	NUM
ejpam-4553	107	10	)	)	PUNCT
ejpam-4553	107	11	(	(	PUNCT
ejpam-4553	107	12	2022	2022	NUM
ejpam-4553	107	13	)	)	PUNCT
ejpam-4553	107	14	,	,	PUNCT
ejpam-4553	107	15	1716	1716	NUM
ejpam-4553	107	16	-	-	SYM
ejpam-4553	107	17	1737	1737	NUM
ejpam-4553	107	18	1720	1720	NUM
ejpam-4553	107	19	(	(	PUNCT
ejpam-4553	107	20	iii	iii	NOUN
ejpam-4553	107	21	)	)	PUNCT
ejpam-4553	107	22	1	1	NUM
ejpam-4553	107	23	p(x	p(x	PROPN
ejpam-4553	107	24	)	)	PUNCT
ejpam-4553	107	25	+	+	CCONJ
ejpam-4553	107	26	1	1	NUM
ejpam-4553	107	27	q(x	q(x	NOUN
ejpam-4553	107	28	)	)	PUNCT
ejpam-4553	107	29	≤	≤	NUM
ejpam-4553	107	30	1	1	NUM
ejpam-4553	107	31	.	.	PUNCT
ejpam-4553	108	1	besov	besov	NOUN
ejpam-4553	108	2	-	-	PUNCT
ejpam-4553	108	3	morrey	morrey	PROPN
ejpam-4553	108	4	spaces	space	VERB
ejpam-4553	108	5	:	:	PUNCT
ejpam-4553	108	6	to	to	PART
ejpam-4553	108	7	define	define	VERB
ejpam-4553	108	8	besov	besov	NOUN
ejpam-4553	108	9	spaces	space	NOUN
ejpam-4553	108	10	based	base	VERB
ejpam-4553	108	11	on	on	ADP
ejpam-4553	108	12	mp(·),u	mp(·),u	PROPN
ejpam-4553	108	13	(	(	PUNCT
ejpam-4553	108	14	·	·	PUNCT
ejpam-4553	108	15	)	)	PUNCT
ejpam-4553	108	16	,	,	PUNCT
ejpam-4553	108	17	let	let	VERB
ejpam-4553	108	18	us	we	PRON
ejpam-4553	108	19	first	first	ADV
ejpam-4553	108	20	recall	recall	VERB
ejpam-4553	108	21	the	the	DET
ejpam-4553	108	22	définition	définition	PROPN
ejpam-4553	108	23	of	of	ADP
ejpam-4553	108	24	a	a	DET
ejpam-4553	108	25	littlewood	littlewood	NOUN
ejpam-4553	108	26	-	-	PUNCT
ejpam-4553	108	27	paley	paley	ADJ
ejpam-4553	108	28	partition	partition	NOUN
ejpam-4553	108	29	of	of	ADP
ejpam-4553	108	30	unity	unity	NOUN
ejpam-4553	108	31	{	{	PUNCT
ejpam-4553	108	32	φν	φν	NOUN
ejpam-4553	108	33	}	}	PUNCT
ejpam-4553	108	34	,	,	PUNCT
ejpam-4553	108	35	ν	ν	X
ejpam-4553	108	36	≥	≥	NOUN
ejpam-4553	108	37	0	0	NUM
ejpam-4553	108	38	.	.	PUNCT
ejpam-4553	109	1	the	the	DET
ejpam-4553	109	2	functions	function	NOUN
ejpam-4553	109	3	φν	φν	PROPN
ejpam-4553	109	4	are	be	AUX
ejpam-4553	109	5	defined	define	VERB
ejpam-4553	109	6	as	as	SCONJ
ejpam-4553	109	7	follows	follow	VERB
ejpam-4553	109	8	.	.	PUNCT
ejpam-4553	110	1	let	let	VERB
ejpam-4553	110	2	φ0	φ0	PROPN
ejpam-4553	110	3	∈	∈	PROPN
ejpam-4553	110	4	c∞	c∞	PROPN
ejpam-4553	110	5	0	0	NUM
ejpam-4553	110	6	(	(	PUNCT
ejpam-4553	110	7	rn	rn	NOUN
ejpam-4553	110	8	)	)	PUNCT
ejpam-4553	110	9	a	a	DET
ejpam-4553	110	10	real	real	ADJ
ejpam-4553	110	11	function	function	NOUN
ejpam-4553	110	12	such	such	ADJ
ejpam-4553	110	13	that	that	SCONJ
ejpam-4553	110	14	φ0	φ0	PROPN
ejpam-4553	110	15	≡	≡	PROPN
ejpam-4553	110	16	1	1	NUM
ejpam-4553	110	17	on	on	ADP
ejpam-4553	110	18	b(0	b(0	NOUN
ejpam-4553	110	19	;	;	PUNCT
ejpam-4553	110	20	1	1	NUM
ejpam-4553	110	21	)	)	PUNCT
ejpam-4553	110	22	and	and	CCONJ
ejpam-4553	110	23	suppφ0	suppφ0	PROPN
ejpam-4553	110	24	⊂	⊂	PROPN
ejpam-4553	110	25	b(0	b(0	PROPN
ejpam-4553	110	26	;	;	PUNCT
ejpam-4553	110	27	2	2	NUM
ejpam-4553	110	28	)	)	PUNCT
ejpam-4553	110	29	.	.	PUNCT
ejpam-4553	111	1	set	set	VERB
ejpam-4553	111	2	φν(ξ	φν(ξ	NOUN
ejpam-4553	111	3	)	)	PUNCT
ejpam-4553	111	4	=	=	SYM
ejpam-4553	111	5	φ0(2	φ0(2	VERB
ejpam-4553	111	6	−νξ)−	−νξ)−	PRON
ejpam-4553	111	7	φ0(2	φ0(2	VERB
ejpam-4553	111	8	−ν+1ξ	−ν+1ξ	NOUN
ejpam-4553	111	9	)	)	PUNCT
ejpam-4553	111	10	for	for	ADP
ejpam-4553	111	11	all	all	DET
ejpam-4553	111	12	ν	ν	X
ejpam-4553	111	13	∈	∈	PROPN
ejpam-4553	111	14	n.	n.	NOUN
ejpam-4553	111	15	then	then	ADV
ejpam-4553	111	16	φν	φν	PROPN
ejpam-4553	111	17	is	be	AUX
ejpam-4553	111	18	supported	support	VERB
ejpam-4553	111	19	on	on	ADP
ejpam-4553	111	20	the	the	DET
ejpam-4553	111	21	dyadic	dyadic	ADJ
ejpam-4553	111	22	shell	shell	NOUN
ejpam-4553	111	23	dν	dν	ADV
ejpam-4553	111	24	=	=	PUNCT
ejpam-4553	111	25	{	{	PUNCT
ejpam-4553	111	26	ξ	ξ	PROPN
ejpam-4553	111	27	∈	∈	PROPN
ejpam-4553	111	28	rn	rn	PROPN
ejpam-4553	111	29	:	:	PUNCT
ejpam-4553	111	30	2ν−1	2ν−1	PROPN
ejpam-4553	111	31	≤	≤	NUM
ejpam-4553	111	32	|ξ|	|ξ|	VERB
ejpam-4553	111	33	≤	≤	NOUN
ejpam-4553	111	34	2ν+1	2ν+1	NUM
ejpam-4553	111	35	}	}	PUNCT
ejpam-4553	111	36	with	with	ADP
ejpam-4553	111	37	dν	dν	ADJ
ejpam-4553	111	38	∩dµ	∩dµ	NOUN
ejpam-4553	111	39	=	=	SYM
ejpam-4553	111	40	∅	∅	NOUN
ejpam-4553	111	41	if	if	SCONJ
ejpam-4553	111	42	|ν	|ν	NOUN
ejpam-4553	111	43	−	−	PROPN
ejpam-4553	111	44	µ|	µ|	PROPN
ejpam-4553	111	45	>	>	X
ejpam-4553	111	46	1	1	X
ejpam-4553	111	47	.	.	X
ejpam-4553	112	1	one	one	NUM
ejpam-4553	112	2	has∑	has∑	PART
ejpam-4553	112	3	ν≥0	ν≥0	NOUN
ejpam-4553	112	4	φν	φν	NOUN
ejpam-4553	112	5	=	=	SYM
ejpam-4553	112	6	1	1	X
ejpam-4553	112	7	.	.	PUNCT
ejpam-4553	113	1	then	then	ADV
ejpam-4553	113	2	for	for	ADP
ejpam-4553	113	3	all	all	DET
ejpam-4553	113	4	f	f	PROPN
ejpam-4553	113	5	∈	∈	PROPN
ejpam-4553	113	6	s	s	PART
ejpam-4553	113	7	′	′	NOUN
ejpam-4553	113	8	,	,	PUNCT
ejpam-4553	113	9	f	f	PROPN
ejpam-4553	113	10	=	=	PUNCT
ejpam-4553	113	11	∑	∑	PROPN
ejpam-4553	113	12	ν≥0	ν≥0	NOUN
ejpam-4553	113	13	φνf	φνf	NOUN
ejpam-4553	113	14	.	.	PUNCT
ejpam-4553	114	1	the	the	DET
ejpam-4553	114	2	littlewood	littlewood	PROPN
ejpam-4553	114	3	-	-	PUNCT
ejpam-4553	114	4	paley	paley	NOUN
ejpam-4553	114	5	partition	partition	NOUN
ejpam-4553	114	6	of	of	ADP
ejpam-4553	114	7	unity	unity	NOUN
ejpam-4553	114	8	is	be	AUX
ejpam-4553	114	9	used	use	VERB
ejpam-4553	114	10	to	to	PART
ejpam-4553	114	11	define	define	VERB
ejpam-4553	114	12	the	the	DET
ejpam-4553	114	13	fourier	fourier	NOUN
ejpam-4553	114	14	multiplier	multipli	ADJ
ejpam-4553	114	15	φj(d	φj(d	NUM
ejpam-4553	114	16	)	)	PUNCT
ejpam-4553	114	17	as	as	SCONJ
ejpam-4553	114	18	followed	follow	VERB
ejpam-4553	114	19	φν(d)f(x	φν(d)f(x	NOUN
ejpam-4553	114	20	)	)	PUNCT
ejpam-4553	115	1	=	=	PUNCT
ejpam-4553	115	2	f−1(φν	f−1(φν	PROPN
ejpam-4553	115	3	·	·	PUNCT
ejpam-4553	115	4	f̂)(x	f̂)(x	PROPN
ejpam-4553	115	5	)	)	PUNCT
ejpam-4553	115	6	=	=	SYM
ejpam-4553	116	1	∫	∫	PROPN
ejpam-4553	116	2	rn	rn	PROPN
ejpam-4553	116	3	φν(ξ)f̂(ξ)e	φν(ξ)f̂(ξ)e	PROPN
ejpam-4553	116	4	ix·ξdξ	ix·ξdξ	PROPN
ejpam-4553	116	5	.	.	PUNCT
ejpam-4553	117	1	definition	definition	NOUN
ejpam-4553	117	2	4	4	NUM
ejpam-4553	117	3	.	.	PUNCT
ejpam-4553	118	1	let	let	AUX
ejpam-4553	118	2	{	{	PUNCT
ejpam-4553	118	3	φν	φν	NOUN
ejpam-4553	118	4	}	}	PUNCT
ejpam-4553	118	5	be	be	VERB
ejpam-4553	118	6	the	the	DET
ejpam-4553	118	7	littlewood	littlewood	NOUN
ejpam-4553	118	8	-	-	PUNCT
ejpam-4553	118	9	paley	paley	ADJ
ejpam-4553	118	10	partition	partition	NOUN
ejpam-4553	118	11	of	of	ADP
ejpam-4553	118	12	unity	unity	NOUN
ejpam-4553	118	13	.	.	PUNCT
ejpam-4553	119	1	let	let	VERB
ejpam-4553	119	2	s	s	PRON
ejpam-4553	119	3	∈	∈	VERB
ejpam-4553	119	4	c	c	PROPN
ejpam-4553	119	5	log	log	PROPN
ejpam-4553	119	6	loc	loc	PROPN
ejpam-4553	119	7	and	and	CCONJ
ejpam-4553	119	8	p	p	X
ejpam-4553	119	9	,	,	PUNCT
ejpam-4553	119	10	q	q	X
ejpam-4553	119	11	,	,	PUNCT
ejpam-4553	119	12	u	u	PROPN
ejpam-4553	119	13	∈	∈	PROPN
ejpam-4553	119	14	p(rn	p(rn	PROPN
ejpam-4553	119	15	)	)	PUNCT
ejpam-4553	119	16	such	such	ADJ
ejpam-4553	119	17	that	that	SCONJ
ejpam-4553	119	18	0	0	NUM
ejpam-4553	119	19	<	<	X
ejpam-4553	119	20	p−	p−	NOUN
ejpam-4553	119	21	≤	≤	NUM
ejpam-4553	119	22	p(x	p(x	PROPN
ejpam-4553	119	23	)	)	PUNCT
ejpam-4553	119	24	≤	≤	NUM
ejpam-4553	119	25	u(x	u(x	NOUN
ejpam-4553	119	26	)	)	PUNCT
ejpam-4553	119	27	≤	≤	NOUN
ejpam-4553	119	28	∞.	∞.	PROPN
ejpam-4553	119	29	the	the	DET
ejpam-4553	119	30	besov	besov	NOUN
ejpam-4553	119	31	-	-	PUNCT
ejpam-4553	119	32	morrey	morrey	NOUN
ejpam-4553	119	33	spaces	space	VERB
ejpam-4553	119	34	n	n	PROPN
ejpam-4553	119	35	s	s	PROPN
ejpam-4553	119	36	(	(	PUNCT
ejpam-4553	119	37	·	·	PUNCT
ejpam-4553	119	38	)	)	PUNCT
ejpam-4553	119	39	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	119	40	(	(	PUNCT
ejpam-4553	119	41	·	·	PUNCT
ejpam-4553	119	42	)	)	PUNCT
ejpam-4553	119	43	consists	consist	VERB
ejpam-4553	119	44	of	of	ADP
ejpam-4553	119	45	all	all	DET
ejpam-4553	119	46	distributions	distribution	NOUN
ejpam-4553	119	47	f	f	PROPN
ejpam-4553	119	48	∈	∈	PROPN
ejpam-4553	119	49	s	s	PART
ejpam-4553	119	50	′(rn	′(rn	PROPN
ejpam-4553	119	51	)	)	PUNCT
ejpam-4553	119	52	such	such	ADJ
ejpam-4553	119	53	that	that	PRON
ejpam-4553	119	54	∥f∥n	∥f∥n	NOUN
ejpam-4553	119	55	s	s	PART
ejpam-4553	119	56	(	(	PUNCT
ejpam-4553	119	57	·	·	PUNCT
ejpam-4553	119	58	)	)	PUNCT
ejpam-4553	119	59	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	119	60	(	(	PUNCT
ejpam-4553	119	61	·	·	PUNCT
ejpam-4553	119	62	)	)	PUNCT
ejpam-4553	119	63	:	:	PUNCT
ejpam-4553	120	1	=	=	SYM
ejpam-4553	120	2	∥φ0(d)f∥mp(·),u	∥φ0(d)f∥mp(·),u	X
ejpam-4553	120	3	(	(	PUNCT
ejpam-4553	120	4	·	·	PUNCT
ejpam-4553	120	5	)	)	PUNCT
ejpam-4553	120	6	+	+	CCONJ
ejpam-4553	120	7	∥∥∥∥(2νs(·)φν(d)f	∥∥∥∥(2νs(·)φν(d)f	NOUN
ejpam-4553	120	8	)	)	PUNCT
ejpam-4553	120	9	ν≥1	ν≥1	PROPN
ejpam-4553	120	10	∥∥∥∥	∥∥∥∥	NUM
ejpam-4553	120	11	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	120	12	(	(	PUNCT
ejpam-4553	120	13	·	·	PUNCT
ejpam-4553	120	14	)	)	PUNCT
ejpam-4553	120	15	)	)	PUNCT
ejpam-4553	121	1	<	<	X
ejpam-4553	121	2	∞.	∞.	PROPN
ejpam-4553	121	3	(	(	PUNCT
ejpam-4553	121	4	5	5	NUM
ejpam-4553	121	5	)	)	PUNCT
ejpam-4553	121	6	remark	remark	NOUN
ejpam-4553	121	7	2	2	NUM
ejpam-4553	121	8	.	.	PUNCT
ejpam-4553	122	1	(	(	PUNCT
ejpam-4553	122	2	i	i	NOUN
ejpam-4553	122	3	)	)	PUNCT
ejpam-4553	122	4	let	let	VERB
ejpam-4553	122	5	us	we	PRON
ejpam-4553	122	6	notice	notice	VERB
ejpam-4553	122	7	that	that	SCONJ
ejpam-4553	122	8	besov	besov	NOUN
ejpam-4553	122	9	-	-	PUNCT
ejpam-4553	122	10	morrey	morrey	NOUN
ejpam-4553	122	11	spaces	space	VERB
ejpam-4553	122	12	n	n	PROPN
ejpam-4553	122	13	s	s	PROPN
ejpam-4553	122	14	(	(	PUNCT
ejpam-4553	122	15	·	·	PUNCT
ejpam-4553	122	16	)	)	PUNCT
ejpam-4553	122	17	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	122	18	(	(	PUNCT
ejpam-4553	122	19	·	·	PUNCT
ejpam-4553	122	20	)	)	PUNCT
ejpam-4553	122	21	are	be	AUX
ejpam-4553	122	22	defined	define	VERB
ejpam-4553	122	23	by	by	ADP
ejpam-4553	122	24	the	the	DET
ejpam-4553	122	25	composite	composite	ADJ
ejpam-4553	122	26	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	NOUN
ejpam-4553	122	27	(	(	PUNCT
ejpam-4553	122	28	·	·	PUNCT
ejpam-4553	122	29	)	)	PUNCT
ejpam-4553	122	30	)	)	PUNCT
ejpam-4553	123	1	while	while	SCONJ
ejpam-4553	123	2	triebel	triebel	NOUN
ejpam-4553	123	3	-	-	PUNCT
ejpam-4553	123	4	lizorkin	lizorkin	NOUN
ejpam-4553	123	5	-	-	PUNCT
ejpam-4553	123	6	morrey	morrey	PROPN
ejpam-4553	123	7	spaces	space	NOUN
ejpam-4553	123	8	es	es	VERB
ejpam-4553	123	9	(	(	PUNCT
ejpam-4553	123	10	·	·	PUNCT
ejpam-4553	123	11	)	)	PUNCT
ejpam-4553	123	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	123	13	(	(	PUNCT
ejpam-4553	123	14	·	·	PUNCT
ejpam-4553	123	15	)	)	PUNCT
ejpam-4553	123	16	are	be	AUX
ejpam-4553	123	17	defined	define	VERB
ejpam-4553	123	18	bymp(·),u	bymp(·),u	PROPN
ejpam-4553	123	19	(	(	PUNCT
ejpam-4553	123	20	·	·	PUNCT
ejpam-4553	123	21	)	)	PUNCT
ejpam-4553	123	22	(	(	PUNCT
ejpam-4553	123	23	ℓq	ℓq	PROPN
ejpam-4553	123	24	(	(	PUNCT
ejpam-4553	123	25	·	·	PUNCT
ejpam-4553	123	26	)	)	PUNCT
ejpam-4553	123	27	)	)	PUNCT
ejpam-4553	123	28	.	.	PUNCT
ejpam-4553	124	1	(	(	PUNCT
ejpam-4553	124	2	ii	ii	X
ejpam-4553	124	3	)	)	PUNCT
ejpam-4553	124	4	the	the	DET
ejpam-4553	124	5	case	case	NOUN
ejpam-4553	124	6	of	of	ADP
ejpam-4553	124	7	the	the	DET
ejpam-4553	124	8	boundedness	boundedness	NOUN
ejpam-4553	124	9	of	of	ADP
ejpam-4553	124	10	non	non	ADJ
ejpam-4553	124	11	-	-	ADJ
ejpam-4553	124	12	regular	regular	ADJ
ejpam-4553	124	13	pdos	pdo	NOUN
ejpam-4553	124	14	on	on	ADP
ejpam-4553	124	15	variable	variable	ADJ
ejpam-4553	124	16	exponent	exponent	NOUN
ejpam-4553	124	17	triebellizorkin	triebellizorkin	NOUN
ejpam-4553	124	18	-	-	PUNCT
ejpam-4553	124	19	morrey	morrey	PROPN
ejpam-4553	124	20	spaces	space	NOUN
ejpam-4553	124	21	has	have	AUX
ejpam-4553	124	22	been	be	AUX
ejpam-4553	124	23	studied	study	VERB
ejpam-4553	124	24	in	in	ADP
ejpam-4553	124	25	[	[	X
ejpam-4553	124	26	4	4	NUM
ejpam-4553	124	27	]	]	PUNCT
ejpam-4553	124	28	.	.	PUNCT
ejpam-4553	125	1	proposition	proposition	NOUN
ejpam-4553	125	2	2	2	NUM
ejpam-4553	125	3	.	.	PUNCT
ejpam-4553	126	1	let	let	VERB
ejpam-4553	126	2	s	s	PRON
ejpam-4553	126	3	∈	∈	VERB
ejpam-4553	126	4	c	c	PROPN
ejpam-4553	126	5	log	log	PROPN
ejpam-4553	126	6	loc	loc	PROPN
ejpam-4553	126	7	,	,	PUNCT
ejpam-4553	126	8	p	p	PROPN
ejpam-4553	126	9	∈	∈	PROPN
ejpam-4553	126	10	p	p	NOUN
ejpam-4553	126	11	log(rn	log(rn	PROPN
ejpam-4553	126	12	)	)	PUNCT
ejpam-4553	126	13	and	and	CCONJ
ejpam-4553	126	14	q	q	X
ejpam-4553	126	15	,	,	PUNCT
ejpam-4553	126	16	u	u	PROPN
ejpam-4553	126	17	∈	∈	PROPN
ejpam-4553	126	18	p(rn	p(rn	PROPN
ejpam-4553	126	19	)	)	PUNCT
ejpam-4553	126	20	with	with	ADP
ejpam-4553	126	21	p(x	p(x	NOUN
ejpam-4553	126	22	)	)	PUNCT
ejpam-4553	126	23	≤	≤	NUM
ejpam-4553	126	24	u(x	u(x	NOUN
ejpam-4553	126	25	)	)	PUNCT
ejpam-4553	126	26	and	and	CCONJ
ejpam-4553	126	27	1	1	NUM
ejpam-4553	126	28	/	/	SYM
ejpam-4553	126	29	q	q	NOUN
ejpam-4553	126	30	locally	locally	ADV
ejpam-4553	126	31	log	log	NOUN
ejpam-4553	126	32	-	-	PUNCT
ejpam-4553	126	33	hölder	hölder	NOUN
ejpam-4553	126	34	continuous	continuous	NOUN
ejpam-4553	126	35	.	.	PUNCT
ejpam-4553	127	1	then	then	ADV
ejpam-4553	127	2	it	it	PRON
ejpam-4553	127	3	holds	hold	VERB
ejpam-4553	127	4	s	s	VERB
ejpam-4553	127	5	↪	↪	PROPN
ejpam-4553	127	6	→	→	SYM
ejpam-4553	127	7	n	n	CCONJ
ejpam-4553	127	8	s	s	PROPN
ejpam-4553	127	9	(	(	PUNCT
ejpam-4553	127	10	·	·	PUNCT
ejpam-4553	127	11	)	)	PUNCT
ejpam-4553	127	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	127	13	(	(	PUNCT
ejpam-4553	127	14	·	·	PUNCT
ejpam-4553	127	15	)	)	PUNCT
ejpam-4553	127	16	↪	↪	PROPN
ejpam-4553	127	17	→	→	SYM
ejpam-4553	127	18	s	s	PART
ejpam-4553	127	19	′.	′.	PROPN
ejpam-4553	127	20	mohamed	mohamed	PROPN
ejpam-4553	127	21	congo	congo	PROPN
ejpam-4553	127	22	,	,	PUNCT
ejpam-4553	127	23	m.	m.	PROPN
ejpam-4553	127	24	f.	f.	PROPN
ejpam-4553	127	25	ouedraogo	ouedraogo	PROPN
ejpam-4553	127	26	/	/	SYM
ejpam-4553	127	27	eur	eur	PROPN
ejpam-4553	127	28	.	.	PUNCT
ejpam-4553	128	1	j.	j.	PROPN
ejpam-4553	128	2	pure	pure	PROPN
ejpam-4553	128	3	appl	appl	PROPN
ejpam-4553	128	4	.	.	PROPN
ejpam-4553	128	5	math	math	PROPN
ejpam-4553	128	6	,	,	PUNCT
ejpam-4553	128	7	15	15	NUM
ejpam-4553	128	8	(	(	PUNCT
ejpam-4553	128	9	4	4	NUM
ejpam-4553	128	10	)	)	PUNCT
ejpam-4553	128	11	(	(	PUNCT
ejpam-4553	128	12	2022	2022	NUM
ejpam-4553	128	13	)	)	PUNCT
ejpam-4553	128	14	,	,	PUNCT
ejpam-4553	128	15	1716	1716	NUM
ejpam-4553	128	16	-	-	SYM
ejpam-4553	128	17	1737	1737	NUM
ejpam-4553	128	18	1721	1721	NUM
ejpam-4553	128	19	3	3	NUM
ejpam-4553	128	20	.	.	PUNCT
ejpam-4553	128	21	basic	basic	ADJ
ejpam-4553	128	22	tools	tool	NOUN
ejpam-4553	128	23	in	in	ADP
ejpam-4553	128	24	the	the	DET
ejpam-4553	128	25	following	following	NOUN
ejpam-4553	129	1	,	,	PUNCT
ejpam-4553	129	2	we	we	PRON
ejpam-4553	129	3	present	present	VERB
ejpam-4553	129	4	some	some	DET
ejpam-4553	129	5	results	result	NOUN
ejpam-4553	129	6	which	which	PRON
ejpam-4553	129	7	will	will	AUX
ejpam-4553	129	8	be	be	AUX
ejpam-4553	129	9	useful	useful	ADJ
ejpam-4553	129	10	in	in	ADP
ejpam-4553	129	11	the	the	DET
ejpam-4553	129	12	last	last	ADJ
ejpam-4553	129	13	section	section	NOUN
ejpam-4553	129	14	.	.	PUNCT
ejpam-4553	130	1	first	first	ADV
ejpam-4553	130	2	of	of	ADP
ejpam-4553	130	3	all	all	PRON
ejpam-4553	130	4	,	,	PUNCT
ejpam-4553	130	5	we	we	PRON
ejpam-4553	130	6	recall	recall	VERB
ejpam-4553	130	7	the	the	DET
ejpam-4553	130	8	η	η	NOUN
ejpam-4553	130	9	-	-	PUNCT
ejpam-4553	130	10	functions	function	NOUN
ejpam-4553	130	11	defined	define	VERB
ejpam-4553	130	12	on	on	ADP
ejpam-4553	130	13	rn	rn	PROPN
ejpam-4553	130	14	by	by	ADP
ejpam-4553	130	15	ην	ην	NOUN
ejpam-4553	130	16	,	,	PUNCT
ejpam-4553	130	17	m(x	m(x	X
ejpam-4553	130	18	)	)	PUNCT
ejpam-4553	131	1	=	=	SYM
ejpam-4553	131	2	2nν	2nν	NOUN
ejpam-4553	131	3	(	(	PUNCT
ejpam-4553	131	4	1	1	NUM
ejpam-4553	131	5	+	+	NUM
ejpam-4553	131	6	2ν	2ν	NOUN
ejpam-4553	131	7	|x|)−m	|x|)−m	NOUN
ejpam-4553	131	8	,	,	PUNCT
ejpam-4553	131	9	ν	ν	PROPN
ejpam-4553	131	10	∈	∈	PROPN
ejpam-4553	131	11	n0	n0	PROPN
ejpam-4553	131	12	,	,	PUNCT
ejpam-4553	131	13	m	m	VERB
ejpam-4553	131	14	>	>	X
ejpam-4553	131	15	0	0	X
ejpam-4553	131	16	.	.	PUNCT
ejpam-4553	131	17	note	note	VERB
ejpam-4553	131	18	that	that	SCONJ
ejpam-4553	131	19	ην	ην	NOUN
ejpam-4553	131	20	,	,	PUNCT
ejpam-4553	131	21	m	m	PROPN
ejpam-4553	131	22	∈	∈	PROPN
ejpam-4553	131	23	l1	l1	PROPN
ejpam-4553	131	24	for	for	ADP
ejpam-4553	131	25	m	m	PROPN
ejpam-4553	131	26	>	>	X
ejpam-4553	131	27	n	n	PROPN
ejpam-4553	131	28	and	and	CCONJ
ejpam-4553	131	29	the	the	DET
ejpam-4553	131	30	corresponding	corresponding	ADJ
ejpam-4553	131	31	l1	l1	PROPN
ejpam-4553	131	32	-	-	PUNCT
ejpam-4553	131	33	norm	norm	NOUN
ejpam-4553	131	34	does	do	AUX
ejpam-4553	131	35	not	not	PART
ejpam-4553	131	36	depend	depend	VERB
ejpam-4553	131	37	on	on	ADP
ejpam-4553	131	38	ν	ν	X
ejpam-4553	131	39	.	.	PUNCT
ejpam-4553	132	1	the	the	DET
ejpam-4553	132	2	next	next	ADJ
ejpam-4553	132	3	lemmas	lemmas	PROPN
ejpam-4553	132	4	can	can	AUX
ejpam-4553	132	5	be	be	AUX
ejpam-4553	132	6	found	find	VERB
ejpam-4553	132	7	in	in	ADP
ejpam-4553	132	8	[	[	PUNCT
ejpam-4553	132	9	7](lemma	7](lemma	NUM
ejpam-4553	132	10	19	19	NUM
ejpam-4553	132	11	)	)	PUNCT
ejpam-4553	132	12	and	and	CCONJ
ejpam-4553	133	1	[	[	X
ejpam-4553	133	2	9](lemma	9](lemma	NOUN
ejpam-4553	133	3	6.1	6.1	NUM
ejpam-4553	133	4	.	.	PUNCT
ejpam-4553	133	5	)	)	PUNCT
ejpam-4553	133	6	.	.	PUNCT
ejpam-4553	134	1	lemma	lemma	PROPN
ejpam-4553	134	2	1	1	X
ejpam-4553	134	3	.	.	PUNCT
ejpam-4553	135	1	let	let	VERB
ejpam-4553	135	2	α	α	PRON
ejpam-4553	135	3	∈	∈	PROPN
ejpam-4553	135	4	c	c	PROPN
ejpam-4553	135	5	log	log	PROPN
ejpam-4553	135	6	loc	loc	X
ejpam-4553	135	7	(	(	PUNCT
ejpam-4553	135	8	r	r	NOUN
ejpam-4553	135	9	n	n	CCONJ
ejpam-4553	135	10	)	)	PUNCT
ejpam-4553	135	11	and	and	CCONJ
ejpam-4553	135	12	let	let	VERB
ejpam-4553	135	13	m	m	PRON
ejpam-4553	135	14	≥	≥	NOUN
ejpam-4553	135	15	0	0	NUM
ejpam-4553	135	16	,	,	PUNCT
ejpam-4553	135	17	l	l	X
ejpam-4553	135	18	≥	≥	NOUN
ejpam-4553	135	19	clog(α	clog(α	NUM
ejpam-4553	135	20	)	)	PUNCT
ejpam-4553	135	21	,	,	PUNCT
ejpam-4553	135	22	where	where	SCONJ
ejpam-4553	135	23	clog	clog	NOUN
ejpam-4553	135	24	is	be	AUX
ejpam-4553	135	25	the	the	DET
ejpam-4553	135	26	constant	constant	ADJ
ejpam-4553	135	27	from	from	ADP
ejpam-4553	135	28	(	(	PUNCT
ejpam-4553	135	29	1	1	NUM
ejpam-4553	135	30	)	)	PUNCT
ejpam-4553	135	31	for	for	ADP
ejpam-4553	135	32	α	α	X
ejpam-4553	135	33	.	.	PUNCT
ejpam-4553	136	1	then	then	ADV
ejpam-4553	136	2	2να(x)ην	2να(x)ην	NUM
ejpam-4553	136	3	,	,	PUNCT
ejpam-4553	136	4	m+l(x−	m+l(x−	NOUN
ejpam-4553	136	5	y	y	NOUN
ejpam-4553	136	6	)	)	PUNCT
ejpam-4553	136	7	≤	≤	ADJ
ejpam-4553	136	8	c2να(y)ην	c2να(y)ην	PROPN
ejpam-4553	136	9	,	,	PUNCT
ejpam-4553	136	10	m(x−	m(x−	PROPN
ejpam-4553	136	11	y	y	NOUN
ejpam-4553	136	12	)	)	PUNCT
ejpam-4553	136	13	with	with	ADP
ejpam-4553	136	14	c	c	PROPN
ejpam-4553	136	15	>	>	SYM
ejpam-4553	136	16	0	0	PROPN
ejpam-4553	136	17	independent	independent	NOUN
ejpam-4553	136	18	of	of	ADP
ejpam-4553	136	19	x	x	PROPN
ejpam-4553	136	20	,	,	PUNCT
ejpam-4553	136	21	y	y	PROPN
ejpam-4553	136	22	∈	∈	PROPN
ejpam-4553	136	23	rn	rn	PROPN
ejpam-4553	136	24	and	and	CCONJ
ejpam-4553	136	25	ν	ν	PROPN
ejpam-4553	136	26	∈	∈	PROPN
ejpam-4553	136	27	n0	n0	PROPN
ejpam-4553	136	28	.	.	PUNCT
ejpam-4553	137	1	lemma	lemma	PROPN
ejpam-4553	137	2	2	2	X
ejpam-4553	137	3	.	.	PUNCT
ejpam-4553	138	1	let	let	VERB
ejpam-4553	138	2	t	t	PROPN
ejpam-4553	138	3	>	>	X
ejpam-4553	138	4	0	0	PROPN
ejpam-4553	138	5	,	,	PUNCT
ejpam-4553	138	6	ν	ν	PROPN
ejpam-4553	138	7	∈	∈	PROPN
ejpam-4553	138	8	n0	n0	PROPN
ejpam-4553	138	9	and	and	CCONJ
ejpam-4553	138	10	m	m	PROPN
ejpam-4553	138	11	>	>	X
ejpam-4553	138	12	n.	n.	NOUN
ejpam-4553	138	13	then	then	ADV
ejpam-4553	138	14	there	there	PRON
ejpam-4553	138	15	exist	exist	VERB
ejpam-4553	138	16	c	c	NOUN
ejpam-4553	138	17	=	=	SYM
ejpam-4553	138	18	c(t	c(t	PROPN
ejpam-4553	138	19	,	,	PUNCT
ejpam-4553	138	20	m	m	NOUN
ejpam-4553	138	21	,	,	PUNCT
ejpam-4553	138	22	n	n	CCONJ
ejpam-4553	138	23	)	)	PUNCT
ejpam-4553	138	24	such	such	ADJ
ejpam-4553	138	25	that	that	DET
ejpam-4553	138	26	for	for	ADP
ejpam-4553	138	27	all	all	PRON
ejpam-4553	138	28	g	g	PROPN
ejpam-4553	138	29	∈	∈	PROPN
ejpam-4553	138	30	s	s	PART
ejpam-4553	138	31	′(rn	′(rn	PROPN
ejpam-4553	138	32	)	)	PUNCT
ejpam-4553	138	33	with	with	ADP
ejpam-4553	138	34	suppfg	suppfg	PROPN
ejpam-4553	138	35	⊂	⊂	PROPN
ejpam-4553	138	36	{	{	PUNCT
ejpam-4553	138	37	ξ	ξ	PROPN
ejpam-4553	138	38	∈	∈	PROPN
ejpam-4553	138	39	rn	rn	PROPN
ejpam-4553	138	40	:	:	PUNCT
ejpam-4553	139	1	|ξ|	|ξ|	VERB
ejpam-4553	139	2	≤	≤	NOUN
ejpam-4553	139	3	2ν+1	2ν+1	NUM
ejpam-4553	139	4	}	}	PUNCT
ejpam-4553	139	5	,	,	PUNCT
ejpam-4553	139	6	|g(x)|	|g(x)|	PROPN
ejpam-4553	139	7	≤	≤	NUM
ejpam-4553	139	8	c	c	NOUN
ejpam-4553	139	9	(	(	PUNCT
ejpam-4553	139	10	ην	ην	NOUN
ejpam-4553	139	11	,	,	PUNCT
ejpam-4553	139	12	m	m	VERB
ejpam-4553	139	13	∗	∗	NOUN
ejpam-4553	139	14	|g|t(x	|g|t(x	PROPN
ejpam-4553	139	15	)	)	PUNCT
ejpam-4553	139	16	)	)	PUNCT
ejpam-4553	139	17	1	1	NUM
ejpam-4553	139	18	/	/	SYM
ejpam-4553	139	19	t	t	NOUN
ejpam-4553	139	20	,	,	PUNCT
ejpam-4553	139	21	x	x	PROPN
ejpam-4553	139	22	∈	∈	PROPN
ejpam-4553	139	23	rn	rn	PROPN
ejpam-4553	139	24	.	.	PUNCT
ejpam-4553	140	1	lemma	lemma	PROPN
ejpam-4553	140	2	3	3	X
ejpam-4553	140	3	.	.	PUNCT
ejpam-4553	141	1	let	let	VERB
ejpam-4553	141	2	p	p	PRON
ejpam-4553	141	3	∈	∈	PROPN
ejpam-4553	141	4	p	p	NOUN
ejpam-4553	141	5	log(rn	log(rn	PROPN
ejpam-4553	141	6	)	)	PUNCT
ejpam-4553	141	7	and	and	CCONJ
ejpam-4553	141	8	u	u	NOUN
ejpam-4553	141	9	,	,	PUNCT
ejpam-4553	141	10	q	q	PROPN
ejpam-4553	141	11	∈	∈	PROPN
ejpam-4553	141	12	p	p	NOUN
ejpam-4553	141	13	such	such	ADJ
ejpam-4553	141	14	that	that	SCONJ
ejpam-4553	141	15	1	1	NUM
ejpam-4553	141	16	q	q	NOUN
ejpam-4553	141	17	∈	∈	PROPN
ejpam-4553	141	18	c	c	PROPN
ejpam-4553	141	19	log	log	PROPN
ejpam-4553	141	20	loc	loc	NOUN
ejpam-4553	141	21	with	with	ADP
ejpam-4553	141	22	1	1	NUM
ejpam-4553	141	23	≤	≤	NOUN
ejpam-4553	141	24	p−	p−	NOUN
ejpam-4553	141	25	≤	≤	NUM
ejpam-4553	141	26	p(x	p(x	PROPN
ejpam-4553	141	27	)	)	PUNCT
ejpam-4553	141	28	≤	≤	NUM
ejpam-4553	141	29	u(x	u(x	NOUN
ejpam-4553	141	30	)	)	PUNCT
ejpam-4553	141	31	≤	≤	NOUN
ejpam-4553	141	32	∞.	∞.	PROPN
ejpam-4553	141	33	ifm	ifm	NOUN
ejpam-4553	141	34	>	>	X
ejpam-4553	141	35	n+clog(1	n+clog(1	PROPN
ejpam-4553	141	36	/	/	SYM
ejpam-4553	141	37	q)+nmax	q)+nmax	PROPN
ejpam-4553	141	38	{	{	PUNCT
ejpam-4553	141	39	0	0	NUM
ejpam-4553	141	40	,	,	PUNCT
ejpam-4553	141	41	supx∈rn	supx∈rn	PUNCT
ejpam-4553	141	42	(	(	PUNCT
ejpam-4553	141	43	1	1	NUM
ejpam-4553	141	44	p(x	p(x	NOUN
ejpam-4553	141	45	)	)	PUNCT
ejpam-4553	141	46	−	−	PROPN
ejpam-4553	141	47	1	1	NUM
ejpam-4553	141	48	u(x	u(x	NOUN
ejpam-4553	141	49	)	)	PUNCT
ejpam-4553	141	50	)	)	PUNCT
ejpam-4553	142	1	−	−	PROPN
ejpam-4553	142	2	1	1	NUM
ejpam-4553	142	3	p∞	p∞	PROPN
ejpam-4553	142	4	}	}	PUNCT
ejpam-4553	142	5	,	,	PUNCT
ejpam-4553	142	6	then	then	ADV
ejpam-4553	142	7	there	there	PRON
ejpam-4553	142	8	exist	exist	VERB
ejpam-4553	142	9	c	c	NOUN
ejpam-4553	142	10	>	>	X
ejpam-4553	142	11	0	0	NUM
ejpam-4553	143	1	such	such	ADJ
ejpam-4553	143	2	that∥∥(ην	that∥∥(ην	PROPN
ejpam-4553	143	3	,	,	PUNCT
ejpam-4553	143	4	m	m	PROPN
ejpam-4553	143	5	∗	∗	NOUN
ejpam-4553	143	6	fν)ν	fν)ν	PROPN
ejpam-4553	143	7	∥∥	∥∥	PUNCT
ejpam-4553	143	8	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	143	9	(	(	PUNCT
ejpam-4553	143	10	·	·	PUNCT
ejpam-4553	143	11	)	)	PUNCT
ejpam-4553	143	12	)	)	PUNCT
ejpam-4553	144	1	≤	≤	NUM
ejpam-4553	144	2	c	c	X
ejpam-4553	144	3	∥(fν)ν∥ℓq(·)(mp(·),u	∥(fν)ν∥ℓq(·)(mp(·),u	NOUN
ejpam-4553	144	4	(	(	PUNCT
ejpam-4553	144	5	·	·	PUNCT
ejpam-4553	144	6	)	)	PUNCT
ejpam-4553	144	7	)	)	PUNCT
ejpam-4553	144	8	for	for	ADP
ejpam-4553	144	9	all	all	DET
ejpam-4553	144	10	sequences	sequence	NOUN
ejpam-4553	144	11	(	(	PUNCT
ejpam-4553	144	12	fν)ν	fν)ν	PROPN
ejpam-4553	144	13	⊂	⊂	PUNCT
ejpam-4553	144	14	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	144	15	(	(	PUNCT
ejpam-4553	144	16	·	·	PUNCT
ejpam-4553	144	17	)	)	PUNCT
ejpam-4553	144	18	)	)	PUNCT
ejpam-4553	144	19	.	.	PUNCT
ejpam-4553	145	1	lemma	lemma	PROPN
ejpam-4553	145	2	4	4	X
ejpam-4553	145	3	.	.	PUNCT
ejpam-4553	146	1	let	let	VERB
ejpam-4553	146	2	p	p	PRON
ejpam-4553	146	3	∈	∈	PROPN
ejpam-4553	146	4	p	p	NOUN
ejpam-4553	146	5	log(rn	log(rn	PROPN
ejpam-4553	146	6	)	)	PUNCT
ejpam-4553	146	7	and	and	CCONJ
ejpam-4553	146	8	u	u	NOUN
ejpam-4553	146	9	∈	∈	PROPN
ejpam-4553	146	10	p	p	NOUN
ejpam-4553	146	11	with	with	ADP
ejpam-4553	146	12	1	1	NUM
ejpam-4553	146	13	≤	≤	NOUN
ejpam-4553	146	14	p−	p−	NOUN
ejpam-4553	146	15	≤	≤	NUM
ejpam-4553	146	16	p(x	p(x	PROPN
ejpam-4553	146	17	)	)	PUNCT
ejpam-4553	146	18	≤	≤	NUM
ejpam-4553	146	19	u(x	u(x	NOUN
ejpam-4553	146	20	)	)	PUNCT
ejpam-4553	146	21	≤	≤	NOUN
ejpam-4553	146	22	∞.	∞.	PROPN
ejpam-4553	146	23	if	if	SCONJ
ejpam-4553	146	24	m	m	PROPN
ejpam-4553	146	25	>	>	X
ejpam-4553	146	26	n+	n+	X
ejpam-4553	146	27	nmax	nmax	PROPN
ejpam-4553	146	28	{	{	PUNCT
ejpam-4553	146	29	0	0	NUM
ejpam-4553	146	30	,	,	PUNCT
ejpam-4553	146	31	supx∈rn	supx∈rn	PUNCT
ejpam-4553	147	1	(	(	PUNCT
ejpam-4553	147	2	1	1	NUM
ejpam-4553	147	3	p(x	p(x	NOUN
ejpam-4553	147	4	)	)	PUNCT
ejpam-4553	147	5	−	−	PROPN
ejpam-4553	147	6	1	1	NUM
ejpam-4553	147	7	u(x	u(x	NOUN
ejpam-4553	147	8	)	)	PUNCT
ejpam-4553	147	9	)	)	PUNCT
ejpam-4553	148	1	−	−	PROPN
ejpam-4553	148	2	1	1	NUM
ejpam-4553	148	3	p∞	p∞	PROPN
ejpam-4553	148	4	}	}	PUNCT
ejpam-4553	148	5	.	.	PUNCT
ejpam-4553	149	1	then	then	ADV
ejpam-4553	149	2	there	there	PRON
ejpam-4553	149	3	exists	exist	VERB
ejpam-4553	149	4	c	c	NOUN
ejpam-4553	149	5	>	>	X
ejpam-4553	149	6	0	0	NUM
ejpam-4553	149	7	such	such	ADJ
ejpam-4553	149	8	that	that	DET
ejpam-4553	149	9	∥ην	∥ην	NOUN
ejpam-4553	149	10	,	,	PUNCT
ejpam-4553	149	11	m	m	NOUN
ejpam-4553	149	12	∗	∗	NOUN
ejpam-4553	149	13	f∥mp(·),u	f∥mp(·),u	PROPN
ejpam-4553	149	14	(	(	PUNCT
ejpam-4553	149	15	·	·	PUNCT
ejpam-4553	149	16	)	)	PUNCT
ejpam-4553	149	17	≤	≤	NUM
ejpam-4553	149	18	∥f∥mp(·),u	∥f∥mp(·),u	PROPN
ejpam-4553	149	19	(	(	PUNCT
ejpam-4553	149	20	·	·	PUNCT
ejpam-4553	149	21	)	)	PUNCT
ejpam-4553	149	22	.	.	PUNCT
ejpam-4553	150	1	lemma	lemma	PROPN
ejpam-4553	150	2	5	5	X
ejpam-4553	150	3	.	.	PUNCT
ejpam-4553	151	1	let	let	VERB
ejpam-4553	151	2	p	p	PRON
ejpam-4553	151	3	,	,	PUNCT
ejpam-4553	151	4	u	u	NOUN
ejpam-4553	151	5	,	,	PUNCT
ejpam-4553	151	6	q	q	PROPN
ejpam-4553	151	7	∈	∈	PROPN
ejpam-4553	151	8	p(rn	p(rn	PROPN
ejpam-4553	151	9	)	)	PUNCT
ejpam-4553	151	10	with	with	ADP
ejpam-4553	151	11	p(x	p(x	NOUN
ejpam-4553	151	12	)	)	PUNCT
ejpam-4553	151	13	≤	≤	NUM
ejpam-4553	151	14	u(x	u(x	NOUN
ejpam-4553	151	15	)	)	PUNCT
ejpam-4553	151	16	.	.	PUNCT
ejpam-4553	152	1	let	let	VERB
ejpam-4553	152	2	δ	δ	PRON
ejpam-4553	152	3	>	>	X
ejpam-4553	152	4	0	0	X
ejpam-4553	152	5	.	.	PUNCT
ejpam-4553	153	1	for	for	ADP
ejpam-4553	153	2	any	any	DET
ejpam-4553	153	3	sequence	sequence	NOUN
ejpam-4553	153	4	(	(	PUNCT
ejpam-4553	153	5	gj)j∈n0	gj)j∈n0	NOUN
ejpam-4553	153	6	of	of	ADP
ejpam-4553	153	7	non	non	ADJ
ejpam-4553	153	8	-	-	ADJ
ejpam-4553	153	9	negative	negative	ADJ
ejpam-4553	153	10	measurable	measurable	ADJ
ejpam-4553	153	11	functions	function	NOUN
ejpam-4553	153	12	on	on	ADP
ejpam-4553	153	13	rn	rn	NOUN
ejpam-4553	153	14	,	,	PUNCT
ejpam-4553	153	15	let	let	VERB
ejpam-4553	153	16	gν(x	gν(x	NOUN
ejpam-4553	153	17	)	)	PUNCT
ejpam-4553	153	18	:	:	PUNCT
ejpam-4553	154	1	=	=	SYM
ejpam-4553	154	2	∞∑	∞∑	NUM
ejpam-4553	154	3	j=0	j=0	PROPN
ejpam-4553	154	4	2−|ν−j|δgj(x	2−|ν−j|δgj(x	NUM
ejpam-4553	154	5	)	)	PUNCT
ejpam-4553	154	6	,	,	PUNCT
ejpam-4553	154	7	x	x	PROPN
ejpam-4553	154	8	∈	∈	PROPN
ejpam-4553	154	9	rn	rn	PROPN
ejpam-4553	154	10	,	,	PUNCT
ejpam-4553	154	11	ν	ν	PROPN
ejpam-4553	154	12	∈	∈	PROPN
ejpam-4553	154	13	n0	n0	PROPN
ejpam-4553	154	14	.	.	PUNCT
ejpam-4553	155	1	then	then	ADV
ejpam-4553	155	2	it	it	PRON
ejpam-4553	155	3	holds	hold	VERB
ejpam-4553	155	4	∥(gν)ν∥ℓq(·)(mp(·),u	∥(gν)ν∥ℓq(·)(mp(·),u	NOUN
ejpam-4553	155	5	(	(	PUNCT
ejpam-4553	155	6	·	·	PUNCT
ejpam-4553	155	7	)	)	PUNCT
ejpam-4553	155	8	)	)	PUNCT
ejpam-4553	156	1	≲	≲	PROPN
ejpam-4553	156	2	∥∥∥(gj)j∥∥∥ℓq(·)(mp(·),u	∥∥∥(gj)j∥∥∥ℓq(·)(mp(·),u	PROPN
ejpam-4553	156	3	(	(	PUNCT
ejpam-4553	156	4	·	·	PUNCT
ejpam-4553	156	5	)	)	PUNCT
ejpam-4553	156	6	)	)	PUNCT
ejpam-4553	156	7	.	.	PUNCT
ejpam-4553	157	1	mohamed	mohamed	PROPN
ejpam-4553	157	2	congo	congo	PROPN
ejpam-4553	157	3	,	,	PUNCT
ejpam-4553	157	4	m.	m.	PROPN
ejpam-4553	157	5	f.	f.	PROPN
ejpam-4553	157	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	157	7	/	/	SYM
ejpam-4553	157	8	eur	eur	PROPN
ejpam-4553	157	9	.	.	PUNCT
ejpam-4553	158	1	j.	j.	PROPN
ejpam-4553	158	2	pure	pure	PROPN
ejpam-4553	158	3	appl	appl	PROPN
ejpam-4553	158	4	.	.	PROPN
ejpam-4553	158	5	math	math	PROPN
ejpam-4553	158	6	,	,	PUNCT
ejpam-4553	158	7	15	15	NUM
ejpam-4553	158	8	(	(	PUNCT
ejpam-4553	158	9	4	4	NUM
ejpam-4553	158	10	)	)	PUNCT
ejpam-4553	158	11	(	(	PUNCT
ejpam-4553	158	12	2022	2022	NUM
ejpam-4553	158	13	)	)	PUNCT
ejpam-4553	158	14	,	,	PUNCT
ejpam-4553	158	15	1716	1716	NUM
ejpam-4553	158	16	-	-	SYM
ejpam-4553	158	17	1737	1737	NUM
ejpam-4553	158	18	1722	1722	NUM
ejpam-4553	158	19	4	4	NUM
ejpam-4553	158	20	.	.	PUNCT
ejpam-4553	159	1	boundedness	boundedness	NOUN
ejpam-4553	159	2	of	of	ADP
ejpam-4553	159	3	pseudo	pseudo	NOUN
ejpam-4553	159	4	-	-	NOUN
ejpam-4553	159	5	differential	differential	ADJ
ejpam-4553	159	6	operators	operator	NOUN
ejpam-4553	159	7	we	we	PRON
ejpam-4553	159	8	will	will	AUX
ejpam-4553	159	9	use	use	VERB
ejpam-4553	159	10	symbols	symbol	NOUN
ejpam-4553	159	11	for	for	ADP
ejpam-4553	159	12	which	which	PRON
ejpam-4553	159	13	x	x	NOUN
ejpam-4553	159	14	-	-	NOUN
ejpam-4553	159	15	regularity	regularity	NOUN
ejpam-4553	159	16	is	be	AUX
ejpam-4553	159	17	measured	measure	VERB
ejpam-4553	159	18	in	in	ADP
ejpam-4553	159	19	hölder	hölder	NOUN
ejpam-4553	159	20	-	-	PUNCT
ejpam-4553	159	21	zygmund	zygmund	NOUN
ejpam-4553	159	22	spaces	space	NOUN
ejpam-4553	159	23	.	.	PUNCT
ejpam-4553	160	1	definition	definition	NOUN
ejpam-4553	160	2	5	5	NUM
ejpam-4553	160	3	.	.	PUNCT
ejpam-4553	161	1	the	the	DET
ejpam-4553	161	2	function	function	NOUN
ejpam-4553	161	3	a(x	a(x	NOUN
ejpam-4553	161	4	,	,	PUNCT
ejpam-4553	161	5	ξ	ξ	NOUN
ejpam-4553	161	6	)	)	PUNCT
ejpam-4553	161	7	on	on	ADP
ejpam-4553	161	8	rn	rn	PROPN
ejpam-4553	161	9	×	×	PROPN
ejpam-4553	161	10	rn	rn	PROPN
ejpam-4553	161	11	belongs	belong	VERB
ejpam-4553	161	12	to	to	ADP
ejpam-4553	161	13	the	the	DET
ejpam-4553	161	14	symbol	symbol	NOUN
ejpam-4553	161	15	class	class	NOUN
ejpam-4553	161	16	cℓ	cℓ	ADP
ejpam-4553	161	17	∗s	∗s	PROPN
ejpam-4553	161	18	m	m	NOUN
ejpam-4553	161	19	1,δ	1,δ	NUM
ejpam-4553	161	20	,	,	PUNCT
ejpam-4553	161	21	δ	δ	PROPN
ejpam-4553	161	22	∈	∈	PROPN
ejpam-4553	162	1	[	[	X
ejpam-4553	162	2	0	0	NUM
ejpam-4553	162	3	,	,	PUNCT
ejpam-4553	162	4	1	1	NUM
ejpam-4553	162	5	]	]	PUNCT
ejpam-4553	162	6	,	,	PUNCT
ejpam-4553	162	7	ℓ	ℓ	INTJ
ejpam-4553	162	8	>	>	X
ejpam-4553	162	9	0	0	PUNCT
ejpam-4553	163	1	if	if	SCONJ
ejpam-4553	163	2	it	it	PRON
ejpam-4553	163	3	is	be	AUX
ejpam-4553	163	4	smooth	smooth	ADJ
ejpam-4553	163	5	in	in	ADP
ejpam-4553	163	6	ξ	ξ	PROPN
ejpam-4553	163	7	and	and	CCONJ
ejpam-4553	163	8	satisfies	satisfy	VERB
ejpam-4553	163	9	the	the	DET
ejpam-4553	163	10	following	follow	VERB
ejpam-4553	163	11	estimates:	estimates:	VERB
ejpam-4553	163	12	∥∥∥∂αξ	∥∥∥∂αξ	ADP
ejpam-4553	163	13	a	a	DET
ejpam-4553	163	14	(	(	PUNCT
ejpam-4553	163	15	·	·	PUNCT
ejpam-4553	163	16	,	,	PUNCT
ejpam-4553	163	17	ξ)∥∥∥	ξ)∥∥∥	PROPN
ejpam-4553	163	18	cℓ	cℓ	ADP
ejpam-4553	163	19	∗	∗	NOUN
ejpam-4553	163	20	≤	≤	NUM
ejpam-4553	163	21	cα	cα	ADP
ejpam-4553	163	22	⟨ξ⟩m−|α|+ℓδ∣∣∣∂αξ	⟨ξ⟩m−|α|+ℓδ∣∣∣∂αξ	PROPN
ejpam-4553	163	23	a(x	a(x	PROPN
ejpam-4553	163	24	,	,	PUNCT
ejpam-4553	163	25	ξ)∣∣∣	ξ)∣∣∣	PROPN
ejpam-4553	163	26	≤	≤	ADJ
ejpam-4553	163	27	c′α	c′α	NOUN
ejpam-4553	164	1	⟨ξ⟩	⟨ξ⟩	ADJ
ejpam-4553	164	2	m−|α|	m−|α|	NOUN
ejpam-4553	164	3	(	(	PUNCT
ejpam-4553	164	4	6	6	NUM
ejpam-4553	164	5	)	)	PUNCT
ejpam-4553	164	6	where	where	SCONJ
ejpam-4553	164	7	⟨ξ⟩	⟨ξ⟩	PROPN
ejpam-4553	164	8	stands	stand	VERB
ejpam-4553	164	9	for	for	ADP
ejpam-4553	164	10	(	(	PUNCT
ejpam-4553	164	11	1	1	NUM
ejpam-4553	164	12	+	+	CCONJ
ejpam-4553	164	13	|ξ|2	|ξ|2	ADJ
ejpam-4553	164	14	)	)	PUNCT
ejpam-4553	164	15	1/2	1/2	NUM
ejpam-4553	164	16	.	.	PUNCT
ejpam-4553	165	1	a	a	DET
ejpam-4553	165	2	pseudo	pseudo	NOUN
ejpam-4553	165	3	-	-	ADJ
ejpam-4553	165	4	differential	differential	ADJ
ejpam-4553	165	5	operator	operator	NOUN
ejpam-4553	165	6	on	on	ADP
ejpam-4553	165	7	s	s	PRON
ejpam-4553	165	8	with	with	ADP
ejpam-4553	165	9	symbol	symbol	NOUN
ejpam-4553	165	10	a	a	DET
ejpam-4553	165	11	∈	∈	NOUN
ejpam-4553	165	12	cℓ	cℓ	ADP
ejpam-4553	165	13	∗s	∗s	PROPN
ejpam-4553	165	14	m	m	PROPN
ejpam-4553	165	15	1,δ	1,δ	NUM
ejpam-4553	165	16	is	be	AUX
ejpam-4553	165	17	defined	define	VERB
ejpam-4553	165	18	by	by	ADP
ejpam-4553	165	19	a(x	a(x	NOUN
ejpam-4553	165	20	,	,	PUNCT
ejpam-4553	165	21	d)f(x	d)f(x	NOUN
ejpam-4553	165	22	)	)	PUNCT
ejpam-4553	165	23	=	=	SYM
ejpam-4553	165	24	1	1	NUM
ejpam-4553	165	25	(	(	PUNCT
ejpam-4553	165	26	2π)n	2π)n	NUM
ejpam-4553	165	27	∫	∫	PROPN
ejpam-4553	165	28	rn	rn	PROPN
ejpam-4553	165	29	eix·ξa(x	eix·ξa(x	PROPN
ejpam-4553	165	30	,	,	PUNCT
ejpam-4553	165	31	ξ)ff(ξ)dξ	ξ)ff(ξ)dξ	NOUN
ejpam-4553	165	32	,	,	PUNCT
ejpam-4553	165	33	f	f	PROPN
ejpam-4553	165	34	∈	∈	PROPN
ejpam-4553	165	35	s.	s.	PROPN
ejpam-4553	165	36	we	we	PRON
ejpam-4553	165	37	write	write	VERB
ejpam-4553	165	38	a(x	a(x	NOUN
ejpam-4553	165	39	,	,	PUNCT
ejpam-4553	165	40	d	d	NOUN
ejpam-4553	165	41	)	)	PUNCT
ejpam-4553	165	42	∈	∈	NOUN
ejpam-4553	165	43	cℓ	cℓ	ADP
ejpam-4553	165	44	∗ops	∗op	NOUN
ejpam-4553	165	45	m	m	VERB
ejpam-4553	165	46	1,δ	1,δ	NUM
ejpam-4553	165	47	if	if	SCONJ
ejpam-4553	165	48	a(x	a(x	NOUN
ejpam-4553	165	49	,	,	PUNCT
ejpam-4553	165	50	ξ	ξ	X
ejpam-4553	165	51	)	)	PUNCT
ejpam-4553	165	52	belongs	belong	VERB
ejpam-4553	165	53	to	to	ADP
ejpam-4553	165	54	the	the	DET
ejpam-4553	165	55	class	class	NOUN
ejpam-4553	165	56	cℓ	cℓ	ADP
ejpam-4553	165	57	∗s	∗s	PROPN
ejpam-4553	165	58	m	m	NOUN
ejpam-4553	165	59	1,δ	1,δ	NUM
ejpam-4553	165	60	.	.	PUNCT
ejpam-4553	166	1	to	to	PART
ejpam-4553	166	2	study	study	VERB
ejpam-4553	166	3	the	the	DET
ejpam-4553	166	4	boundedness	boundedness	NOUN
ejpam-4553	166	5	of	of	ADP
ejpam-4553	166	6	a(x	a(x	NOUN
ejpam-4553	166	7	,	,	PUNCT
ejpam-4553	166	8	d	d	NOUN
ejpam-4553	166	9	)	)	PUNCT
ejpam-4553	166	10	,	,	PUNCT
ejpam-4553	166	11	we	we	PRON
ejpam-4553	166	12	will	will	AUX
ejpam-4553	166	13	resolve	resolve	VERB
ejpam-4553	166	14	its	its	PRON
ejpam-4553	166	15	symbol	symbol	NOUN
ejpam-4553	166	16	a	a	PRON
ejpam-4553	166	17	into	into	ADP
ejpam-4553	166	18	elementary	elementary	ADJ
ejpam-4553	166	19	symbols	symbol	NOUN
ejpam-4553	166	20	.	.	PUNCT
ejpam-4553	167	1	therefore	therefore	ADV
ejpam-4553	167	2	,	,	PUNCT
ejpam-4553	167	3	the	the	DET
ejpam-4553	167	4	operator	operator	NOUN
ejpam-4553	167	5	a(x	a(x	NOUN
ejpam-4553	167	6	,	,	PUNCT
ejpam-4553	167	7	d	d	NOUN
ejpam-4553	167	8	)	)	PUNCT
ejpam-4553	167	9	with	with	ADP
ejpam-4553	167	10	symbol	symbol	NOUN
ejpam-4553	167	11	a	a	PRON
ejpam-4553	167	12	can	can	AUX
ejpam-4553	167	13	be	be	AUX
ejpam-4553	167	14	resolved	resolve	VERB
ejpam-4553	167	15	into	into	ADP
ejpam-4553	167	16	”	"	PUNCT
ejpam-4553	167	17	elementary	elementary	ADJ
ejpam-4553	167	18	operators	operator	NOUN
ejpam-4553	167	19	”	"	PUNCT
ejpam-4553	167	20	ak(x	ak(x	NOUN
ejpam-4553	167	21	,	,	PUNCT
ejpam-4553	167	22	d	d	NOUN
ejpam-4553	167	23	)	)	PUNCT
ejpam-4553	167	24	with	with	ADP
ejpam-4553	167	25	symbols	symbols	PROPN
ejpam-4553	167	26	ak	ak	PROPN
ejpam-4553	167	27	.	.	PROPN
ejpam-4553	168	1	this	this	DET
ejpam-4553	168	2	idea	idea	NOUN
ejpam-4553	168	3	has	have	AUX
ejpam-4553	168	4	been	be	AUX
ejpam-4553	168	5	exploited	exploit	VERB
ejpam-4553	168	6	to	to	PART
ejpam-4553	168	7	establish	establish	VERB
ejpam-4553	168	8	boundedness	boundedness	NOUN
ejpam-4553	168	9	of	of	ADP
ejpam-4553	168	10	pseudo	pseudo	NOUN
ejpam-4553	168	11	-	-	ADJ
ejpam-4553	168	12	differential	differential	ADJ
ejpam-4553	168	13	operators	operator	NOUN
ejpam-4553	168	14	with	with	ADP
ejpam-4553	168	15	non	non	ADJ
ejpam-4553	168	16	-	-	ADJ
ejpam-4553	168	17	regular	regular	ADJ
ejpam-4553	168	18	symbols	symbol	NOUN
ejpam-4553	168	19	in	in	ADP
ejpam-4553	168	20	sobolev	sobolev	PROPN
ejpam-4553	168	21	spaces	space	NOUN
ejpam-4553	168	22	hs	hs	PROPN
ejpam-4553	168	23	,	,	PUNCT
ejpam-4553	168	24	p	p	NOUN
ejpam-4553	168	25	and	and	CCONJ
ejpam-4553	168	26	hölder	hölder	NOUN
ejpam-4553	168	27	-	-	PUNCT
ejpam-4553	168	28	zygmund	zygmund	NOUN
ejpam-4553	168	29	spaces	space	NOUN
ejpam-4553	168	30	cℓ	cℓ	ADP
ejpam-4553	168	31	∗	∗	NOUN
ejpam-4553	168	32	(	(	PUNCT
ejpam-4553	168	33	see	see	VERB
ejpam-4553	168	34	[	[	X
ejpam-4553	168	35	11	11	NUM
ejpam-4553	168	36	]	]	PUNCT
ejpam-4553	168	37	,	,	PUNCT
ejpam-4553	168	38	[	[	X
ejpam-4553	168	39	2	2	NUM
ejpam-4553	168	40	]	]	NUM
ejpam-4553	168	41	)	)	PUNCT
ejpam-4553	168	42	.	.	PUNCT
ejpam-4553	169	1	we	we	PRON
ejpam-4553	169	2	will	will	AUX
ejpam-4553	169	3	proceed	proceed	VERB
ejpam-4553	169	4	in	in	ADP
ejpam-4553	169	5	the	the	DET
ejpam-4553	169	6	same	same	ADJ
ejpam-4553	169	7	way	way	NOUN
ejpam-4553	169	8	with	with	ADP
ejpam-4553	169	9	the	the	DET
ejpam-4553	169	10	adjoint	adjoint	NOUN
ejpam-4553	169	11	operator	operator	NOUN
ejpam-4553	169	12	.	.	PUNCT
ejpam-4553	170	1	definition	definition	NOUN
ejpam-4553	170	2	6	6	NUM
ejpam-4553	170	3	.	.	PUNCT
ejpam-4553	171	1	[	[	X
ejpam-4553	171	2	13	13	NUM
ejpam-4553	171	3	]	]	PUNCT
ejpam-4553	171	4	we	we	PRON
ejpam-4553	171	5	call	call	VERB
ejpam-4553	171	6	elementary	elementary	ADJ
ejpam-4553	171	7	symbol	symbol	NOUN
ejpam-4553	171	8	in	in	ADP
ejpam-4553	171	9	the	the	DET
ejpam-4553	171	10	class	class	NOUN
ejpam-4553	171	11	cℓ	cℓ	ADP
ejpam-4553	171	12	∗s	∗s	PROPN
ejpam-4553	171	13	m	m	NOUN
ejpam-4553	171	14	1,δ	1,δ	NUM
ejpam-4553	171	15	,	,	PUNCT
ejpam-4553	171	16	δ	δ	PROPN
ejpam-4553	171	17	∈	∈	PROPN
ejpam-4553	172	1	[	[	X
ejpam-4553	172	2	0	0	NUM
ejpam-4553	172	3	,	,	PUNCT
ejpam-4553	172	4	1	1	NUM
ejpam-4553	172	5	]	]	PUNCT
ejpam-4553	172	6	,	,	PUNCT
ejpam-4553	172	7	ℓ	ℓ	INTJ
ejpam-4553	172	8	>	>	X
ejpam-4553	172	9	0	0	PUNCT
ejpam-4553	173	1	an	an	DET
ejpam-4553	173	2	expression	expression	NOUN
ejpam-4553	173	3	of	of	ADP
ejpam-4553	173	4	the	the	DET
ejpam-4553	173	5	form	form	NOUN
ejpam-4553	173	6	a(x	a(x	NOUN
ejpam-4553	173	7	,	,	PUNCT
ejpam-4553	173	8	ξ	ξ	NOUN
ejpam-4553	173	9	)	)	PUNCT
ejpam-4553	173	10	=	=	SYM
ejpam-4553	173	11	∑	∑	PUNCT
ejpam-4553	173	12	j≥0	j≥0	PROPN
ejpam-4553	173	13	σj(x)φj(ξ	σj(x)φj(ξ	PROPN
ejpam-4553	173	14	)	)	PUNCT
ejpam-4553	173	15	where	where	SCONJ
ejpam-4553	173	16	φ0	φ0	PROPN
ejpam-4553	173	17	is	be	AUX
ejpam-4553	173	18	smooth	smooth	ADJ
ejpam-4553	173	19	supported	support	VERB
ejpam-4553	173	20	on	on	ADP
ejpam-4553	173	21	the	the	DET
ejpam-4553	173	22	ball	ball	NOUN
ejpam-4553	173	23	b(0	b(0	NOUN
ejpam-4553	173	24	,	,	PUNCT
ejpam-4553	173	25	2	2	NUM
ejpam-4553	173	26	)	)	PUNCT
ejpam-4553	173	27	,	,	PUNCT
ejpam-4553	173	28	φj(ξ	φj(ξ	ADV
ejpam-4553	173	29	)	)	PUNCT
ejpam-4553	173	30	=	=	SYM
ejpam-4553	173	31	φ(2−jξ	φ(2−jξ	NOUN
ejpam-4553	173	32	)	)	PUNCT
ejpam-4553	173	33	and	and	CCONJ
ejpam-4553	173	34	φ	φ	PROPN
ejpam-4553	173	35	∈	∈	PROPN
ejpam-4553	173	36	c∞	c∞	PROPN
ejpam-4553	173	37	0	0	NUM
ejpam-4553	173	38	is	be	AUX
ejpam-4553	173	39	supported	support	VERB
ejpam-4553	173	40	on	on	ADP
ejpam-4553	173	41	the	the	DET
ejpam-4553	173	42	dyadic	dyadic	ADJ
ejpam-4553	173	43	shell	shell	NOUN
ejpam-4553	173	44	d0	d0	NOUN
ejpam-4553	173	45	=	=	SYM
ejpam-4553	173	46	{	{	PUNCT
ejpam-4553	173	47	ξ	ξ	X
ejpam-4553	173	48	∈	∈	PROPN
ejpam-4553	173	49	rn|	rn|	NOUN
ejpam-4553	173	50	1/2	1/2	NUM
ejpam-4553	173	51	≤	≤	NUM
ejpam-4553	173	52	|ξ|	|ξ|	PROPN
ejpam-4553	173	53	≤	≤	PROPN
ejpam-4553	173	54	2	2	NUM
ejpam-4553	173	55	}	}	PUNCT
ejpam-4553	173	56	,	,	PUNCT
ejpam-4553	173	57	while	while	SCONJ
ejpam-4553	173	58	σj	σj	ADJ
ejpam-4553	173	59	is	be	AUX
ejpam-4553	173	60	a	a	DET
ejpam-4553	173	61	uniformly	uniformly	ADV
ejpam-4553	173	62	bounded	bound	VERB
ejpam-4553	173	63	sequence	sequence	NOUN
ejpam-4553	173	64	such	such	ADJ
ejpam-4553	173	65	that	that	SCONJ
ejpam-4553	173	66	∥σj∥cℓ	∥σj∥cℓ	NOUN
ejpam-4553	173	67	∗s	∗s	ADP
ejpam-4553	173	68	m	m	NOUN
ejpam-4553	173	69	1,δ	1,δ	NOUN
ejpam-4553	173	70	≤	≤	NOUN
ejpam-4553	173	71	c2j(m+ℓδ	c2j(m+ℓδ	PROPN
ejpam-4553	173	72	)	)	PUNCT
ejpam-4553	173	73	.	.	PUNCT
ejpam-4553	174	1	example	example	NOUN
ejpam-4553	175	1	1	1	X
ejpam-4553	175	2	.	.	PUNCT
ejpam-4553	176	1	let	let	AUX
ejpam-4553	176	2	{	{	PUNCT
ejpam-4553	176	3	φj	φj	PART
ejpam-4553	176	4	}	}	PUNCT
ejpam-4553	176	5	be	be	AUX
ejpam-4553	176	6	a	a	DET
ejpam-4553	176	7	littlewood	littlewood	NOUN
ejpam-4553	176	8	-	-	PUNCT
ejpam-4553	176	9	paley	paley	NOUN
ejpam-4553	176	10	partition	partition	NOUN
ejpam-4553	176	11	of	of	ADP
ejpam-4553	176	12	unity	unity	NOUN
ejpam-4553	176	13	and	and	CCONJ
ejpam-4553	176	14	{	{	PUNCT
ejpam-4553	176	15	σj	σj	PROPN
ejpam-4553	176	16	}	}	PUNCT
ejpam-4553	176	17	a	a	DET
ejpam-4553	176	18	sequence	sequence	NOUN
ejpam-4553	176	19	uniformly	uniformly	ADV
ejpam-4553	176	20	bounded	bound	VERB
ejpam-4553	176	21	in	in	ADP
ejpam-4553	176	22	cℓ	cℓ	ADP
ejpam-4553	176	23	∗.	∗.	PROPN
ejpam-4553	176	24	set	set	NOUN
ejpam-4553	176	25	a(x	a(x	NOUN
ejpam-4553	176	26	,	,	PUNCT
ejpam-4553	176	27	d)f(x	d)f(x	NOUN
ejpam-4553	176	28	)	)	PUNCT
ejpam-4553	176	29	=	=	PUNCT
ejpam-4553	177	1	∑	∑	PUNCT
ejpam-4553	177	2	j≥0	j≥0	PROPN
ejpam-4553	177	3	σj(2	σj(2	PROPN
ejpam-4553	177	4	jδx)φj(d)f(x	jδx)φj(d)f(x	NOUN
ejpam-4553	177	5	)	)	PUNCT
ejpam-4553	177	6	,	,	PUNCT
ejpam-4553	177	7	f	f	PROPN
ejpam-4553	177	8	∈	∈	PROPN
ejpam-4553	177	9	s	s	VERB
ejpam-4553	177	10	then	then	ADV
ejpam-4553	177	11	a(x	a(x	NOUN
ejpam-4553	177	12	,	,	PUNCT
ejpam-4553	177	13	d	d	NOUN
ejpam-4553	177	14	)	)	PUNCT
ejpam-4553	177	15	∈	∈	NOUN
ejpam-4553	177	16	cℓ	cℓ	ADP
ejpam-4553	177	17	∗ops	∗op	NOUN
ejpam-4553	177	18	0	0	NUM
ejpam-4553	177	19	1,δ	1,δ	NUM
ejpam-4553	177	20	.	.	PUNCT
ejpam-4553	178	1	lemma	lemma	PROPN
ejpam-4553	178	2	6	6	NUM
ejpam-4553	178	3	.	.	PUNCT
ejpam-4553	179	1	[	[	X
ejpam-4553	179	2	13	13	NUM
ejpam-4553	179	3	]	]	PUNCT
ejpam-4553	179	4	let	let	VERB
ejpam-4553	179	5	f	f	PROPN
ejpam-4553	179	6	=	=	PUNCT
ejpam-4553	179	7	∑	∑	PUNCT
ejpam-4553	179	8	j≥0	j≥0	PROPN
ejpam-4553	179	9	fj	fj	PROPN
ejpam-4553	179	10	in	in	ADP
ejpam-4553	179	11	s	s	PROPN
ejpam-4553	179	12	′	′	NOUN
ejpam-4553	179	13	,	,	PUNCT
ejpam-4553	179	14	with	with	ADP
ejpam-4553	179	15	suppf̂j	suppf̂j	PROPN
ejpam-4553	179	16	⊂	⊂	PROPN
ejpam-4553	179	17	b(0	b(0	PROPN
ejpam-4553	179	18	,	,	PUNCT
ejpam-4553	179	19	a2j	a2j	PROPN
ejpam-4553	179	20	)	)	PUNCT
ejpam-4553	179	21	for	for	ADP
ejpam-4553	179	22	some	some	DET
ejpam-4553	179	23	a	a	DET
ejpam-4553	179	24	>	>	X
ejpam-4553	179	25	0	0	NUM
ejpam-4553	179	26	.	.	PUNCT
ejpam-4553	180	1	then	then	ADV
ejpam-4553	180	2	,	,	PUNCT
ejpam-4553	180	3	for	for	ADP
ejpam-4553	180	4	ℓ	ℓ	PROPN
ejpam-4553	180	5	>	>	X
ejpam-4553	180	6	0	0	PROPN
ejpam-4553	180	7	,	,	PUNCT
ejpam-4553	180	8	∥f∥cℓ	∥f∥cℓ	NOUN
ejpam-4553	180	9	∗	∗	X
ejpam-4553	180	10	≤	≤	NUM
ejpam-4553	180	11	c(a	c(a	NOUN
ejpam-4553	180	12	)	)	PUNCT
ejpam-4553	180	13	sup	sup	NOUN
ejpam-4553	180	14	j≥0	j≥0	PROPN
ejpam-4553	180	15	{	{	PUNCT
ejpam-4553	180	16	2jℓ	2jℓ	ADJ
ejpam-4553	180	17	∥fj∥l∞	∥fj∥l∞	NOUN
ejpam-4553	180	18	}	}	PUNCT
ejpam-4553	180	19	.	.	PUNCT
ejpam-4553	181	1	(	(	PUNCT
ejpam-4553	181	2	7	7	X
ejpam-4553	181	3	)	)	PUNCT
ejpam-4553	181	4	mohamed	mohamed	PROPN
ejpam-4553	181	5	congo	congo	PROPN
ejpam-4553	181	6	,	,	PUNCT
ejpam-4553	181	7	m.	m.	PROPN
ejpam-4553	181	8	f.	f.	PROPN
ejpam-4553	181	9	ouedraogo	ouedraogo	PROPN
ejpam-4553	181	10	/	/	SYM
ejpam-4553	181	11	eur	eur	PROPN
ejpam-4553	181	12	.	.	PUNCT
ejpam-4553	182	1	j.	j.	PROPN
ejpam-4553	182	2	pure	pure	PROPN
ejpam-4553	182	3	appl	appl	PROPN
ejpam-4553	182	4	.	.	PROPN
ejpam-4553	182	5	math	math	PROPN
ejpam-4553	182	6	,	,	PUNCT
ejpam-4553	182	7	15	15	NUM
ejpam-4553	182	8	(	(	PUNCT
ejpam-4553	182	9	4	4	NUM
ejpam-4553	182	10	)	)	PUNCT
ejpam-4553	182	11	(	(	PUNCT
ejpam-4553	182	12	2022	2022	NUM
ejpam-4553	182	13	)	)	PUNCT
ejpam-4553	182	14	,	,	PUNCT
ejpam-4553	182	15	1716	1716	NUM
ejpam-4553	182	16	-	-	SYM
ejpam-4553	182	17	1737	1737	NUM
ejpam-4553	182	18	1723	1723	NUM
ejpam-4553	182	19	let	let	VERB
ejpam-4553	182	20	us	we	PRON
ejpam-4553	182	21	establish	establish	VERB
ejpam-4553	182	22	the	the	DET
ejpam-4553	182	23	two	two	NUM
ejpam-4553	182	24	following	follow	VERB
ejpam-4553	182	25	lemmas	lemma	NOUN
ejpam-4553	182	26	which	which	PRON
ejpam-4553	182	27	play	play	VERB
ejpam-4553	182	28	a	a	DET
ejpam-4553	182	29	fundamental	fundamental	ADJ
ejpam-4553	182	30	role	role	NOUN
ejpam-4553	182	31	in	in	ADP
ejpam-4553	182	32	the	the	DET
ejpam-4553	182	33	proof	proof	NOUN
ejpam-4553	182	34	of	of	ADP
ejpam-4553	182	35	the	the	DET
ejpam-4553	182	36	boundedness	boundedness	NOUN
ejpam-4553	182	37	of	of	ADP
ejpam-4553	182	38	pseudo	pseudo	NOUN
ejpam-4553	182	39	-	-	ADJ
ejpam-4553	182	40	differential	differential	ADJ
ejpam-4553	182	41	operators	operator	NOUN
ejpam-4553	182	42	on	on	ADP
ejpam-4553	182	43	n	n	PRON
ejpam-4553	182	44	s	s	PROPN
ejpam-4553	182	45	(	(	PUNCT
ejpam-4553	182	46	·	·	PUNCT
ejpam-4553	182	47	)	)	PUNCT
ejpam-4553	182	48	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	182	49	(	(	PUNCT
ejpam-4553	182	50	·	·	PUNCT
ejpam-4553	182	51	)	)	PUNCT
ejpam-4553	182	52	.	.	PUNCT
ejpam-4553	183	1	lemma	lemma	PROPN
ejpam-4553	183	2	7	7	X
ejpam-4553	183	3	.	.	PUNCT
ejpam-4553	184	1	let	let	VERB
ejpam-4553	184	2	c1	c1	PROPN
ejpam-4553	184	3	,	,	PUNCT
ejpam-4553	184	4	c2	c2	PROPN
ejpam-4553	184	5	>	>	X
ejpam-4553	184	6	0	0	PROPN
ejpam-4553	184	7	,	,	PUNCT
ejpam-4553	184	8	p	p	NOUN
ejpam-4553	184	9	∈	∈	PROPN
ejpam-4553	184	10	p	p	NOUN
ejpam-4553	184	11	log(rn	log(rn	PROPN
ejpam-4553	184	12	)	)	PUNCT
ejpam-4553	184	13	,	,	PUNCT
ejpam-4553	184	14	u	u	NOUN
ejpam-4553	184	15	,	,	PUNCT
ejpam-4553	185	1	q	q	PROPN
ejpam-4553	185	2	∈	∈	PROPN
ejpam-4553	185	3	p	p	NOUN
ejpam-4553	186	1	such	such	ADJ
ejpam-4553	186	2	that	that	SCONJ
ejpam-4553	186	3	,	,	PUNCT
ejpam-4553	186	4	1q	1q	NUM
ejpam-4553	186	5	∈	∈	PROPN
ejpam-4553	186	6	c	c	PROPN
ejpam-4553	186	7	log	log	PROPN
ejpam-4553	186	8	loc	loc	PROPN
ejpam-4553	186	9	with	with	ADP
ejpam-4553	186	10	1	1	NUM
ejpam-4553	186	11	≤	≤	NOUN
ejpam-4553	186	12	p−	p−	NOUN
ejpam-4553	186	13	≤	≤	NUM
ejpam-4553	186	14	p(x	p(x	PROPN
ejpam-4553	186	15	)	)	PUNCT
ejpam-4553	186	16	≤	≤	NUM
ejpam-4553	186	17	u(x	u(x	NOUN
ejpam-4553	186	18	)	)	PUNCT
ejpam-4553	186	19	≤	≤	NOUN
ejpam-4553	186	20	∞.	∞.	PROPN
ejpam-4553	186	21	let	let	VERB
ejpam-4553	186	22	{	{	PUNCT
ejpam-4553	186	23	fk}k∈n0	fk}k∈n0	INTJ
ejpam-4553	186	24	be	be	AUX
ejpam-4553	186	25	a	a	DET
ejpam-4553	186	26	sequence	sequence	NOUN
ejpam-4553	186	27	of	of	ADP
ejpam-4553	186	28	tempered	temper	VERB
ejpam-4553	186	29	distributions	distribution	NOUN
ejpam-4553	187	1	such	such	ADJ
ejpam-4553	187	2	that	that	DET
ejpam-4553	187	3	suppff0	suppff0	PROPN
ejpam-4553	187	4	⊂	⊂	PROPN
ejpam-4553	187	5	b(0	b(0	PROPN
ejpam-4553	187	6	,	,	PUNCT
ejpam-4553	187	7	2c2	2c2	NUM
ejpam-4553	187	8	)	)	PUNCT
ejpam-4553	187	9	and	and	CCONJ
ejpam-4553	187	10	suppffk	suppffk	VERB
ejpam-4553	187	11	⊂	⊂	PRON
ejpam-4553	187	12	{	{	PUNCT
ejpam-4553	187	13	ξ	ξ	PROPN
ejpam-4553	187	14	∈	∈	PROPN
ejpam-4553	187	15	rn	rn	PROPN
ejpam-4553	187	16	:	:	PUNCT
ejpam-4553	187	17	c12	c12	PROPN
ejpam-4553	187	18	k−1	k−1	PROPN
ejpam-4553	187	19	≤	≤	PROPN
ejpam-4553	187	20	|ξ|	|ξ|	PROPN
ejpam-4553	187	21	≤	≤	PROPN
ejpam-4553	187	22	c22	c22	NOUN
ejpam-4553	187	23	k+1	k+1	PROPN
ejpam-4553	187	24	}	}	PUNCT
ejpam-4553	187	25	for	for	ADP
ejpam-4553	187	26	k	k	PROPN
ejpam-4553	187	27	>	>	X
ejpam-4553	187	28	0	0	PROPN
ejpam-4553	187	29	.	.	PUNCT
ejpam-4553	188	1	then	then	ADV
ejpam-4553	188	2	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-4553	188	3	∞∑	∞∑	PROPN
ejpam-4553	188	4	k=0	k=0	PROPN
ejpam-4553	188	5	fk	fk	INTJ
ejpam-4553	188	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	188	7	n	n	PRON
ejpam-4553	188	8	s	s	PROPN
ejpam-4553	188	9	(	(	PUNCT
ejpam-4553	188	10	·	·	PUNCT
ejpam-4553	188	11	)	)	PUNCT
ejpam-4553	188	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	188	13	(	(	PUNCT
ejpam-4553	188	14	·	·	PUNCT
ejpam-4553	188	15	)	)	PUNCT
ejpam-4553	189	1	≲	≲	PROPN
ejpam-4553	189	2	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4553	189	3	)	)	PUNCT
ejpam-4553	189	4	k	k	PROPN
ejpam-4553	189	5	∥∥∥	∥∥∥	PROPN
ejpam-4553	189	6	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	189	7	(	(	PUNCT
ejpam-4553	189	8	·	·	PUNCT
ejpam-4553	189	9	)	)	PUNCT
ejpam-4553	189	10	)	)	PUNCT
ejpam-4553	189	11	.	.	PUNCT
ejpam-4553	190	1	proof	proof	NOUN
ejpam-4553	190	2	.	.	PUNCT
ejpam-4553	191	1	using	use	VERB
ejpam-4553	191	2	(	(	PUNCT
ejpam-4553	191	3	5	5	NUM
ejpam-4553	191	4	)	)	PUNCT
ejpam-4553	191	5	we	we	PRON
ejpam-4553	191	6	have∥∥∥∥∥	have∥∥∥∥∥	VERB
ejpam-4553	191	7	∞∑	∞∑	PROPN
ejpam-4553	191	8	k=0	k=0	PROPN
ejpam-4553	191	9	fk	fk	INTJ
ejpam-4553	191	10	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	191	11	n	n	PRON
ejpam-4553	191	12	s	s	PROPN
ejpam-4553	191	13	(	(	PUNCT
ejpam-4553	191	14	·	·	PUNCT
ejpam-4553	191	15	)	)	PUNCT
ejpam-4553	191	16	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	191	17	(	(	PUNCT
ejpam-4553	191	18	·	·	PUNCT
ejpam-4553	191	19	)	)	PUNCT
ejpam-4553	191	20	=	=	SYM
ejpam-4553	191	21	∥∥∥∥∥φ0(d	∥∥∥∥∥φ0(d	ADJ
ejpam-4553	191	22	)	)	PUNCT
ejpam-4553	191	23	(	(	PUNCT
ejpam-4553	192	1	∞∑	∞∑	DET
ejpam-4553	192	2	k=0	k=0	PROPN
ejpam-4553	192	3	fk	fk	INTJ
ejpam-4553	192	4	)	)	PUNCT
ejpam-4553	192	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	192	6	mp(·),u	mp(·),u	PROPN
ejpam-4553	192	7	(	(	PUNCT
ejpam-4553	192	8	·	·	PUNCT
ejpam-4553	192	9	)	)	PUNCT
ejpam-4553	192	10	+	+	SYM
ejpam-4553	192	11	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	192	12	{	{	PUNCT
ejpam-4553	192	13	2js(·)φj(d	2js(·)φj(d	NUM
ejpam-4553	192	14	)	)	PUNCT
ejpam-4553	192	15	(	(	PUNCT
ejpam-4553	192	16	∞∑	∞∑	X
ejpam-4553	192	17	k=1	k=1	PRON
ejpam-4553	192	18	fk	fk	INTJ
ejpam-4553	192	19	)	)	PUNCT
ejpam-4553	192	20	}	}	PUNCT
ejpam-4553	192	21	j	j	PROPN
ejpam-4553	192	22	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	192	23	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	192	24	(	(	PUNCT
ejpam-4553	192	25	·	·	PUNCT
ejpam-4553	192	26	)	)	PUNCT
ejpam-4553	192	27	)	)	PUNCT
ejpam-4553	192	28	.	.	PUNCT
ejpam-4553	193	1	since	since	SCONJ
ejpam-4553	193	2	φj	φj	PROPN
ejpam-4553	193	3	is	be	AUX
ejpam-4553	193	4	supported	support	VERB
ejpam-4553	193	5	on	on	ADP
ejpam-4553	193	6	the	the	DET
ejpam-4553	193	7	dyadic	dyadic	ADJ
ejpam-4553	193	8	shell	shell	NOUN
ejpam-4553	193	9	dj	dj	NOUN
ejpam-4553	193	10	,	,	PUNCT
ejpam-4553	193	11	while	while	SCONJ
ejpam-4553	193	12	φ0	φ0	PROPN
ejpam-4553	193	13	is	be	AUX
ejpam-4553	193	14	supported	support	VERB
ejpam-4553	193	15	on	on	ADP
ejpam-4553	193	16	the	the	DET
ejpam-4553	193	17	ball	ball	NOUN
ejpam-4553	193	18	b(0	b(0	NOUN
ejpam-4553	193	19	;	;	PUNCT
ejpam-4553	193	20	2	2	NUM
ejpam-4553	193	21	)	)	PUNCT
ejpam-4553	193	22	,	,	PUNCT
ejpam-4553	193	23	there	there	PRON
ejpam-4553	193	24	are	be	VERB
ejpam-4553	193	25	n1	n1	NOUN
ejpam-4553	193	26	,	,	PUNCT
ejpam-4553	193	27	n2	n2	PROPN
ejpam-4553	193	28	∈	∈	PROPN
ejpam-4553	193	29	n0	n0	X
ejpam-4553	194	1	such	such	ADJ
ejpam-4553	194	2	that	that	DET
ejpam-4553	194	3	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-4553	194	4	∞∑	∞∑	NUM
ejpam-4553	194	5	k=0	k=0	PROPN
ejpam-4553	194	6	fk	fk	INTJ
ejpam-4553	194	7	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	194	8	n	n	PRON
ejpam-4553	194	9	s	s	PROPN
ejpam-4553	194	10	(	(	PUNCT
ejpam-4553	194	11	·	·	PUNCT
ejpam-4553	194	12	)	)	PUNCT
ejpam-4553	194	13	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	194	14	(	(	PUNCT
ejpam-4553	194	15	·	·	PUNCT
ejpam-4553	194	16	)	)	PUNCT
ejpam-4553	194	17	=	=	SYM
ejpam-4553	194	18	∥∥∥∥∥φ0(d	∥∥∥∥∥φ0(d	ADJ
ejpam-4553	194	19	)	)	PUNCT
ejpam-4553	194	20	(	(	PUNCT
ejpam-4553	194	21	n1∑	n1∑	PROPN
ejpam-4553	194	22	k=0	k=0	PROPN
ejpam-4553	194	23	fk	fk	INTJ
ejpam-4553	194	24	)	)	PUNCT
ejpam-4553	194	25	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	194	26	mp(·),u	mp(·),u	PROPN
ejpam-4553	194	27	(	(	PUNCT
ejpam-4553	194	28	·	·	PUNCT
ejpam-4553	194	29	)	)	PUNCT
ejpam-4553	194	30	+	+	NUM
ejpam-4553	194	31	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	194	32	2js(·)φj(d	2js(·)φj(d	X
ejpam-4553	194	33	)	)	PUNCT
ejpam-4553	194	34			PROPN
ejpam-4553	194	35	j+n2∑	j+n2∑	PROPN
ejpam-4553	194	36	k	k	NOUN
ejpam-4553	194	37	=	=	NOUN
ejpam-4553	194	38	j−n1	j−n1	NOUN
ejpam-4553	194	39	fk	fk	X
ejpam-4553	194	40			X
ejpam-4553	194	41	j	j	PROPN
ejpam-4553	194	42	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	194	43	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	194	44	(	(	PUNCT
ejpam-4553	194	45	·	·	PUNCT
ejpam-4553	194	46	)	)	PUNCT
ejpam-4553	194	47	)	)	PUNCT
ejpam-4553	195	1	=	=	SYM
ejpam-4553	195	2	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	195	3	n1∑	n1∑	PROPN
ejpam-4553	195	4	k=0	k=0	PROPN
ejpam-4553	195	5	φ̌0	φ̌0	NUM
ejpam-4553	195	6	∗	∗	NOUN
ejpam-4553	195	7	fk	fk	INTJ
ejpam-4553	195	8	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	195	9	mp(·),u	mp(·),u	PROPN
ejpam-4553	195	10	(	(	PUNCT
ejpam-4553	195	11	·	·	PUNCT
ejpam-4553	195	12	)	)	PUNCT
ejpam-4553	195	13	+	+	NUM
ejpam-4553	195	14	∥∥∥∥∥∥	∥∥∥∥∥∥	X
ejpam-4553	196	1	2js	2js	ADJ
ejpam-4553	196	2	(	(	PUNCT
ejpam-4553	196	3	·	·	PUNCT
ejpam-4553	196	4	)	)	PUNCT
ejpam-4553	196	5	j+n2∑	j+n2∑	PROPN
ejpam-4553	197	1	k	k	NOUN
ejpam-4553	197	2	=	=	NOUN
ejpam-4553	197	3	j−n1	j−n1	VERB
ejpam-4553	197	4	φ̌j	φ̌j	NOUN
ejpam-4553	197	5	∗	∗	NOUN
ejpam-4553	197	6	fk	fk	INTJ
ejpam-4553	198	1			PROPN
ejpam-4553	198	2	j	j	PROPN
ejpam-4553	198	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	198	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	198	5	(	(	PUNCT
ejpam-4553	198	6	·	·	PUNCT
ejpam-4553	198	7	)	)	PUNCT
ejpam-4553	198	8	)	)	PUNCT
ejpam-4553	198	9	.	.	PUNCT
ejpam-4553	199	1	let	let	VERB
ejpam-4553	199	2	us	we	PRON
ejpam-4553	199	3	now	now	ADV
ejpam-4553	199	4	estimate	estimate	VERB
ejpam-4553	199	5	these	these	DET
ejpam-4553	199	6	two	two	NUM
ejpam-4553	199	7	terms	term	NOUN
ejpam-4553	199	8	.	.	PUNCT
ejpam-4553	200	1	•	•	NUM
ejpam-4553	200	2	estimation	estimation	NOUN
ejpam-4553	200	3	of	of	ADP
ejpam-4553	200	4	the	the	DET
ejpam-4553	200	5	term	term	NOUN
ejpam-4553	200	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	200	7	n1∑	n1∑	PROPN
ejpam-4553	200	8	k=0	k=0	PROPN
ejpam-4553	200	9	φ̌0	φ̌0	NUM
ejpam-4553	200	10	∗	∗	NOUN
ejpam-4553	200	11	fk	fk	INTJ
ejpam-4553	200	12	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	200	13	mp(·),u	mp(·),u	PROPN
ejpam-4553	200	14	(	(	PUNCT
ejpam-4553	200	15	·	·	PUNCT
ejpam-4553	200	16	)	)	PUNCT
ejpam-4553	200	17	one	one	NOUN
ejpam-4553	200	18	has	have	VERB
ejpam-4553	200	19	suppf	suppf	NOUN
ejpam-4553	200	20	(	(	PUNCT
ejpam-4553	200	21	φ̌0	φ̌0	X
ejpam-4553	200	22	∗	∗	NUM
ejpam-4553	200	23	fk	fk	INTJ
ejpam-4553	200	24	)	)	PUNCT
ejpam-4553	200	25	⊂	⊂	PROPN
ejpam-4553	200	26	{	{	PUNCT
ejpam-4553	200	27	ξ	ξ	PROPN
ejpam-4553	200	28	∈	∈	PROPN
ejpam-4553	200	29	rn	rn	PROPN
ejpam-4553	200	30	:	:	PUNCT
ejpam-4553	200	31	|ξ|	|ξ|	VERB
ejpam-4553	200	32	≤	≤	NOUN
ejpam-4553	200	33	2	2	NUM
ejpam-4553	200	34	}	}	PUNCT
ejpam-4553	200	35	.	.	PUNCT
ejpam-4553	201	1	then	then	ADV
ejpam-4553	201	2	by	by	ADP
ejpam-4553	201	3	lemma	lemma	PROPN
ejpam-4553	201	4	2	2	NUM
ejpam-4553	201	5	,	,	PUNCT
ejpam-4553	201	6	|φ̌0	|φ̌0	PROPN
ejpam-4553	201	7	∗	∗	NOUN
ejpam-4553	201	8	fk|	fk|	ADJ
ejpam-4553	201	9	≲	≲	PROPN
ejpam-4553	201	10	|fk|	|fk|	PROPN
ejpam-4553	201	11	.	.	PUNCT
ejpam-4553	202	1	it	it	PRON
ejpam-4553	202	2	follows	follow	VERB
ejpam-4553	202	3	that∥∥∥∥∥	that∥∥∥∥∥	PROPN
ejpam-4553	202	4	n1∑	n1∑	PROPN
ejpam-4553	202	5	k=0	k=0	PROPN
ejpam-4553	202	6	φ̌0	φ̌0	NUM
ejpam-4553	202	7	∗	∗	NOUN
ejpam-4553	202	8	fk	fk	INTJ
ejpam-4553	202	9	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	202	10	mp(·),u	mp(·),u	PROPN
ejpam-4553	202	11	(	(	PUNCT
ejpam-4553	202	12	·	·	PUNCT
ejpam-4553	202	13	)	)	PUNCT
ejpam-4553	203	1	≲	≲	PROPN
ejpam-4553	203	2	n1∑	n1∑	PROPN
ejpam-4553	203	3	k=0	k=0	PROPN
ejpam-4553	203	4	∥fk∥mp(·),u	∥fk∥mp(·),u	PROPN
ejpam-4553	203	5	(	(	PUNCT
ejpam-4553	203	6	·	·	PUNCT
ejpam-4553	203	7	)	)	PUNCT
ejpam-4553	203	8	mohamed	mohamed	PROPN
ejpam-4553	203	9	congo	congo	PROPN
ejpam-4553	203	10	,	,	PUNCT
ejpam-4553	203	11	m.	m.	PROPN
ejpam-4553	203	12	f.	f.	PROPN
ejpam-4553	203	13	ouedraogo	ouedraogo	PROPN
ejpam-4553	203	14	/	/	SYM
ejpam-4553	203	15	eur	eur	PROPN
ejpam-4553	203	16	.	.	PUNCT
ejpam-4553	204	1	j.	j.	PROPN
ejpam-4553	204	2	pure	pure	PROPN
ejpam-4553	204	3	appl	appl	PROPN
ejpam-4553	204	4	.	.	PROPN
ejpam-4553	204	5	math	math	PROPN
ejpam-4553	204	6	,	,	PUNCT
ejpam-4553	204	7	15	15	NUM
ejpam-4553	204	8	(	(	PUNCT
ejpam-4553	204	9	4	4	NUM
ejpam-4553	204	10	)	)	PUNCT
ejpam-4553	204	11	(	(	PUNCT
ejpam-4553	204	12	2022	2022	NUM
ejpam-4553	204	13	)	)	PUNCT
ejpam-4553	204	14	,	,	PUNCT
ejpam-4553	204	15	1716	1716	NUM
ejpam-4553	204	16	-	-	SYM
ejpam-4553	204	17	1737	1737	NUM
ejpam-4553	204	18	1724	1724	NUM
ejpam-4553	204	19	=	=	PUNCT
ejpam-4553	204	20	n1∑	n1∑	PROPN
ejpam-4553	204	21	k=0	k=0	PROPN
ejpam-4553	204	22	∥(0	∥(0	VERB
ejpam-4553	204	23	,	,	PUNCT
ejpam-4553	204	24	.	.	PUNCT
ejpam-4553	204	25	.	.	PUNCT
ejpam-4553	204	26	.	.	PUNCT
ejpam-4553	205	1	,	,	PUNCT
ejpam-4553	205	2	fk	fk	INTJ
ejpam-4553	205	3	,	,	PUNCT
ejpam-4553	205	4	0	0	NUM
ejpam-4553	205	5	,	,	PUNCT
ejpam-4553	205	6	.	.	PUNCT
ejpam-4553	205	7	.	.	PUNCT
ejpam-4553	206	1	.)∥ℓq(·)(mp(·),u	.)∥ℓq(·)(mp(·),u	PROPN
ejpam-4553	206	2	(	(	PUNCT
ejpam-4553	206	3	·	·	PUNCT
ejpam-4553	206	4	)	)	PUNCT
ejpam-4553	206	5	)	)	PUNCT
ejpam-4553	207	1	by	by	ADP
ejpam-4553	207	2	proposition	proposition	NOUN
ejpam-4553	207	3	1	1	NUM
ejpam-4553	207	4	≲	≲	PROPN
ejpam-4553	207	5	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	PROPN
ejpam-4553	207	6	)	)	PUNCT
ejpam-4553	207	7	k	k	PROPN
ejpam-4553	207	8	∥∥∥	∥∥∥	PROPN
ejpam-4553	207	9	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	207	10	(	(	PUNCT
ejpam-4553	207	11	·	·	PUNCT
ejpam-4553	207	12	)	)	PUNCT
ejpam-4553	207	13	)	)	PUNCT
ejpam-4553	207	14	.	.	PUNCT
ejpam-4553	208	1	•	•	NUM
ejpam-4553	208	2	estimation	estimation	NOUN
ejpam-4553	208	3	of	of	ADP
ejpam-4553	208	4	the	the	DET
ejpam-4553	208	5	term	term	NOUN
ejpam-4553	208	6	∥∥∥∥∥∥	∥∥∥∥∥∥	SYM
ejpam-4553	209	1	2js	2js	PROPN
ejpam-4553	209	2	(	(	PUNCT
ejpam-4553	209	3	·	·	PUNCT
ejpam-4553	209	4	)	)	PUNCT
ejpam-4553	210	1	j+n∑	j+n∑	PROPN
ejpam-4553	210	2	k	k	X
ejpam-4553	211	1	=	=	NOUN
ejpam-4553	211	2	j−n	j−n	PROPN
ejpam-4553	211	3	φ̌j	φ̌j	PROPN
ejpam-4553	211	4	∗	∗	NOUN
ejpam-4553	211	5	fk	fk	INTJ
ejpam-4553	211	6			PROPN
ejpam-4553	211	7	j	j	PROPN
ejpam-4553	211	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	211	9	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	211	10	(	(	PUNCT
ejpam-4553	211	11	·	·	PUNCT
ejpam-4553	211	12	)	)	PUNCT
ejpam-4553	211	13	)	)	PUNCT
ejpam-4553	211	14	.	.	PUNCT
ejpam-4553	212	1	since	since	SCONJ
ejpam-4553	212	2	φ̌j	φ̌j	NOUN
ejpam-4553	212	3	∗	∗	NOUN
ejpam-4553	212	4	fk	fk	INTJ
ejpam-4553	213	1	∈	∈	PROPN
ejpam-4553	213	2	s	s	PART
ejpam-4553	213	3	′	′	NOUN
ejpam-4553	213	4	and	and	CCONJ
ejpam-4553	213	5	suppf	suppf	NOUN
ejpam-4553	213	6	(	(	PUNCT
ejpam-4553	213	7	φ̌j	φ̌j	NOUN
ejpam-4553	213	8	∗	∗	X
ejpam-4553	213	9	fk	fk	INTJ
ejpam-4553	213	10	)	)	PUNCT
ejpam-4553	213	11	⊂	⊂	PROPN
ejpam-4553	213	12	{	{	PUNCT
ejpam-4553	213	13	ξ	ξ	PROPN
ejpam-4553	213	14	∈	∈	PROPN
ejpam-4553	213	15	rn	rn	PROPN
ejpam-4553	213	16	:	:	PUNCT
ejpam-4553	213	17	|ξ|	|ξ|	VERB
ejpam-4553	213	18	≤	≤	ADJ
ejpam-4553	213	19	2j+1	2j+1	PROPN
ejpam-4553	213	20	}	}	PUNCT
ejpam-4553	213	21	,	,	PUNCT
ejpam-4553	213	22	then	then	ADV
ejpam-4553	213	23	by	by	ADP
ejpam-4553	213	24	lemma	lemma	PROPN
ejpam-4553	213	25	2	2	NUM
ejpam-4553	213	26	,	,	PUNCT
ejpam-4553	213	27	|φ̌j	|φ̌j	PROPN
ejpam-4553	213	28	∗	∗	NOUN
ejpam-4553	213	29	fk|	fk|	PROPN
ejpam-4553	213	30	≲	≲	PROPN
ejpam-4553	213	31	(	(	PUNCT
ejpam-4553	213	32	ηj	ηj	NOUN
ejpam-4553	213	33	,	,	PUNCT
ejpam-4553	213	34	m	m	NOUN
ejpam-4553	213	35	∗	∗	NOUN
ejpam-4553	213	36	|fk|t	|fk|t	PROPN
ejpam-4553	213	37	)	)	PUNCT
ejpam-4553	213	38	1	1	NUM
ejpam-4553	213	39	/	/	SYM
ejpam-4553	213	40	t	t	PROPN
ejpam-4553	213	41	for	for	ADP
ejpam-4553	213	42	any	any	DET
ejpam-4553	213	43	m	m	NOUN
ejpam-4553	213	44	>	>	X
ejpam-4553	213	45	n+	n+	NUM
ejpam-4553	213	46	clog(s	clog(s	NOUN
ejpam-4553	213	47	)	)	PUNCT
ejpam-4553	213	48	+	+	CCONJ
ejpam-4553	213	49	clog	clog	PROPN
ejpam-4553	213	50	(	(	PUNCT
ejpam-4553	213	51	1	1	NUM
ejpam-4553	213	52	q	q	NOUN
ejpam-4553	213	53	)	)	PUNCT
ejpam-4553	214	1	+	+	CCONJ
ejpam-4553	214	2	nmax	nmax	ADJ
ejpam-4553	214	3	{	{	PUNCT
ejpam-4553	214	4	0	0	NUM
ejpam-4553	214	5	,	,	PUNCT
ejpam-4553	214	6	supx∈rn	supx∈rn	PUNCT
ejpam-4553	214	7	(	(	PUNCT
ejpam-4553	214	8	1	1	NUM
ejpam-4553	214	9	p(x	p(x	NOUN
ejpam-4553	214	10	)	)	PUNCT
ejpam-4553	214	11	−	−	PROPN
ejpam-4553	214	12	1	1	NUM
ejpam-4553	214	13	u(x	u(x	NOUN
ejpam-4553	214	14	)	)	PUNCT
ejpam-4553	214	15	)	)	PUNCT
ejpam-4553	215	1	−	−	PROPN
ejpam-4553	215	2	1	1	NUM
ejpam-4553	215	3	p∞	p∞	PROPN
ejpam-4553	215	4	}	}	PUNCT
ejpam-4553	215	5	and	and	CCONJ
ejpam-4553	215	6	any	any	DET
ejpam-4553	215	7	t	t	NOUN
ejpam-4553	215	8	>	>	X
ejpam-4553	215	9	0	0	NUM
ejpam-4553	215	10	.	.	PUNCT
ejpam-4553	216	1	thus	thus	ADV
ejpam-4553	216	2	with	with	ADP
ejpam-4553	216	3	t	t	PROPN
ejpam-4553	216	4	=	=	SYM
ejpam-4553	216	5	1,∥∥∥∥∥∥	1,∥∥∥∥∥∥	PROPN
ejpam-4553	216	6	2js	2js	PROPN
ejpam-4553	216	7	(	(	PUNCT
ejpam-4553	216	8	·	·	PUNCT
ejpam-4553	216	9	)	)	PUNCT
ejpam-4553	216	10	j+n2∑	j+n2∑	PROPN
ejpam-4553	217	1	k	k	NOUN
ejpam-4553	217	2	=	=	NOUN
ejpam-4553	217	3	j−n1	j−n1	VERB
ejpam-4553	217	4	φ̌j	φ̌j	NOUN
ejpam-4553	217	5	∗	∗	NOUN
ejpam-4553	217	6	fk	fk	INTJ
ejpam-4553	218	1			PROPN
ejpam-4553	218	2	j	j	PROPN
ejpam-4553	218	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	218	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	218	5	(	(	PUNCT
ejpam-4553	218	6	·	·	PUNCT
ejpam-4553	218	7	)	)	PUNCT
ejpam-4553	218	8	)	)	PUNCT
ejpam-4553	219	1	≲	≲	PROPN
ejpam-4553	219	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	219	3			PUNCT
ejpam-4553	219	4	j+n2∑	j+n2∑	NOUN
ejpam-4553	219	5	k	k	NOUN
ejpam-4553	219	6	=	=	NOUN
ejpam-4553	219	7	j−n1	j−n1	NOUN
ejpam-4553	219	8	2js	2js	NOUN
ejpam-4553	219	9	(	(	PUNCT
ejpam-4553	219	10	·	·	PUNCT
ejpam-4553	219	11	)	)	PUNCT
ejpam-4553	219	12	(	(	PUNCT
ejpam-4553	219	13	ηj	ηj	NOUN
ejpam-4553	219	14	,	,	PUNCT
ejpam-4553	219	15	m	m	PROPN
ejpam-4553	219	16	∗	∗	NOUN
ejpam-4553	219	17	|fk|	|fk|	PROPN
ejpam-4553	219	18	)	)	PUNCT
ejpam-4553	220	1			PROPN
ejpam-4553	220	2	j	j	PROPN
ejpam-4553	220	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	220	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	220	5	(	(	PUNCT
ejpam-4553	220	6	·	·	PUNCT
ejpam-4553	220	7	)	)	PUNCT
ejpam-4553	220	8	)	)	PUNCT
ejpam-4553	220	9	.	.	PUNCT
ejpam-4553	221	1	by	by	ADP
ejpam-4553	221	2	lemma	lemma	PROPN
ejpam-4553	221	3	1	1	NUM
ejpam-4553	221	4	,	,	PUNCT
ejpam-4553	221	5	we	we	PRON
ejpam-4553	221	6	can	can	AUX
ejpam-4553	221	7	move	move	VERB
ejpam-4553	221	8	2js	2js	NOUN
ejpam-4553	221	9	(	(	PUNCT
ejpam-4553	221	10	·	·	PUNCT
ejpam-4553	221	11	)	)	PUNCT
ejpam-4553	221	12	inside	inside	ADP
ejpam-4553	221	13	the	the	DET
ejpam-4553	221	14	convolution	convolution	NOUN
ejpam-4553	221	15	and	and	CCONJ
ejpam-4553	221	16	get	get	VERB
ejpam-4553	221	17	2js	2js	NOUN
ejpam-4553	221	18	(	(	PUNCT
ejpam-4553	221	19	·	·	PUNCT
ejpam-4553	221	20	)	)	PUNCT
ejpam-4553	221	21	(	(	PUNCT
ejpam-4553	221	22	ηj	ηj	NOUN
ejpam-4553	221	23	,	,	PUNCT
ejpam-4553	221	24	m	m	PROPN
ejpam-4553	221	25	∗	∗	NOUN
ejpam-4553	221	26	|fk|	|fk|	PROPN
ejpam-4553	221	27	)	)	PUNCT
ejpam-4553	221	28	≲	≲	PROPN
ejpam-4553	221	29	ηj	ηj	PROPN
ejpam-4553	221	30	,	,	PUNCT
ejpam-4553	221	31	m−clog(s	m−clog(s	PROPN
ejpam-4553	221	32	)	)	PUNCT
ejpam-4553	221	33	∗	∗	NOUN
ejpam-4553	221	34	2	2	NUM
ejpam-4553	221	35	js(·)|fk|	js(·)|fk|	PROPN
ejpam-4553	221	36	.	.	PUNCT
ejpam-4553	222	1	let	let	VERB
ejpam-4553	222	2	us	we	PRON
ejpam-4553	222	3	notice	notice	VERB
ejpam-4553	222	4	that	that	SCONJ
ejpam-4553	222	5	if	if	SCONJ
ejpam-4553	222	6	m	m	PROPN
ejpam-4553	222	7	>	>	X
ejpam-4553	222	8	n+clog(s)+clog	n+clog(s)+clog	PROPN
ejpam-4553	222	9	(	(	PUNCT
ejpam-4553	222	10	1	1	NUM
ejpam-4553	222	11	q	q	NOUN
ejpam-4553	222	12	)	)	PUNCT
ejpam-4553	222	13	+	+	ADJ
ejpam-4553	222	14	nmax	nmax	ADJ
ejpam-4553	222	15	{	{	PUNCT
ejpam-4553	222	16	0	0	NUM
ejpam-4553	222	17	,	,	PUNCT
ejpam-4553	222	18	supx∈rn	supx∈rn	PUNCT
ejpam-4553	222	19	(	(	PUNCT
ejpam-4553	222	20	1	1	NUM
ejpam-4553	222	21	p(x	p(x	NOUN
ejpam-4553	222	22	)	)	PUNCT
ejpam-4553	222	23	−	−	PROPN
ejpam-4553	222	24	1	1	NUM
ejpam-4553	222	25	u(x	u(x	NOUN
ejpam-4553	222	26	)	)	PUNCT
ejpam-4553	222	27	)	)	PUNCT
ejpam-4553	222	28	−	−	PROPN
ejpam-4553	222	29	1	1	NUM
ejpam-4553	222	30	p∞	p∞	PROPN
ejpam-4553	222	31	}	}	PUNCT
ejpam-4553	222	32	then	then	ADV
ejpam-4553	222	33	m−	m−	PROPN
ejpam-4553	222	34	clog(s	clog(s	PROPN
ejpam-4553	222	35	)	)	PUNCT
ejpam-4553	222	36	verifies	verifie	NOUN
ejpam-4553	222	37	the	the	DET
ejpam-4553	222	38	hypothesis	hypothesis	NOUN
ejpam-4553	222	39	of	of	ADP
ejpam-4553	222	40	the	the	DET
ejpam-4553	222	41	lemma	lemma	PROPN
ejpam-4553	222	42	3	3	NUM
ejpam-4553	222	43	.	.	PUNCT
ejpam-4553	223	1	therefore∥∥∥∥∥∥	therefore∥∥∥∥∥∥	VERB
ejpam-4553	223	2	2js	2js	PROPN
ejpam-4553	223	3	(	(	PUNCT
ejpam-4553	223	4	·	·	PUNCT
ejpam-4553	223	5	)	)	PUNCT
ejpam-4553	223	6	j+n2∑	j+n2∑	PROPN
ejpam-4553	224	1	k	k	NOUN
ejpam-4553	224	2	=	=	NOUN
ejpam-4553	224	3	j−n1	j−n1	VERB
ejpam-4553	224	4	φ̌j	φ̌j	NOUN
ejpam-4553	224	5	∗	∗	NOUN
ejpam-4553	224	6	fk	fk	INTJ
ejpam-4553	225	1			PROPN
ejpam-4553	225	2	j	j	PROPN
ejpam-4553	225	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	225	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	225	5	(	(	PUNCT
ejpam-4553	225	6	·	·	PUNCT
ejpam-4553	225	7	)	)	PUNCT
ejpam-4553	225	8	)	)	PUNCT
ejpam-4553	226	1	≲	≲	PROPN
ejpam-4553	226	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	226	3			PUNCT
ejpam-4553	226	4	j+n2∑	j+n2∑	NOUN
ejpam-4553	226	5	k	k	NOUN
ejpam-4553	226	6	=	=	NOUN
ejpam-4553	226	7	j−n1	j−n1	NOUN
ejpam-4553	226	8	(	(	PUNCT
ejpam-4553	226	9	ηj	ηj	NOUN
ejpam-4553	226	10	,	,	PUNCT
ejpam-4553	226	11	m−clog(s	m−clog(s	PROPN
ejpam-4553	226	12	)	)	PUNCT
ejpam-4553	226	13	∗	∗	NOUN
ejpam-4553	226	14	2	2	NUM
ejpam-4553	226	15	js(·)|fk|	js(·)|fk|	PROPN
ejpam-4553	226	16	)	)	PUNCT
ejpam-4553	227	1			PROPN
ejpam-4553	227	2	j	j	PROPN
ejpam-4553	227	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	227	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	227	5	(	(	PUNCT
ejpam-4553	227	6	·	·	PUNCT
ejpam-4553	227	7	)	)	PUNCT
ejpam-4553	227	8	)	)	PUNCT
ejpam-4553	227	9	≤	≤	NUM
ejpam-4553	227	10	j+n2∑	j+n2∑	PROPN
ejpam-4553	228	1	k	k	NOUN
ejpam-4553	228	2	=	=	NOUN
ejpam-4553	228	3	j−n1	j−n1	NOUN
ejpam-4553	228	4	∥∥∥∥{(ηj	∥∥∥∥{(ηj	NOUN
ejpam-4553	228	5	,	,	PUNCT
ejpam-4553	228	6	m−clog(s	m−clog(s	PROPN
ejpam-4553	228	7	)	)	PUNCT
ejpam-4553	228	8	∗	∗	NOUN
ejpam-4553	228	9	2	2	NUM
ejpam-4553	228	10	js(·)|fk|	js(·)|fk|	PROPN
ejpam-4553	228	11	)	)	PUNCT
ejpam-4553	228	12	}	}	PUNCT
ejpam-4553	228	13	j	j	PROPN
ejpam-4553	228	14	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4553	228	15	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	228	16	(	(	PUNCT
ejpam-4553	228	17	·	·	PUNCT
ejpam-4553	228	18	)	)	PUNCT
ejpam-4553	228	19	)	)	PUNCT
ejpam-4553	228	20	.	.	PUNCT
ejpam-4553	229	1	by	by	ADP
ejpam-4553	229	2	lemma	lemma	PROPN
ejpam-4553	229	3	3	3	NUM
ejpam-4553	229	4	,	,	PUNCT
ejpam-4553	229	5	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	230	1	2js	2js	PROPN
ejpam-4553	230	2	(	(	PUNCT
ejpam-4553	230	3	·	·	PUNCT
ejpam-4553	230	4	)	)	PUNCT
ejpam-4553	230	5	j+n2∑	j+n2∑	PROPN
ejpam-4553	231	1	k	k	NOUN
ejpam-4553	231	2	=	=	NOUN
ejpam-4553	231	3	j−n1	j−n1	VERB
ejpam-4553	231	4	φ̌j	φ̌j	NOUN
ejpam-4553	231	5	∗	∗	NOUN
ejpam-4553	231	6	fk	fk	INTJ
ejpam-4553	232	1			PROPN
ejpam-4553	232	2	j	j	PROPN
ejpam-4553	232	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	232	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	232	5	(	(	PUNCT
ejpam-4553	232	6	·	·	PUNCT
ejpam-4553	232	7	)	)	PUNCT
ejpam-4553	232	8	)	)	PUNCT
ejpam-4553	233	1	≲	≲	PROPN
ejpam-4553	233	2	n1+n2∑	n1+n2∑	AUX
ejpam-4553	233	3	k=0	k=0	PROPN
ejpam-4553	233	4	∥∥∥∥(2js(·)fj+k−n1	∥∥∥∥(2js(·)fj+k−n1	PROPN
ejpam-4553	233	5	)	)	PUNCT
ejpam-4553	233	6	j	j	PROPN
ejpam-4553	233	7	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4553	233	8	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	233	9	(	(	PUNCT
ejpam-4553	233	10	·	·	PUNCT
ejpam-4553	233	11	)	)	PUNCT
ejpam-4553	233	12	)	)	PUNCT
ejpam-4553	234	1	≲	≲	PROPN
ejpam-4553	234	2	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4553	234	3	)	)	PUNCT
ejpam-4553	234	4	k	k	PROPN
ejpam-4553	234	5	∥∥∥	∥∥∥	PROPN
ejpam-4553	234	6	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	234	7	(	(	PUNCT
ejpam-4553	234	8	·	·	PUNCT
ejpam-4553	234	9	)	)	PUNCT
ejpam-4553	234	10	)	)	PUNCT
ejpam-4553	234	11	.	.	PUNCT
ejpam-4553	235	1	the	the	DET
ejpam-4553	235	2	two	two	NUM
ejpam-4553	235	3	estimations	estimation	NOUN
ejpam-4553	235	4	yield	yield	VERB
ejpam-4553	235	5	the	the	DET
ejpam-4553	235	6	desired	desire	VERB
ejpam-4553	235	7	estimate	estimate	NOUN
ejpam-4553	235	8	.	.	PUNCT
ejpam-4553	236	1	□	□	PUNCT
ejpam-4553	236	2	mohamed	mohamed	ADJ
ejpam-4553	236	3	congo	congo	PROPN
ejpam-4553	236	4	,	,	PUNCT
ejpam-4553	236	5	m.	m.	PROPN
ejpam-4553	236	6	f.	f.	PROPN
ejpam-4553	236	7	ouedraogo	ouedraogo	PROPN
ejpam-4553	236	8	/	/	SYM
ejpam-4553	236	9	eur	eur	PROPN
ejpam-4553	236	10	.	.	PUNCT
ejpam-4553	237	1	j.	j.	PROPN
ejpam-4553	237	2	pure	pure	PROPN
ejpam-4553	237	3	appl	appl	PROPN
ejpam-4553	237	4	.	.	PROPN
ejpam-4553	237	5	math	math	PROPN
ejpam-4553	237	6	,	,	PUNCT
ejpam-4553	237	7	15	15	NUM
ejpam-4553	237	8	(	(	PUNCT
ejpam-4553	237	9	4	4	NUM
ejpam-4553	237	10	)	)	PUNCT
ejpam-4553	237	11	(	(	PUNCT
ejpam-4553	237	12	2022	2022	NUM
ejpam-4553	237	13	)	)	PUNCT
ejpam-4553	237	14	,	,	PUNCT
ejpam-4553	237	15	1716	1716	NUM
ejpam-4553	237	16	-	-	SYM
ejpam-4553	237	17	1737	1737	NUM
ejpam-4553	237	18	1725	1725	NUM
ejpam-4553	237	19	lemma	lemma	PROPN
ejpam-4553	237	20	8	8	NUM
ejpam-4553	237	21	.	.	PUNCT
ejpam-4553	238	1	let	let	VERB
ejpam-4553	238	2	c	c	PROPN
ejpam-4553	238	3	>	>	X
ejpam-4553	238	4	0	0	PROPN
ejpam-4553	238	5	,	,	PUNCT
ejpam-4553	238	6	p	p	NOUN
ejpam-4553	238	7	∈	∈	PROPN
ejpam-4553	238	8	p	p	NOUN
ejpam-4553	238	9	log(rn	log(rn	PROPN
ejpam-4553	238	10	)	)	PUNCT
ejpam-4553	238	11	and	and	CCONJ
ejpam-4553	238	12	u	u	NOUN
ejpam-4553	238	13	,	,	PUNCT
ejpam-4553	238	14	q	q	PROPN
ejpam-4553	239	1	∈	∈	PROPN
ejpam-4553	239	2	p	p	NOUN
ejpam-4553	239	3	such	such	ADJ
ejpam-4553	239	4	that	that	SCONJ
ejpam-4553	239	5	1	1	NUM
ejpam-4553	239	6	q	q	NOUN
ejpam-4553	239	7	∈	∈	PROPN
ejpam-4553	239	8	c	c	PROPN
ejpam-4553	239	9	log	log	PROPN
ejpam-4553	239	10	loc	loc	NOUN
ejpam-4553	239	11	with	with	ADP
ejpam-4553	239	12	1	1	NUM
ejpam-4553	239	13	≤	≤	NOUN
ejpam-4553	239	14	p−	p−	NOUN
ejpam-4553	239	15	≤	≤	NUM
ejpam-4553	239	16	p(x	p(x	PROPN
ejpam-4553	239	17	)	)	PUNCT
ejpam-4553	239	18	≤	≤	NUM
ejpam-4553	239	19	u(x	u(x	NOUN
ejpam-4553	239	20	)	)	PUNCT
ejpam-4553	239	21	≤	≤	NOUN
ejpam-4553	239	22	∞.	∞.	PROPN
ejpam-4553	239	23	let	let	VERB
ejpam-4553	239	24	s	s	PRON
ejpam-4553	239	25	∈	∈	VERB
ejpam-4553	239	26	c	c	PROPN
ejpam-4553	239	27	log	log	PROPN
ejpam-4553	239	28	loc	loc	PROPN
ejpam-4553	239	29	such	such	ADJ
ejpam-4553	239	30	that	that	SCONJ
ejpam-4553	239	31	s−	s−	PROPN
ejpam-4553	239	32	>	>	X
ejpam-4553	239	33	0	0	X
ejpam-4553	239	34	.	.	PUNCT
ejpam-4553	240	1	let	let	VERB
ejpam-4553	240	2	{	{	PUNCT
ejpam-4553	240	3	fk}k∈n0	fk}k∈n0	INTJ
ejpam-4553	240	4	be	be	AUX
ejpam-4553	240	5	a	a	DET
ejpam-4553	240	6	sequence	sequence	NOUN
ejpam-4553	240	7	of	of	ADP
ejpam-4553	240	8	tempered	temper	VERB
ejpam-4553	240	9	distributions	distribution	NOUN
ejpam-4553	240	10	such	such	ADJ
ejpam-4553	240	11	that	that	PRON
ejpam-4553	240	12	suppffk	suppffk	VERB
ejpam-4553	240	13	⊂	⊂	PRON
ejpam-4553	240	14	{	{	PUNCT
ejpam-4553	240	15	ξ	ξ	PROPN
ejpam-4553	240	16	∈	∈	PROPN
ejpam-4553	240	17	rn	rn	PROPN
ejpam-4553	240	18	:	:	PUNCT
ejpam-4553	240	19	|ξ|	|ξ|	VERB
ejpam-4553	240	20	≤	≤	NOUN
ejpam-4553	240	21	c2k+1	c2k+1	VERB
ejpam-4553	240	22	}	}	PUNCT
ejpam-4553	240	23	.	.	PUNCT
ejpam-4553	241	1	then	then	ADV
ejpam-4553	241	2	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-4553	241	3	∞∑	∞∑	PROPN
ejpam-4553	241	4	k=0	k=0	PROPN
ejpam-4553	241	5	fk	fk	INTJ
ejpam-4553	241	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	241	7	n	n	PRON
ejpam-4553	241	8	s	s	PROPN
ejpam-4553	241	9	(	(	PUNCT
ejpam-4553	241	10	·	·	PUNCT
ejpam-4553	241	11	)	)	PUNCT
ejpam-4553	241	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	241	13	(	(	PUNCT
ejpam-4553	241	14	·	·	PUNCT
ejpam-4553	241	15	)	)	PUNCT
ejpam-4553	241	16	≲	≲	PROPN
ejpam-4553	241	17	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4553	241	18	)	)	PUNCT
ejpam-4553	241	19	k	k	PROPN
ejpam-4553	241	20	∥∥∥	∥∥∥	PROPN
ejpam-4553	241	21	ℓq(mp(·),u	ℓq(mp(·),u	PROPN
ejpam-4553	241	22	(	(	PUNCT
ejpam-4553	241	23	·	·	PUNCT
ejpam-4553	241	24	)	)	PUNCT
ejpam-4553	241	25	)	)	PUNCT
ejpam-4553	241	26	.	.	PUNCT
ejpam-4553	242	1	proof	proof	NOUN
ejpam-4553	242	2	.	.	PUNCT
ejpam-4553	243	1	using	use	VERB
ejpam-4553	243	2	the	the	DET
ejpam-4553	243	3	hypothesis	hypothesis	NOUN
ejpam-4553	243	4	on	on	ADP
ejpam-4553	243	5	suppφj	suppφj	NOUN
ejpam-4553	243	6	,	,	PUNCT
ejpam-4553	243	7	there	there	PRON
ejpam-4553	243	8	is	be	VERB
ejpam-4553	243	9	n	n	DET
ejpam-4553	243	10	∈	∈	PROPN
ejpam-4553	243	11	n0	n0	NOUN
ejpam-4553	243	12	such	such	ADJ
ejpam-4553	243	13	that∥∥∥∥∥	that∥∥∥∥∥	PROPN
ejpam-4553	243	14	∞∑	∞∑	PROPN
ejpam-4553	243	15	k=0	k=0	PROPN
ejpam-4553	243	16	fk	fk	INTJ
ejpam-4553	243	17	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	243	18	n	n	PRON
ejpam-4553	243	19	s	s	PROPN
ejpam-4553	243	20	(	(	PUNCT
ejpam-4553	243	21	·	·	PUNCT
ejpam-4553	243	22	)	)	PUNCT
ejpam-4553	243	23	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	243	24	(	(	PUNCT
ejpam-4553	243	25	·	·	PUNCT
ejpam-4553	243	26	)	)	PUNCT
ejpam-4553	243	27	=	=	SYM
ejpam-4553	243	28	∥∥∥∥∥φ0(d	∥∥∥∥∥φ0(d	ADJ
ejpam-4553	243	29	)	)	PUNCT
ejpam-4553	243	30	(	(	PUNCT
ejpam-4553	244	1	∞∑	∞∑	DET
ejpam-4553	244	2	k=0	k=0	PROPN
ejpam-4553	244	3	fk	fk	INTJ
ejpam-4553	244	4	)	)	PUNCT
ejpam-4553	244	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	244	6	mp(·),u	mp(·),u	PROPN
ejpam-4553	244	7	(	(	PUNCT
ejpam-4553	244	8	·	·	PUNCT
ejpam-4553	244	9	)	)	PUNCT
ejpam-4553	244	10	+	+	NUM
ejpam-4553	244	11	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	245	1	2js(·)φj(d	2js(·)φj(d	X
ejpam-4553	245	2	)	)	PUNCT
ejpam-4553	245	3			PROPN
ejpam-4553	245	4	∞∑	∞∑	PROPN
ejpam-4553	245	5	k	k	X
ejpam-4553	245	6	=	=	PROPN
ejpam-4553	245	7	j−n	j−n	PROPN
ejpam-4553	245	8	fk	fk	INTJ
ejpam-4553	245	9			NOUN
ejpam-4553	245	10	j≥n	j≥n	PROPN
ejpam-4553	245	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	246	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	246	2	(	(	PUNCT
ejpam-4553	246	3	·	·	PUNCT
ejpam-4553	246	4	)	)	PUNCT
ejpam-4553	246	5	)	)	PUNCT
ejpam-4553	246	6	.	.	PUNCT
ejpam-4553	247	1	(	(	PUNCT
ejpam-4553	247	2	8)	8)	NUM
ejpam-4553	247	3	(	(	PUNCT
ejpam-4553	247	4	i	i	NOUN
ejpam-4553	247	5	)	)	PUNCT
ejpam-4553	247	6	let	let	VERB
ejpam-4553	247	7	us	we	PRON
ejpam-4553	247	8	first	first	ADV
ejpam-4553	247	9	estimate	estimate	VERB
ejpam-4553	247	10	the	the	DET
ejpam-4553	247	11	term	term	NOUN
ejpam-4553	247	12	∥∥∥∥∥φ0(d	∥∥∥∥∥φ0(d	ADJ
ejpam-4553	247	13	)	)	PUNCT
ejpam-4553	248	1	(	(	PUNCT
ejpam-4553	248	2	∞∑	∞∑	PRON
ejpam-4553	248	3	k=0	k=0	PROPN
ejpam-4553	248	4	fk	fk	INTJ
ejpam-4553	248	5	)	)	PUNCT
ejpam-4553	248	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	248	7	mp(·),u	mp(·),u	PROPN
ejpam-4553	248	8	(	(	PUNCT
ejpam-4553	248	9	·	·	PUNCT
ejpam-4553	248	10	)	)	PUNCT
ejpam-4553	248	11	=	=	SYM
ejpam-4553	248	12	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	248	13	n∑	n∑	X
ejpam-4553	248	14	k=0	k=0	PROPN
ejpam-4553	248	15	φ̌0	φ̌0	NUM
ejpam-4553	248	16	∗	∗	NOUN
ejpam-4553	248	17	fk	fk	INTJ
ejpam-4553	248	18	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	248	19	mp(·),u	mp(·),u	PROPN
ejpam-4553	248	20	(	(	PUNCT
ejpam-4553	248	21	·	·	PUNCT
ejpam-4553	248	22	)	)	PUNCT
ejpam-4553	248	23	.	.	PUNCT
ejpam-4553	249	1	since	since	SCONJ
ejpam-4553	249	2	suppf	suppf	PROPN
ejpam-4553	249	3	(	(	PUNCT
ejpam-4553	249	4	ψ̌0	ψ̌0	X
ejpam-4553	249	5	∗	∗	PROPN
ejpam-4553	249	6	fk	fk	INTJ
ejpam-4553	249	7	)	)	PUNCT
ejpam-4553	249	8	⊂	⊂	PROPN
ejpam-4553	249	9	{	{	PUNCT
ejpam-4553	249	10	ξ	ξ	X
ejpam-4553	249	11	∈	∈	PROPN
ejpam-4553	249	12	rn	rn	PROPN
ejpam-4553	249	13	:	:	PUNCT
ejpam-4553	249	14	|ξ|	|ξ|	VERB
ejpam-4553	249	15	≤	≤	NOUN
ejpam-4553	249	16	2k+1	2k+1	PROPN
ejpam-4553	249	17	}	}	PUNCT
ejpam-4553	249	18	,	,	PUNCT
ejpam-4553	249	19	by	by	ADP
ejpam-4553	249	20	lemma	lemma	PROPN
ejpam-4553	249	21	2	2	NUM
ejpam-4553	249	22	∥∥∥∥∥φ0(d	∥∥∥∥∥φ0(d	NOUN
ejpam-4553	249	23	)	)	PUNCT
ejpam-4553	249	24	(	(	PUNCT
ejpam-4553	250	1	∞∑	∞∑	DET
ejpam-4553	250	2	k=0	k=0	PROPN
ejpam-4553	250	3	fk	fk	INTJ
ejpam-4553	250	4	)	)	PUNCT
ejpam-4553	250	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	250	6	mp(·),u	mp(·),u	PROPN
ejpam-4553	250	7	(	(	PUNCT
ejpam-4553	250	8	·	·	PUNCT
ejpam-4553	250	9	)	)	PUNCT
ejpam-4553	251	1	≲	≲	PROPN
ejpam-4553	251	2	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-4553	251	3	∞∑	∞∑	NUM
ejpam-4553	251	4	k=0	k=0	PROPN
ejpam-4553	251	5	ηk	ηk	NOUN
ejpam-4553	251	6	,	,	PUNCT
ejpam-4553	251	7	m	m	VERB
ejpam-4553	251	8	∗	∗	NOUN
ejpam-4553	251	9	|fk|	|fk|	PROPN
ejpam-4553	251	10	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	251	11	mp(·),u	mp(·),u	PROPN
ejpam-4553	251	12	(	(	PUNCT
ejpam-4553	251	13	·	·	PUNCT
ejpam-4553	251	14	)	)	PUNCT
ejpam-4553	251	15	,	,	PUNCT
ejpam-4553	251	16	for	for	ADP
ejpam-4553	251	17	any	any	DET
ejpam-4553	251	18	m	m	NOUN
ejpam-4553	251	19	>	>	X
ejpam-4553	251	20	n+	n+	NUM
ejpam-4553	251	21	clog(s	clog(s	NOUN
ejpam-4553	251	22	)	)	PUNCT
ejpam-4553	251	23	+	+	CCONJ
ejpam-4553	251	24	clog	clog	PROPN
ejpam-4553	251	25	(	(	PUNCT
ejpam-4553	251	26	1	1	NUM
ejpam-4553	251	27	q	q	NOUN
ejpam-4553	251	28	)	)	PUNCT
ejpam-4553	252	1	+	+	CCONJ
ejpam-4553	252	2	nmax	nmax	ADJ
ejpam-4553	252	3	{	{	PUNCT
ejpam-4553	252	4	0	0	NUM
ejpam-4553	252	5	,	,	PUNCT
ejpam-4553	252	6	supx∈rn	supx∈rn	PUNCT
ejpam-4553	252	7	(	(	PUNCT
ejpam-4553	252	8	1	1	NUM
ejpam-4553	252	9	p(x	p(x	NOUN
ejpam-4553	252	10	)	)	PUNCT
ejpam-4553	252	11	−	−	PROPN
ejpam-4553	252	12	1	1	NUM
ejpam-4553	252	13	u(x	u(x	NOUN
ejpam-4553	252	14	)	)	PUNCT
ejpam-4553	252	15	)	)	PUNCT
ejpam-4553	253	1	−	−	PROPN
ejpam-4553	253	2	1	1	NUM
ejpam-4553	253	3	p∞	p∞	PROPN
ejpam-4553	253	4	}	}	PUNCT
ejpam-4553	253	5	.	.	PUNCT
ejpam-4553	254	1	then∥∥∥∥∥φ0(d	then∥∥∥∥∥φ0(d	PROPN
ejpam-4553	254	2	)	)	PUNCT
ejpam-4553	255	1	(	(	PUNCT
ejpam-4553	255	2	∞∑	∞∑	DET
ejpam-4553	255	3	k=0	k=0	PROPN
ejpam-4553	255	4	fk	fk	INTJ
ejpam-4553	255	5	)	)	PUNCT
ejpam-4553	255	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	255	7	mp(·),u	mp(·),u	PROPN
ejpam-4553	255	8	(	(	PUNCT
ejpam-4553	255	9	·	·	PUNCT
ejpam-4553	255	10	)	)	PUNCT
ejpam-4553	256	1	≲	≲	PROPN
ejpam-4553	256	2	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-4553	256	3	∞∑	∞∑	NUM
ejpam-4553	256	4	k=0	k=0	PROPN
ejpam-4553	256	5	2−ks−	2−ks−	NUM
ejpam-4553	256	6	(	(	PUNCT
ejpam-4553	256	7	ηk	ηk	PROPN
ejpam-4553	256	8	,	,	PUNCT
ejpam-4553	256	9	m−clog(s	m−clog(s	PROPN
ejpam-4553	256	10	)	)	PUNCT
ejpam-4553	256	11	∗	∗	NOUN
ejpam-4553	256	12	2	2	NUM
ejpam-4553	256	13	ks(·)|fk|	ks(·)|fk|	NOUN
ejpam-4553	256	14	)	)	PUNCT
ejpam-4553	256	15	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	257	1	mp(·),u	mp(·),u	PROPN
ejpam-4553	257	2	(	(	PUNCT
ejpam-4553	257	3	·	·	PUNCT
ejpam-4553	257	4	)	)	PUNCT
ejpam-4553	257	5	by	by	ADP
ejpam-4553	257	6	lemma	lemma	PROPN
ejpam-4553	257	7	1	1	NUM
ejpam-4553	257	8	.	.	PUNCT
ejpam-4553	257	9	using	use	VERB
ejpam-4553	257	10	proposition	proposition	NOUN
ejpam-4553	257	11	1	1	NUM
ejpam-4553	257	12	,	,	PUNCT
ejpam-4553	257	13	we	we	PRON
ejpam-4553	257	14	have∥∥∥∥∥	have∥∥∥∥∥	VERB
ejpam-4553	257	15	∞∑	∞∑	ADJ
ejpam-4553	257	16	k=0	k=0	PROPN
ejpam-4553	257	17	2−ks−	2−ks−	NUM
ejpam-4553	257	18	(	(	PUNCT
ejpam-4553	257	19	ηk	ηk	PROPN
ejpam-4553	257	20	,	,	PUNCT
ejpam-4553	257	21	m−clog(s	m−clog(s	PROPN
ejpam-4553	257	22	)	)	PUNCT
ejpam-4553	257	23	∗	∗	NOUN
ejpam-4553	257	24	2	2	NUM
ejpam-4553	257	25	ks(·)|fk|	ks(·)|fk|	NOUN
ejpam-4553	257	26	)	)	PUNCT
ejpam-4553	257	27	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	258	1	mp(·),u	mp(·),u	PROPN
ejpam-4553	258	2	(	(	PUNCT
ejpam-4553	258	3	·	·	PUNCT
ejpam-4553	258	4	)	)	PUNCT
ejpam-4553	258	5	=	=	SYM
ejpam-4553	258	6	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	258	7	{	{	PUNCT
ejpam-4553	258	8	∞∑	∞∑	DET
ejpam-4553	258	9	k=0	k=0	PROPN
ejpam-4553	258	10	2−ks−	2−ks−	NUM
ejpam-4553	258	11	(	(	PUNCT
ejpam-4553	258	12	ηk	ηk	PROPN
ejpam-4553	258	13	,	,	PUNCT
ejpam-4553	258	14	m−clog(s	m−clog(s	PROPN
ejpam-4553	258	15	)	)	PUNCT
ejpam-4553	258	16	∗	∗	NOUN
ejpam-4553	258	17	2	2	NUM
ejpam-4553	258	18	ks(·)fk	ks(·)fk	X
ejpam-4553	258	19	)	)	PUNCT
ejpam-4553	258	20	}	}	PUNCT
ejpam-4553	258	21	j	j	PROPN
ejpam-4553	258	22	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	258	23	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	258	24	(	(	PUNCT
ejpam-4553	258	25	·	·	PUNCT
ejpam-4553	258	26	)	)	PUNCT
ejpam-4553	258	27	)	)	PUNCT
ejpam-4553	259	1	≲	≲	PROPN
ejpam-4553	259	2	∥∥∥(ηk	∥∥∥(ηk	PROPN
ejpam-4553	259	3	,	,	PUNCT
ejpam-4553	259	4	m−clog(s	m−clog(s	PROPN
ejpam-4553	259	5	)	)	PUNCT
ejpam-4553	259	6	∗	∗	NOUN
ejpam-4553	259	7	2	2	NUM
ejpam-4553	259	8	ks(·)fk	ks(·)fk	X
ejpam-4553	259	9	)	)	PUNCT
ejpam-4553	260	1	k	k	PROPN
ejpam-4553	260	2	∥∥∥	∥∥∥	PROPN
ejpam-4553	260	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	260	4	(	(	PUNCT
ejpam-4553	260	5	·	·	PUNCT
ejpam-4553	260	6	)	)	PUNCT
ejpam-4553	260	7	)	)	PUNCT
ejpam-4553	260	8	by	by	ADP
ejpam-4553	260	9	lemma	lemma	PROPN
ejpam-4553	260	10	5	5	NUM
ejpam-4553	260	11	thus	thus	ADV
ejpam-4553	260	12	,	,	PUNCT
ejpam-4553	260	13	by	by	ADP
ejpam-4553	260	14	lemma	lemma	PROPN
ejpam-4553	260	15	2	2	NUM
ejpam-4553	260	16	,	,	PUNCT
ejpam-4553	260	17	it	it	PRON
ejpam-4553	260	18	follows	follow	VERB
ejpam-4553	260	19	that∥∥∥∥∥φ0(d	that∥∥∥∥∥φ0(d	ADV
ejpam-4553	260	20	)	)	PUNCT
ejpam-4553	261	1	(	(	PUNCT
ejpam-4553	261	2	∞∑	∞∑	PRON
ejpam-4553	261	3	k=0	k=0	PROPN
ejpam-4553	261	4	fk	fk	INTJ
ejpam-4553	261	5	)	)	PUNCT
ejpam-4553	261	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4553	261	7	mp(·),u	mp(·),u	PROPN
ejpam-4553	261	8	(	(	PUNCT
ejpam-4553	261	9	·	·	PUNCT
ejpam-4553	261	10	)	)	PUNCT
ejpam-4553	261	11	≲	≲	PROPN
ejpam-4553	261	12	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4553	261	13	)	)	PUNCT
ejpam-4553	261	14	k	k	PROPN
ejpam-4553	261	15	∥∥∥	∥∥∥	PROPN
ejpam-4553	261	16	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	261	17	(	(	PUNCT
ejpam-4553	261	18	·	·	PUNCT
ejpam-4553	261	19	)	)	PUNCT
ejpam-4553	261	20	)	)	PUNCT
ejpam-4553	261	21	.	.	PUNCT
ejpam-4553	262	1	mohamed	mohamed	PROPN
ejpam-4553	262	2	congo	congo	PROPN
ejpam-4553	262	3	,	,	PUNCT
ejpam-4553	262	4	m.	m.	PROPN
ejpam-4553	262	5	f.	f.	PROPN
ejpam-4553	262	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	262	7	/	/	SYM
ejpam-4553	262	8	eur	eur	PROPN
ejpam-4553	262	9	.	.	PUNCT
ejpam-4553	263	1	j.	j.	PROPN
ejpam-4553	263	2	pure	pure	PROPN
ejpam-4553	263	3	appl	appl	PROPN
ejpam-4553	263	4	.	.	PROPN
ejpam-4553	263	5	math	math	PROPN
ejpam-4553	263	6	,	,	PUNCT
ejpam-4553	263	7	15	15	NUM
ejpam-4553	263	8	(	(	PUNCT
ejpam-4553	263	9	4	4	NUM
ejpam-4553	263	10	)	)	PUNCT
ejpam-4553	263	11	(	(	PUNCT
ejpam-4553	263	12	2022	2022	NUM
ejpam-4553	263	13	)	)	PUNCT
ejpam-4553	263	14	,	,	PUNCT
ejpam-4553	263	15	1716	1716	NUM
ejpam-4553	263	16	-	-	SYM
ejpam-4553	263	17	1737	1737	NUM
ejpam-4553	263	18	1726	1726	NUM
ejpam-4553	263	19	(	(	PUNCT
ejpam-4553	263	20	ii	ii	NOUN
ejpam-4553	263	21	)	)	PUNCT
ejpam-4553	263	22	now	now	ADV
ejpam-4553	263	23	let	let	VERB
ejpam-4553	263	24	us	we	PRON
ejpam-4553	263	25	estimate	estimate	VERB
ejpam-4553	263	26	the	the	DET
ejpam-4553	263	27	term	term	NOUN
ejpam-4553	263	28	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	264	1	2js(·)φj(d	2js(·)φj(d	X
ejpam-4553	264	2	)	)	PUNCT
ejpam-4553	264	3			PROPN
ejpam-4553	264	4	∞∑	∞∑	PROPN
ejpam-4553	264	5	k	k	X
ejpam-4553	264	6	=	=	PROPN
ejpam-4553	264	7	j−n	j−n	PROPN
ejpam-4553	264	8	fk	fk	INTJ
ejpam-4553	264	9			NOUN
ejpam-4553	264	10	j≥n	j≥n	PROPN
ejpam-4553	264	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	265	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	265	2	(	(	PUNCT
ejpam-4553	265	3	·	·	PUNCT
ejpam-4553	265	4	)	)	PUNCT
ejpam-4553	265	5	)	)	PUNCT
ejpam-4553	265	6	.	.	PUNCT
ejpam-4553	265	7	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4553	266	1	2js(·)φj(d	2js(·)φj(d	X
ejpam-4553	266	2	)	)	PUNCT
ejpam-4553	266	3			PROPN
ejpam-4553	266	4	∞∑	∞∑	PROPN
ejpam-4553	266	5	k	k	X
ejpam-4553	266	6	=	=	PROPN
ejpam-4553	266	7	j−n	j−n	PROPN
ejpam-4553	266	8	fk	fk	INTJ
ejpam-4553	266	9			NOUN
ejpam-4553	266	10	j≥n	j≥n	PROPN
ejpam-4553	266	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	267	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	267	2	(	(	PUNCT
ejpam-4553	267	3	·	·	PUNCT
ejpam-4553	267	4	)	)	PUNCT
ejpam-4553	267	5	)	)	PUNCT
ejpam-4553	268	1	=	=	SYM
ejpam-4553	268	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	268	3			PUNCT
ejpam-4553	268	4	∞∑	∞∑	NUM
ejpam-4553	268	5	k	k	X
ejpam-4553	268	6	=	=	NOUN
ejpam-4553	268	7	j−n	j−n	ADJ
ejpam-4553	268	8	2js	2js	NOUN
ejpam-4553	268	9	(	(	PUNCT
ejpam-4553	268	10	·	·	PUNCT
ejpam-4553	268	11	)	)	PUNCT
ejpam-4553	268	12	(	(	PUNCT
ejpam-4553	268	13	φ̌j	φ̌j	NOUN
ejpam-4553	268	14	∗	∗	X
ejpam-4553	268	15	fk	fk	INTJ
ejpam-4553	268	16	)	)	PUNCT
ejpam-4553	268	17			PROPN
ejpam-4553	268	18	j≥n	j≥n	PROPN
ejpam-4553	268	19	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	269	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	269	2	(	(	PUNCT
ejpam-4553	269	3	·	·	PUNCT
ejpam-4553	269	4	)	)	PUNCT
ejpam-4553	269	5	)	)	PUNCT
ejpam-4553	269	6	.	.	PUNCT
ejpam-4553	270	1	since	since	SCONJ
ejpam-4553	270	2	{	{	PUNCT
ejpam-4553	270	3	suppf	suppf	NOUN
ejpam-4553	270	4	(	(	PUNCT
ejpam-4553	270	5	φ̌j	φ̌j	NOUN
ejpam-4553	270	6	∗	∗	X
ejpam-4553	270	7	fk	fk	INTJ
ejpam-4553	270	8	)	)	PUNCT
ejpam-4553	270	9	⊂	⊂	PROPN
ejpam-4553	270	10	{	{	PUNCT
ejpam-4553	270	11	ξ	ξ	PROPN
ejpam-4553	270	12	∈	∈	PROPN
ejpam-4553	270	13	rn	rn	PROPN
ejpam-4553	270	14	:	:	PUNCT
ejpam-4553	270	15	|ξ|	|ξ|	VERB
ejpam-4553	270	16	≤	≤	ADJ
ejpam-4553	270	17	2j+1	2j+1	PROPN
ejpam-4553	270	18	}	}	PUNCT
ejpam-4553	270	19	suppf	suppf	NOUN
ejpam-4553	270	20	(	(	PUNCT
ejpam-4553	270	21	φ̌j	φ̌j	NOUN
ejpam-4553	270	22	∗	∗	X
ejpam-4553	270	23	fk	fk	INTJ
ejpam-4553	270	24	)	)	PUNCT
ejpam-4553	271	1	⊂	⊂	PROPN
ejpam-4553	271	2	{	{	PUNCT
ejpam-4553	271	3	ξ	ξ	PROPN
ejpam-4553	271	4	∈	∈	PROPN
ejpam-4553	271	5	rn	rn	PROPN
ejpam-4553	271	6	:	:	PUNCT
ejpam-4553	271	7	|ξ|	|ξ|	VERB
ejpam-4553	271	8	≤	≤	NOUN
ejpam-4553	271	9	2k+1	2k+1	PROPN
ejpam-4553	271	10	}	}	PUNCT
ejpam-4553	271	11	,	,	PUNCT
ejpam-4553	271	12	by	by	ADP
ejpam-4553	271	13	lemma	lemma	PROPN
ejpam-4553	271	14	2	2	NUM
ejpam-4553	271	15	{	{	PUNCT
ejpam-4553	271	16	2js	2js	NOUN
ejpam-4553	271	17	(	(	PUNCT
ejpam-4553	271	18	·	·	PUNCT
ejpam-4553	271	19	)	)	PUNCT
ejpam-4553	271	20	(	(	PUNCT
ejpam-4553	271	21	φ̌j	φ̌j	NOUN
ejpam-4553	271	22	∗	∗	X
ejpam-4553	271	23	fk	fk	INTJ
ejpam-4553	271	24	)	)	PUNCT
ejpam-4553	271	25	≲	≲	PROPN
ejpam-4553	271	26	2js	2js	NOUN
ejpam-4553	271	27	(	(	PUNCT
ejpam-4553	271	28	·	·	PUNCT
ejpam-4553	271	29	)	)	PUNCT
ejpam-4553	271	30	(	(	PUNCT
ejpam-4553	271	31	ηj	ηj	NOUN
ejpam-4553	271	32	,	,	PUNCT
ejpam-4553	271	33	m	m	PROPN
ejpam-4553	271	34	∗	∗	NOUN
ejpam-4553	271	35	|fk|	|fk|	PROPN
ejpam-4553	271	36	)	)	PUNCT
ejpam-4553	271	37	2js	2js	NOUN
ejpam-4553	271	38	(	(	PUNCT
ejpam-4553	271	39	·	·	PUNCT
ejpam-4553	271	40	)	)	PUNCT
ejpam-4553	271	41	(	(	PUNCT
ejpam-4553	271	42	φ̌j	φ̌j	NOUN
ejpam-4553	271	43	∗	∗	X
ejpam-4553	271	44	fk	fk	INTJ
ejpam-4553	271	45	)	)	PUNCT
ejpam-4553	271	46	≲	≲	PROPN
ejpam-4553	271	47	2js	2js	NOUN
ejpam-4553	271	48	(	(	PUNCT
ejpam-4553	271	49	·	·	PUNCT
ejpam-4553	271	50	)	)	PUNCT
ejpam-4553	271	51	(	(	PUNCT
ejpam-4553	271	52	ηk	ηk	PROPN
ejpam-4553	271	53	,	,	PUNCT
ejpam-4553	271	54	m	m	PROPN
ejpam-4553	271	55	∗	∗	NOUN
ejpam-4553	271	56	|fk|	|fk|	PROPN
ejpam-4553	271	57	)	)	PUNCT
ejpam-4553	271	58	for	for	ADP
ejpam-4553	271	59	m	m	PROPN
ejpam-4553	271	60	>	>	X
ejpam-4553	271	61	n+	n+	PUNCT
ejpam-4553	271	62	clog(1	clog(1	NOUN
ejpam-4553	271	63	/	/	SYM
ejpam-4553	271	64	q	q	NOUN
ejpam-4553	271	65	)	)	PUNCT
ejpam-4553	271	66	+	+	NUM
ejpam-4553	271	67	clog(s	clog(s	NOUN
ejpam-4553	271	68	)	)	PUNCT
ejpam-4553	272	1	+	+	CCONJ
ejpam-4553	272	2	nmax	nmax	ADJ
ejpam-4553	272	3	{	{	PUNCT
ejpam-4553	272	4	0	0	NUM
ejpam-4553	272	5	,	,	PUNCT
ejpam-4553	272	6	supx∈rn	supx∈rn	PUNCT
ejpam-4553	272	7	(	(	PUNCT
ejpam-4553	272	8	1	1	NUM
ejpam-4553	272	9	p(x	p(x	NOUN
ejpam-4553	272	10	)	)	PUNCT
ejpam-4553	272	11	−	−	PROPN
ejpam-4553	272	12	1	1	NUM
ejpam-4553	272	13	u(x	u(x	NOUN
ejpam-4553	272	14	)	)	PUNCT
ejpam-4553	272	15	)	)	PUNCT
ejpam-4553	273	1	−	−	PROPN
ejpam-4553	273	2	1	1	NUM
ejpam-4553	273	3	p∞	p∞	PROPN
ejpam-4553	273	4	}	}	PUNCT
ejpam-4553	273	5	.	.	PUNCT
ejpam-4553	274	1	therefore∥∥∥∥∥∥2js(·)φj(d	therefore∥∥∥∥∥∥2js(·)φj(d	X
ejpam-4553	274	2	)	)	PUNCT
ejpam-4553	274	3			PROPN
ejpam-4553	274	4	∞∑	∞∑	PROPN
ejpam-4553	274	5	k	k	X
ejpam-4553	274	6	=	=	PROPN
ejpam-4553	274	7	j−n	j−n	ADJ
ejpam-4553	274	8	fk	fk	INTJ
ejpam-4553	274	9	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4553	275	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	275	2	(	(	PUNCT
ejpam-4553	275	3	·	·	PUNCT
ejpam-4553	275	4	)	)	PUNCT
ejpam-4553	275	5	)	)	PUNCT
ejpam-4553	276	1	≲	≲	PROPN
ejpam-4553	276	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	276	3			PUNCT
ejpam-4553	276	4	j∑	j∑	PROPN
ejpam-4553	276	5	k	k	X
ejpam-4553	276	6	=	=	PROPN
ejpam-4553	276	7	j−n	j−n	ADJ
ejpam-4553	276	8	2js	2js	NOUN
ejpam-4553	276	9	(	(	PUNCT
ejpam-4553	276	10	·	·	PUNCT
ejpam-4553	276	11	)	)	PUNCT
ejpam-4553	276	12	(	(	PUNCT
ejpam-4553	276	13	ηj	ηj	NOUN
ejpam-4553	276	14	,	,	PUNCT
ejpam-4553	276	15	m	m	PROPN
ejpam-4553	276	16	∗	∗	NOUN
ejpam-4553	276	17	|fk|	|fk|	PROPN
ejpam-4553	276	18	)	)	PUNCT
ejpam-4553	277	1			PROPN
ejpam-4553	277	2	j≥n	j≥n	PROPN
ejpam-4553	277	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	278	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	278	2	(	(	PUNCT
ejpam-4553	278	3	·	·	PUNCT
ejpam-4553	278	4	)	)	PUNCT
ejpam-4553	278	5	)	)	PUNCT
ejpam-4553	279	1	+	+	CCONJ
ejpam-4553	279	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	280	1			PUNCT
ejpam-4553	280	2	∞∑	∞∑	ADJ
ejpam-4553	280	3	k	k	X
ejpam-4553	280	4	=	=	NOUN
ejpam-4553	280	5	j+1	j+1	ADJ
ejpam-4553	280	6	2−(k−j)s(·)2ks	2−(k−j)s(·)2ks	NUM
ejpam-4553	280	7	(	(	PUNCT
ejpam-4553	280	8	·	·	PUNCT
ejpam-4553	280	9	)	)	PUNCT
ejpam-4553	280	10	(	(	PUNCT
ejpam-4553	280	11	ηk	ηk	PROPN
ejpam-4553	280	12	,	,	PUNCT
ejpam-4553	280	13	m	m	PROPN
ejpam-4553	280	14	∗	∗	NOUN
ejpam-4553	280	15	|fk|	|fk|	PROPN
ejpam-4553	280	16	)	)	PUNCT
ejpam-4553	281	1			PROPN
ejpam-4553	281	2	j≥n	j≥n	PROPN
ejpam-4553	281	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	282	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	282	2	(	(	PUNCT
ejpam-4553	282	3	·	·	PUNCT
ejpam-4553	282	4	)	)	PUNCT
ejpam-4553	282	5	)	)	PUNCT
ejpam-4553	282	6	.	.	PUNCT
ejpam-4553	283	1	we	we	PRON
ejpam-4553	283	2	are	be	AUX
ejpam-4553	283	3	left	leave	VERB
ejpam-4553	283	4	now	now	ADV
ejpam-4553	283	5	to	to	PART
ejpam-4553	283	6	estimate	estimate	VERB
ejpam-4553	283	7	each	each	DET
ejpam-4553	283	8	terms	term	NOUN
ejpam-4553	283	9	on	on	ADP
ejpam-4553	283	10	the	the	DET
ejpam-4553	283	11	right	right	ADJ
ejpam-4553	283	12	-	-	PUNCT
ejpam-4553	283	13	hand	hand	NOUN
ejpam-4553	283	14	side	side	NOUN
ejpam-4553	283	15	.	.	PUNCT
ejpam-4553	284	1	using	use	VERB
ejpam-4553	284	2	lemma	lemma	PROPN
ejpam-4553	284	3	1	1	NUM
ejpam-4553	284	4	we	we	PRON
ejpam-4553	284	5	can	can	AUX
ejpam-4553	284	6	move	move	VERB
ejpam-4553	284	7	2νs	2νs	ADJ
ejpam-4553	284	8	(	(	PUNCT
ejpam-4553	284	9	·	·	PUNCT
ejpam-4553	284	10	)	)	PUNCT
ejpam-4553	284	11	inside	inside	ADP
ejpam-4553	284	12	the	the	DET
ejpam-4553	284	13	convolution	convolution	NOUN
ejpam-4553	284	14	2νs	2νs	NOUN
ejpam-4553	284	15	(	(	PUNCT
ejpam-4553	284	16	·	·	PUNCT
ejpam-4553	284	17	)	)	PUNCT
ejpam-4553	284	18	(	(	PUNCT
ejpam-4553	284	19	ην	ην	NOUN
ejpam-4553	284	20	,	,	PUNCT
ejpam-4553	284	21	m	m	PROPN
ejpam-4553	284	22	∗	∗	NOUN
ejpam-4553	284	23	|fk|	|fk|	PROPN
ejpam-4553	284	24	)	)	PUNCT
ejpam-4553	284	25	and	and	CCONJ
ejpam-4553	284	26	get	get	VERB
ejpam-4553	284	27	2νs	2νs	ADJ
ejpam-4553	284	28	(	(	PUNCT
ejpam-4553	284	29	·	·	PUNCT
ejpam-4553	284	30	)	)	PUNCT
ejpam-4553	284	31	(	(	PUNCT
ejpam-4553	284	32	ην	ην	NOUN
ejpam-4553	284	33	,	,	PUNCT
ejpam-4553	284	34	m	m	PROPN
ejpam-4553	284	35	∗	∗	NOUN
ejpam-4553	284	36	|fk|	|fk|	PROPN
ejpam-4553	284	37	)	)	PUNCT
ejpam-4553	284	38	≲	≲	PROPN
ejpam-4553	284	39	(	(	PUNCT
ejpam-4553	284	40	ην	ην	NOUN
ejpam-4553	284	41	,	,	PUNCT
ejpam-4553	284	42	m0	m0	PROPN
ejpam-4553	284	43	∗	∗	X
ejpam-4553	284	44	2νs(·)|fk|	2νs(·)|fk|	PROPN
ejpam-4553	284	45	)	)	PUNCT
ejpam-4553	284	46	,	,	PUNCT
ejpam-4553	284	47	ν	ν	X
ejpam-4553	284	48	=	=	SYM
ejpam-4553	284	49	j	j	PROPN
ejpam-4553	284	50	or	or	CCONJ
ejpam-4553	284	51	k	k	PROPN
ejpam-4553	284	52	where	where	SCONJ
ejpam-4553	284	53	m0	m0	PROPN
ejpam-4553	284	54	=	=	PUNCT
ejpam-4553	284	55	m−	m−	PROPN
ejpam-4553	284	56	clog(s	clog(s	PROPN
ejpam-4553	284	57	)	)	PUNCT
ejpam-4553	284	58	.	.	PUNCT
ejpam-4553	285	1	thus	thus	ADV
ejpam-4553	285	2	•	•	NUM
ejpam-4553	285	3	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	285	4			NUM
ejpam-4553	285	5	j∑	j∑	PROPN
ejpam-4553	285	6	k	k	X
ejpam-4553	285	7	=	=	PROPN
ejpam-4553	285	8	j−n	j−n	ADJ
ejpam-4553	285	9	2js	2js	NOUN
ejpam-4553	285	10	(	(	PUNCT
ejpam-4553	285	11	·	·	PUNCT
ejpam-4553	285	12	)	)	PUNCT
ejpam-4553	285	13	(	(	PUNCT
ejpam-4553	285	14	ηj	ηj	NOUN
ejpam-4553	285	15	,	,	PUNCT
ejpam-4553	285	16	m	m	PROPN
ejpam-4553	285	17	∗	∗	NOUN
ejpam-4553	285	18	|fk|	|fk|	PROPN
ejpam-4553	285	19	)	)	PUNCT
ejpam-4553	286	1			PROPN
ejpam-4553	286	2	j	j	PROPN
ejpam-4553	286	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	286	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	286	5	(	(	PUNCT
ejpam-4553	286	6	·	·	PUNCT
ejpam-4553	286	7	)	)	PUNCT
ejpam-4553	286	8	)	)	PUNCT
ejpam-4553	287	1	≲	≲	PROPN
ejpam-4553	287	2	0∑	0∑	NUM
ejpam-4553	287	3	ℓ=−n	ℓ=−n	PROPN
ejpam-4553	287	4	∥∥∥∥{(ηj	∥∥∥∥{(ηj	PROPN
ejpam-4553	287	5	,	,	PUNCT
ejpam-4553	287	6	m0	m0	NOUN
ejpam-4553	287	7	∗	∗	NOUN
ejpam-4553	287	8	2js(·)|fj+ℓ|	2js(·)|fj+ℓ|	NUM
ejpam-4553	287	9	)	)	PUNCT
ejpam-4553	287	10	}	}	PUNCT
ejpam-4553	287	11	j	j	PROPN
ejpam-4553	287	12	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4553	287	13	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	287	14	(	(	PUNCT
ejpam-4553	287	15	·	·	PUNCT
ejpam-4553	287	16	)	)	PUNCT
ejpam-4553	287	17	)	)	PUNCT
ejpam-4553	288	1	≲	≲	PROPN
ejpam-4553	288	2	∥∥∥∥(2js(·)fj)j	∥∥∥∥(2js(·)fj)j	NUM
ejpam-4553	288	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4553	288	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	288	5	(	(	PUNCT
ejpam-4553	288	6	·	·	PUNCT
ejpam-4553	288	7	)	)	PUNCT
ejpam-4553	288	8	)	)	PUNCT
ejpam-4553	288	9	by	by	ADP
ejpam-4553	288	10	lemma	lemma	PROPN
ejpam-4553	288	11	3	3	NUM
ejpam-4553	288	12	.	.	PUNCT
ejpam-4553	288	13	also	also	ADV
ejpam-4553	288	14	•	•	NUM
ejpam-4553	288	15	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	288	16			PUNCT
ejpam-4553	288	17	∞∑	∞∑	ADJ
ejpam-4553	288	18	k	k	X
ejpam-4553	288	19	=	=	NOUN
ejpam-4553	288	20	j+1	j+1	ADJ
ejpam-4553	288	21	2−(k−j)s(·)2ks	2−(k−j)s(·)2ks	NUM
ejpam-4553	288	22	(	(	PUNCT
ejpam-4553	288	23	·	·	PUNCT
ejpam-4553	288	24	)	)	PUNCT
ejpam-4553	288	25	(	(	PUNCT
ejpam-4553	288	26	ηk	ηk	PROPN
ejpam-4553	288	27	,	,	PUNCT
ejpam-4553	288	28	m	m	PROPN
ejpam-4553	288	29	∗	∗	NOUN
ejpam-4553	288	30	|fk|	|fk|	PROPN
ejpam-4553	288	31	)	)	PUNCT
ejpam-4553	289	1			PROPN
ejpam-4553	289	2	j	j	PROPN
ejpam-4553	289	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	289	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	289	5	(	(	PUNCT
ejpam-4553	289	6	·	·	PUNCT
ejpam-4553	289	7	)	)	PUNCT
ejpam-4553	289	8	)	)	PUNCT
ejpam-4553	289	9	mohamed	mohamed	PROPN
ejpam-4553	289	10	congo	congo	PROPN
ejpam-4553	289	11	,	,	PUNCT
ejpam-4553	289	12	m.	m.	PROPN
ejpam-4553	289	13	f.	f.	PROPN
ejpam-4553	289	14	ouedraogo	ouedraogo	PROPN
ejpam-4553	289	15	/	/	SYM
ejpam-4553	289	16	eur	eur	PROPN
ejpam-4553	289	17	.	.	PUNCT
ejpam-4553	290	1	j.	j.	PROPN
ejpam-4553	290	2	pure	pure	PROPN
ejpam-4553	290	3	appl	appl	PROPN
ejpam-4553	290	4	.	.	PROPN
ejpam-4553	290	5	math	math	PROPN
ejpam-4553	290	6	,	,	PUNCT
ejpam-4553	290	7	15	15	NUM
ejpam-4553	290	8	(	(	PUNCT
ejpam-4553	290	9	4	4	NUM
ejpam-4553	290	10	)	)	PUNCT
ejpam-4553	290	11	(	(	PUNCT
ejpam-4553	290	12	2022	2022	NUM
ejpam-4553	290	13	)	)	PUNCT
ejpam-4553	290	14	,	,	PUNCT
ejpam-4553	290	15	1716	1716	NUM
ejpam-4553	290	16	-	-	SYM
ejpam-4553	290	17	1737	1737	NUM
ejpam-4553	290	18	1727	1727	NUM
ejpam-4553	290	19	≲	≲	PROPN
ejpam-4553	290	20	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	290	21			PUNCT
ejpam-4553	291	1	∞∑	∞∑	NUM
ejpam-4553	291	2	k	k	X
ejpam-4553	291	3	=	=	NOUN
ejpam-4553	291	4	j+1	j+1	ADJ
ejpam-4553	291	5	2−|j−k|s	2−|j−k|s	NUM
ejpam-4553	291	6	(	(	PUNCT
ejpam-4553	291	7	·	·	PUNCT
ejpam-4553	291	8	)	)	PUNCT
ejpam-4553	291	9	(	(	PUNCT
ejpam-4553	291	10	ηk	ηk	PROPN
ejpam-4553	291	11	,	,	PUNCT
ejpam-4553	291	12	m0	m0	NOUN
ejpam-4553	291	13	∗	∗	NOUN
ejpam-4553	291	14	2ks(·)|fk|	2ks(·)|fk|	NUM
ejpam-4553	291	15	)	)	PUNCT
ejpam-4553	292	1			PROPN
ejpam-4553	292	2	j	j	PROPN
ejpam-4553	292	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	292	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	292	5	(	(	PUNCT
ejpam-4553	292	6	·	·	PUNCT
ejpam-4553	292	7	)	)	PUNCT
ejpam-4553	292	8	)	)	PUNCT
ejpam-4553	293	1	≲	≲	PROPN
ejpam-4553	293	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	293	3	{	{	PUNCT
ejpam-4553	293	4	∞∑	∞∑	NUM
ejpam-4553	293	5	k=0	k=0	PROPN
ejpam-4553	293	6	2−|j−k|s−	2−|j−k|s−	NUM
ejpam-4553	293	7	(	(	PUNCT
ejpam-4553	293	8	ηk	ηk	PROPN
ejpam-4553	293	9	,	,	PUNCT
ejpam-4553	293	10	m0	m0	NOUN
ejpam-4553	293	11	∗	∗	NOUN
ejpam-4553	293	12	2ks(·)|fk|	2ks(·)|fk|	NUM
ejpam-4553	293	13	)	)	PUNCT
ejpam-4553	293	14	}	}	PUNCT
ejpam-4553	293	15	j	j	PROPN
ejpam-4553	293	16	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	293	17	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	293	18	(	(	PUNCT
ejpam-4553	293	19	·	·	PUNCT
ejpam-4553	293	20	)	)	PUNCT
ejpam-4553	293	21	)	)	PUNCT
ejpam-4553	294	1	≲	≲	PROPN
ejpam-4553	294	2	∥∥∥(ηk	∥∥∥(ηk	PROPN
ejpam-4553	294	3	,	,	PUNCT
ejpam-4553	294	4	m0	m0	NOUN
ejpam-4553	294	5	∗	∗	NOUN
ejpam-4553	294	6	2ks(·)|fk|	2ks(·)|fk|	NUM
ejpam-4553	294	7	)	)	PUNCT
ejpam-4553	295	1	k	k	PROPN
ejpam-4553	295	2	∥∥∥	∥∥∥	PROPN
ejpam-4553	295	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	295	4	(	(	PUNCT
ejpam-4553	295	5	·	·	PUNCT
ejpam-4553	295	6	)	)	PUNCT
ejpam-4553	295	7	)	)	PUNCT
ejpam-4553	296	1	≲	≲	PROPN
ejpam-4553	296	2	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4553	296	3	)	)	PUNCT
ejpam-4553	296	4	k	k	PROPN
ejpam-4553	296	5	∥∥∥	∥∥∥	PROPN
ejpam-4553	296	6	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	296	7	(	(	PUNCT
ejpam-4553	296	8	·	·	PUNCT
ejpam-4553	296	9	)	)	PUNCT
ejpam-4553	296	10	)	)	PUNCT
ejpam-4553	296	11	by	by	ADP
ejpam-4553	296	12	lemma	lemma	PROPN
ejpam-4553	296	13	5	5	NUM
ejpam-4553	296	14	and	and	CCONJ
ejpam-4553	296	15	3	3	NUM
ejpam-4553	296	16	.	.	PUNCT
ejpam-4553	296	17	.	.	PUNCT
ejpam-4553	297	1	□	□	PUNCT
ejpam-4553	297	2	4.1	4.1	NUM
ejpam-4553	297	3	.	.	PUNCT
ejpam-4553	298	1	the	the	DET
ejpam-4553	298	2	main	main	ADJ
ejpam-4553	298	3	estimate	estimate	NOUN
ejpam-4553	298	4	in	in	ADP
ejpam-4553	298	5	this	this	DET
ejpam-4553	298	6	subsection	subsection	NOUN
ejpam-4553	298	7	,	,	PUNCT
ejpam-4553	298	8	we	we	PRON
ejpam-4553	298	9	will	will	AUX
ejpam-4553	298	10	establish	establish	VERB
ejpam-4553	298	11	the	the	DET
ejpam-4553	298	12	boundedness	boundedness	NOUN
ejpam-4553	298	13	of	of	ADP
ejpam-4553	298	14	pseudo	pseudo	NOUN
ejpam-4553	298	15	-	-	ADJ
ejpam-4553	298	16	differential	differential	ADJ
ejpam-4553	298	17	operators	operator	NOUN
ejpam-4553	298	18	on	on	ADP
ejpam-4553	298	19	n	n	PRON
ejpam-4553	298	20	s	s	PROPN
ejpam-4553	298	21	(	(	PUNCT
ejpam-4553	298	22	·	·	PUNCT
ejpam-4553	298	23	)	)	PUNCT
ejpam-4553	298	24	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	298	25	(	(	PUNCT
ejpam-4553	298	26	·	·	PUNCT
ejpam-4553	298	27	)	)	PUNCT
ejpam-4553	298	28	.	.	PUNCT
ejpam-4553	299	1	theorem	theorem	NOUN
ejpam-4553	299	2	2	2	NUM
ejpam-4553	299	3	.	.	PUNCT
ejpam-4553	300	1	let	let	VERB
ejpam-4553	300	2	a(x	a(x	NOUN
ejpam-4553	300	3	,	,	PUNCT
ejpam-4553	300	4	ξ	ξ	NOUN
ejpam-4553	300	5	)	)	PUNCT
ejpam-4553	300	6	∈	∈	NOUN
ejpam-4553	300	7	cℓ	cℓ	ADP
ejpam-4553	300	8	∗s	∗s	PROPN
ejpam-4553	300	9	m	m	PROPN
ejpam-4553	300	10	1,δ	1,δ	NUM
ejpam-4553	300	11	where	where	SCONJ
ejpam-4553	300	12	m	m	VERB
ejpam-4553	300	13	∈	∈	PROPN
ejpam-4553	300	14	r	r	NOUN
ejpam-4553	300	15	,	,	PUNCT
ejpam-4553	300	16	δ	δ	PROPN
ejpam-4553	300	17	∈	∈	PROPN
ejpam-4553	301	1	[	[	X
ejpam-4553	301	2	0	0	NUM
ejpam-4553	301	3	,	,	PUNCT
ejpam-4553	301	4	1	1	NUM
ejpam-4553	301	5	]	]	PUNCT
ejpam-4553	301	6	and	and	CCONJ
ejpam-4553	301	7	ℓ	ℓ	INTJ
ejpam-4553	301	8	>	>	X
ejpam-4553	301	9	0	0	X
ejpam-4553	301	10	.	.	PUNCT
ejpam-4553	302	1	let	let	VERB
ejpam-4553	302	2	p	p	PRON
ejpam-4553	302	3	∈	∈	PROPN
ejpam-4553	302	4	p	p	NOUN
ejpam-4553	302	5	log(rn	log(rn	PROPN
ejpam-4553	302	6	)	)	PUNCT
ejpam-4553	302	7	and	and	CCONJ
ejpam-4553	302	8	u	u	NOUN
ejpam-4553	302	9	,	,	PUNCT
ejpam-4553	302	10	q	q	PROPN
ejpam-4553	302	11	∈	∈	PROPN
ejpam-4553	302	12	p	p	NOUN
ejpam-4553	302	13	such	such	ADJ
ejpam-4553	302	14	that	that	SCONJ
ejpam-4553	302	15	1	1	NUM
ejpam-4553	302	16	q	q	NOUN
ejpam-4553	302	17	∈	∈	PROPN
ejpam-4553	302	18	c	c	PROPN
ejpam-4553	302	19	log	log	PROPN
ejpam-4553	302	20	loc	loc	NOUN
ejpam-4553	302	21	with	with	ADP
ejpam-4553	302	22	1	1	NUM
ejpam-4553	302	23	≤	≤	NOUN
ejpam-4553	302	24	p−	p−	NOUN
ejpam-4553	302	25	≤	≤	NUM
ejpam-4553	302	26	p(x	p(x	PROPN
ejpam-4553	302	27	)	)	PUNCT
ejpam-4553	302	28	≤	≤	NUM
ejpam-4553	302	29	u(x	u(x	NOUN
ejpam-4553	302	30	)	)	PUNCT
ejpam-4553	302	31	≤	≤	NOUN
ejpam-4553	302	32	∞.	∞.	PROPN
ejpam-4553	302	33	let	let	VERB
ejpam-4553	302	34	s	s	PRON
ejpam-4553	302	35	∈	∈	VERB
ejpam-4553	302	36	c	c	PROPN
ejpam-4553	302	37	log	log	PROPN
ejpam-4553	302	38	loc	loc	PROPN
ejpam-4553	302	39	such	such	ADJ
ejpam-4553	302	40	that	that	SCONJ
ejpam-4553	302	41	0	0	NUM
ejpam-4553	302	42	<	<	X
ejpam-4553	302	43	s−	s−	PROPN
ejpam-4553	302	44	≤	≤	NUM
ejpam-4553	302	45	s(x	s(x	PROPN
ejpam-4553	302	46	)	)	PUNCT
ejpam-4553	302	47	<	<	X
ejpam-4553	302	48	ℓ.	ℓ.	NOUN
ejpam-4553	302	49	then	then	ADV
ejpam-4553	302	50	a(x	a(x	NOUN
ejpam-4553	302	51	,	,	PUNCT
ejpam-4553	302	52	d	d	NOUN
ejpam-4553	302	53	)	)	PUNCT
ejpam-4553	302	54	:	:	PUNCT
ejpam-4553	303	1	n	n	PROPN
ejpam-4553	303	2	s(·)+m	s(·)+m	PROPN
ejpam-4553	303	3	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	303	4	(	(	PUNCT
ejpam-4553	303	5	·	·	PUNCT
ejpam-4553	303	6	)	)	PUNCT
ejpam-4553	304	1	−→	−→	NOUN
ejpam-4553	304	2	n	n	CCONJ
ejpam-4553	304	3	s	s	PROPN
ejpam-4553	304	4	(	(	PUNCT
ejpam-4553	304	5	·	·	PUNCT
ejpam-4553	304	6	)	)	PUNCT
ejpam-4553	304	7	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	304	8	(	(	PUNCT
ejpam-4553	304	9	·	·	PUNCT
ejpam-4553	304	10	)	)	PUNCT
ejpam-4553	304	11	is	be	AUX
ejpam-4553	304	12	bounded	bound	VERB
ejpam-4553	304	13	.	.	PUNCT
ejpam-4553	305	1	remark	remark	PROPN
ejpam-4553	305	2	3	3	NUM
ejpam-4553	305	3	.	.	PUNCT
ejpam-4553	306	1	the	the	DET
ejpam-4553	306	2	operator	operator	NOUN
ejpam-4553	306	3	(	(	PUNCT
ejpam-4553	306	4	1	1	NUM
ejpam-4553	306	5	−∆	−∆	NOUN
ejpam-4553	306	6	)	)	PUNCT
ejpam-4553	306	7	m	m	VERB
ejpam-4553	306	8	2	2	NUM
ejpam-4553	306	9	,	,	PUNCT
ejpam-4553	306	10	m	m	VERB
ejpam-4553	306	11	∈	∈	NOUN
ejpam-4553	306	12	r	r	NOUN
ejpam-4553	306	13	is	be	AUX
ejpam-4553	306	14	an	an	DET
ejpam-4553	306	15	isomorphism	isomorphism	NOUN
ejpam-4553	306	16	that	that	PRON
ejpam-4553	306	17	composes	compose	VERB
ejpam-4553	306	18	well	well	ADV
ejpam-4553	306	19	with	with	ADP
ejpam-4553	306	20	pseudo	pseudo	NOUN
ejpam-4553	306	21	-	-	ADJ
ejpam-4553	306	22	differential	differential	ADJ
ejpam-4553	306	23	operators	operator	NOUN
ejpam-4553	306	24	(	(	PUNCT
ejpam-4553	306	25	see[13	see[13	PROPN
ejpam-4553	306	26	]	]	PUNCT
ejpam-4553	306	27	and	and	CCONJ
ejpam-4553	306	28	[	[	X
ejpam-4553	306	29	15	15	NUM
ejpam-4553	306	30	]	]	NUM
ejpam-4553	306	31	)	)	PUNCT
ejpam-4553	306	32	.	.	PUNCT
ejpam-4553	307	1	thus	thus	ADV
ejpam-4553	307	2	,	,	PUNCT
ejpam-4553	307	3	it	it	PRON
ejpam-4553	307	4	is	be	AUX
ejpam-4553	307	5	enough	enough	ADJ
ejpam-4553	307	6	to	to	PART
ejpam-4553	307	7	treat	treat	VERB
ejpam-4553	307	8	the	the	DET
ejpam-4553	307	9	case	case	NOUN
ejpam-4553	307	10	m	m	NOUN
ejpam-4553	307	11	=	=	NOUN
ejpam-4553	307	12	0	0	X
ejpam-4553	307	13	.	.	PUNCT
ejpam-4553	308	1	therefore	therefore	ADV
ejpam-4553	308	2	let	let	VERB
ejpam-4553	308	3	us	we	PRON
ejpam-4553	308	4	set	set	VERB
ejpam-4553	308	5	a(x	a(x	NOUN
ejpam-4553	308	6	,	,	PUNCT
ejpam-4553	308	7	ξ	ξ	NOUN
ejpam-4553	308	8	)	)	PUNCT
ejpam-4553	308	9	∈	∈	NOUN
ejpam-4553	308	10	cℓ	cℓ	ADP
ejpam-4553	308	11	∗s	∗s	PROPN
ejpam-4553	308	12	0	0	NUM
ejpam-4553	308	13	1,δ	1,δ	NUM
ejpam-4553	308	14	.	.	PUNCT
ejpam-4553	309	1	the	the	DET
ejpam-4553	309	2	symbol	symbol	NOUN
ejpam-4553	309	3	reduction	reduction	NOUN
ejpam-4553	309	4	method	method	NOUN
ejpam-4553	309	5	due	due	ADP
ejpam-4553	309	6	to	to	ADP
ejpam-4553	309	7	coifman	coifman	NOUN
ejpam-4553	309	8	and	and	CCONJ
ejpam-4553	309	9	meyer[3	meyer[3	PROPN
ejpam-4553	309	10	]	]	X
ejpam-4553	309	11	,	,	PUNCT
ejpam-4553	309	12	makes	make	VERB
ejpam-4553	309	13	it	it	PRON
ejpam-4553	309	14	possible	possible	ADJ
ejpam-4553	309	15	to	to	PART
ejpam-4553	309	16	be	be	AUX
ejpam-4553	309	17	limited	limit	VERB
ejpam-4553	309	18	to	to	ADP
ejpam-4553	309	19	symbols	symbol	NOUN
ejpam-4553	309	20	of	of	ADP
ejpam-4553	309	21	the	the	DET
ejpam-4553	309	22	form(see	form(see	ADJ
ejpam-4553	310	1	[	[	X
ejpam-4553	310	2	13	13	NUM
ejpam-4553	310	3	]	]	PUNCT
ejpam-4553	310	4	,	,	PUNCT
ejpam-4553	310	5	[	[	X
ejpam-4553	310	6	11	11	NUM
ejpam-4553	310	7	]	]	PUNCT
ejpam-4553	310	8	,	,	PUNCT
ejpam-4553	310	9	[	[	X
ejpam-4553	310	10	2	2	NUM
ejpam-4553	310	11	]	]	PUNCT
ejpam-4553	310	12	and	and	CCONJ
ejpam-4553	310	13	[	[	X
ejpam-4553	310	14	16	16	NUM
ejpam-4553	310	15	]	]	SYM
ejpam-4553	310	16	)	)	PUNCT
ejpam-4553	310	17	a(x	a(x	PROPN
ejpam-4553	310	18	,	,	PUNCT
ejpam-4553	310	19	ξ	ξ	NOUN
ejpam-4553	310	20	)	)	PUNCT
ejpam-4553	310	21	=	=	SYM
ejpam-4553	310	22	∑	∑	PUNCT
ejpam-4553	310	23	j≥0	j≥0	PROPN
ejpam-4553	310	24	σj(x)φj(ξ	σj(x)φj(ξ	PROPN
ejpam-4553	310	25	)	)	PUNCT
ejpam-4553	310	26	where	where	SCONJ
ejpam-4553	310	27	σj	σj	ADJ
ejpam-4553	310	28	satisfies	satisfie	NOUN
ejpam-4553	310	29	∥σj∥cℓ	∥σj∥cℓ	X
ejpam-4553	310	30	∗	∗	NOUN
ejpam-4553	310	31	≤	≤	NUM
ejpam-4553	310	32	c2jℓδ	c2jℓδ	X
ejpam-4553	310	33	(	(	PUNCT
ejpam-4553	310	34	9	9	NUM
ejpam-4553	310	35	)	)	PUNCT
ejpam-4553	310	36	and	and	CCONJ
ejpam-4553	310	37	∥σj∥l∞	∥σj∥l∞	SYM
ejpam-4553	310	38	≤	≤	NUM
ejpam-4553	310	39	c	c	NOUN
ejpam-4553	310	40	(	(	PUNCT
ejpam-4553	310	41	10	10	NUM
ejpam-4553	310	42	)	)	PUNCT
ejpam-4553	310	43	with	with	ADP
ejpam-4553	310	44	c	c	NOUN
ejpam-4553	310	45	depending	depend	VERB
ejpam-4553	310	46	on	on	ADP
ejpam-4553	310	47	δ	δ	PROPN
ejpam-4553	310	48	and	and	CCONJ
ejpam-4553	310	49	ℓ	ℓ	PROPN
ejpam-4553	310	50	but	but	CCONJ
ejpam-4553	310	51	not	not	PART
ejpam-4553	310	52	on	on	ADP
ejpam-4553	310	53	j	j	PROPN
ejpam-4553	310	54	and	and	CCONJ
ejpam-4553	310	55	φj	φj	PROPN
ejpam-4553	310	56	is	be	AUX
ejpam-4553	310	57	exactly	exactly	ADV
ejpam-4553	310	58	a	a	DET
ejpam-4553	310	59	littlewood	littlewood	NOUN
ejpam-4553	310	60	-	-	PUNCT
ejpam-4553	310	61	paley	paley	NOUN
ejpam-4553	310	62	function	function	NOUN
ejpam-4553	310	63	.	.	PUNCT
ejpam-4553	311	1	mohamed	mohamed	PROPN
ejpam-4553	311	2	congo	congo	PROPN
ejpam-4553	311	3	,	,	PUNCT
ejpam-4553	311	4	m.	m.	PROPN
ejpam-4553	311	5	f.	f.	PROPN
ejpam-4553	311	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	311	7	/	/	SYM
ejpam-4553	311	8	eur	eur	PROPN
ejpam-4553	311	9	.	.	PUNCT
ejpam-4553	312	1	j.	j.	PROPN
ejpam-4553	312	2	pure	pure	PROPN
ejpam-4553	312	3	appl	appl	PROPN
ejpam-4553	312	4	.	.	PROPN
ejpam-4553	312	5	math	math	PROPN
ejpam-4553	312	6	,	,	PUNCT
ejpam-4553	312	7	15	15	NUM
ejpam-4553	312	8	(	(	PUNCT
ejpam-4553	312	9	4	4	NUM
ejpam-4553	312	10	)	)	PUNCT
ejpam-4553	312	11	(	(	PUNCT
ejpam-4553	312	12	2022	2022	NUM
ejpam-4553	312	13	)	)	PUNCT
ejpam-4553	312	14	,	,	PUNCT
ejpam-4553	312	15	1716	1716	NUM
ejpam-4553	312	16	-	-	SYM
ejpam-4553	312	17	1737	1737	NUM
ejpam-4553	312	18	1728	1728	NUM
ejpam-4553	312	19	proof	proof	NOUN
ejpam-4553	312	20	.	.	PUNCT
ejpam-4553	313	1	let	let	VERB
ejpam-4553	313	2	a(x	a(x	NOUN
ejpam-4553	313	3	,	,	PUNCT
ejpam-4553	313	4	ξ	ξ	NOUN
ejpam-4553	313	5	)	)	PUNCT
ejpam-4553	313	6	=	=	SYM
ejpam-4553	313	7	∑	∑	PUNCT
ejpam-4553	313	8	j≥0	j≥0	PROPN
ejpam-4553	313	9	σj(x)φj(ξ	σj(x)φj(ξ	PROPN
ejpam-4553	313	10	)	)	PUNCT
ejpam-4553	313	11	with	with	ADP
ejpam-4553	313	12	the	the	DET
ejpam-4553	313	13	conditions	condition	NOUN
ejpam-4553	313	14	given	give	VERB
ejpam-4553	313	15	above	above	ADV
ejpam-4553	313	16	.	.	PUNCT
ejpam-4553	314	1	let	let	VERB
ejpam-4553	314	2	us	we	PRON
ejpam-4553	314	3	decompose	decompose	VERB
ejpam-4553	314	4	this	this	DET
ejpam-4553	314	5	symbol	symbol	NOUN
ejpam-4553	314	6	into	into	ADP
ejpam-4553	314	7	three	three	NUM
ejpam-4553	314	8	parts	part	NOUN
ejpam-4553	314	9	.	.	PUNCT
ejpam-4553	315	1	first	first	ADV
ejpam-4553	315	2	of	of	ADP
ejpam-4553	315	3	all	all	PRON
ejpam-4553	315	4	we	we	PRON
ejpam-4553	315	5	have	have	VERB
ejpam-4553	315	6	σj(x	σj(x	NOUN
ejpam-4553	315	7	)	)	PUNCT
ejpam-4553	316	1	=	=	NOUN
ejpam-4553	316	2	∞∑	∞∑	NUM
ejpam-4553	316	3	k=0	k=0	PROPN
ejpam-4553	316	4	φk(d)σj(x	φk(d)σj(x	PROPN
ejpam-4553	316	5	)	)	PUNCT
ejpam-4553	316	6	.	.	PUNCT
ejpam-4553	317	1	by	by	ADP
ejpam-4553	317	2	multiplying	multiply	VERB
ejpam-4553	317	3	each	each	DET
ejpam-4553	317	4	member	member	NOUN
ejpam-4553	317	5	by	by	ADP
ejpam-4553	317	6	φj(ξ	φj(ξ	NOUN
ejpam-4553	317	7	)	)	PUNCT
ejpam-4553	317	8	,	,	PUNCT
ejpam-4553	317	9	we	we	PRON
ejpam-4553	317	10	obtain	obtain	VERB
ejpam-4553	317	11	σj(x)φj(ξ	σj(x)φj(ξ	PROPN
ejpam-4553	317	12	)	)	PUNCT
ejpam-4553	318	1	=	=	PUNCT
ejpam-4553	318	2	(	(	PUNCT
ejpam-4553	318	3	∞∑	∞∑	DET
ejpam-4553	318	4	k=0	k=0	PROPN
ejpam-4553	318	5	φk(d)σj(x	φk(d)σj(x	PROPN
ejpam-4553	318	6	)	)	PUNCT
ejpam-4553	318	7	)	)	PUNCT
ejpam-4553	318	8	φj(ξ	φj(ξ	ADV
ejpam-4553	318	9	)	)	PUNCT
ejpam-4553	318	10	.	.	PUNCT
ejpam-4553	319	1	and	and	CCONJ
ejpam-4553	319	2	then	then	ADV
ejpam-4553	319	3	a(x	a(x	PROPN
ejpam-4553	319	4	,	,	PUNCT
ejpam-4553	319	5	ξ	ξ	NOUN
ejpam-4553	319	6	)	)	PUNCT
ejpam-4553	319	7	=	=	SYM
ejpam-4553	320	1	∞∑	∞∑	NUM
ejpam-4553	320	2	j=0	j=0	PROPN
ejpam-4553	320	3	(	(	PUNCT
ejpam-4553	320	4	∞∑	∞∑	NUM
ejpam-4553	320	5	k=0	k=0	PROPN
ejpam-4553	320	6	φk(d)σj(x	φk(d)σj(x	PROPN
ejpam-4553	320	7	)	)	PUNCT
ejpam-4553	320	8	)	)	PUNCT
ejpam-4553	320	9	φj(ξ	φj(ξ	ADV
ejpam-4553	320	10	)	)	PUNCT
ejpam-4553	320	11	.	.	PUNCT
ejpam-4553	321	1	by	by	ADP
ejpam-4553	321	2	setting	set	VERB
ejpam-4553	321	3	akj	akj	ADJ
ejpam-4553	321	4	=	=	SYM
ejpam-4553	321	5	φk(d)σj	φk(d)σj	ADV
ejpam-4553	321	6	we	we	PRON
ejpam-4553	321	7	have	have	VERB
ejpam-4553	321	8	a(x	a(x	NOUN
ejpam-4553	321	9	,	,	PUNCT
ejpam-4553	321	10	ξ	ξ	NOUN
ejpam-4553	321	11	)	)	PUNCT
ejpam-4553	321	12	=	=	SYM
ejpam-4553	322	1	∞∑	∞∑	NUM
ejpam-4553	322	2	j=0	j=0	PROPN
ejpam-4553	322	3	(	(	PUNCT
ejpam-4553	322	4	∞∑	∞∑	DET
ejpam-4553	322	5	k=0	k=0	PROPN
ejpam-4553	322	6	akj	akj	ADJ
ejpam-4553	322	7	)	)	PUNCT
ejpam-4553	322	8	φj(ξ	φj(ξ	ADV
ejpam-4553	322	9	)	)	PUNCT
ejpam-4553	322	10	.	.	PUNCT
ejpam-4553	323	1	(	(	PUNCT
ejpam-4553	323	2	11	11	NUM
ejpam-4553	323	3	)	)	PUNCT
ejpam-4553	323	4	now	now	ADV
ejpam-4553	323	5	we	we	PRON
ejpam-4553	323	6	rewrite	rewrite	VERB
ejpam-4553	323	7	(	(	PUNCT
ejpam-4553	323	8	11	11	NUM
ejpam-4553	323	9	)	)	PUNCT
ejpam-4553	323	10	as	as	ADP
ejpam-4553	323	11	a	a	DET
ejpam-4553	323	12	sum	sum	NOUN
ejpam-4553	323	13	of	of	ADP
ejpam-4553	323	14	three	three	NUM
ejpam-4553	323	15	parts	part	NOUN
ejpam-4553	323	16	a(x	a(x	NOUN
ejpam-4553	323	17	,	,	PUNCT
ejpam-4553	323	18	ξ	ξ	NOUN
ejpam-4553	323	19	)	)	PUNCT
ejpam-4553	323	20	=	=	SYM
ejpam-4553	323	21	∑	∑	PUNCT
ejpam-4553	323	22	j≥0	j≥0	PROPN
ejpam-4553	323	23	j−4∑	j−4∑	ADP
ejpam-4553	323	24	k=0	k=0	PROPN
ejpam-4553	323	25	akj(x	akj(x	PROPN
ejpam-4553	323	26	)	)	PUNCT
ejpam-4553	324	1	+	+	CCONJ
ejpam-4553	324	2	j+3∑	j+3∑	PROPN
ejpam-4553	324	3	k	k	PROPN
ejpam-4553	324	4	=	=	PROPN
ejpam-4553	324	5	j−3	j−3	PROPN
ejpam-4553	324	6	akj(x	akj(x	PROPN
ejpam-4553	324	7	)	)	PUNCT
ejpam-4553	324	8	+	+	CCONJ
ejpam-4553	325	1	∞∑	∞∑	NUM
ejpam-4553	325	2	k	k	X
ejpam-4553	325	3	=	=	SYM
ejpam-4553	325	4	j+4	j+4	NUM
ejpam-4553	325	5	akj(x	akj(x	NOUN
ejpam-4553	325	6	)	)	PUNCT
ejpam-4553	325	7	φj(ξ	φj(ξ	X
ejpam-4553	325	8	)	)	PUNCT
ejpam-4553	325	9	=	=	SYM
ejpam-4553	325	10	a1(x	a1(x	PROPN
ejpam-4553	325	11	,	,	PUNCT
ejpam-4553	325	12	ξ	ξ	NOUN
ejpam-4553	325	13	)	)	PUNCT
ejpam-4553	325	14	+	+	CCONJ
ejpam-4553	325	15	a2(x	a2(x	PROPN
ejpam-4553	325	16	,	,	PUNCT
ejpam-4553	325	17	ξ	ξ	X
ejpam-4553	325	18	)	)	PUNCT
ejpam-4553	325	19	+	+	CCONJ
ejpam-4553	325	20	a3(x	a3(x	PROPN
ejpam-4553	325	21	,	,	PUNCT
ejpam-4553	325	22	ξ	ξ	X
ejpam-4553	325	23	)	)	PUNCT
ejpam-4553	325	24	(	(	PUNCT
ejpam-4553	325	25	i	i	NOUN
ejpam-4553	325	26	)	)	PUNCT
ejpam-4553	325	27	let	let	VERB
ejpam-4553	325	28	φj(d)f	φj(d)f	VERB
ejpam-4553	326	1	=	=	SYM
ejpam-4553	326	2	fj	fj	PROPN
ejpam-4553	326	3	.	.	PUNCT
ejpam-4553	327	1	then	then	ADV
ejpam-4553	327	2	we	we	PRON
ejpam-4553	327	3	define	define	VERB
ejpam-4553	327	4	three	three	NUM
ejpam-4553	327	5	”	"	PUNCT
ejpam-4553	327	6	elementary	elementary	ADJ
ejpam-4553	327	7	”	"	PUNCT
ejpam-4553	327	8	pseudo	pseudo	NOUN
ejpam-4553	327	9	-	-	NOUN
ejpam-4553	327	10	differential	differential	ADJ
ejpam-4553	327	11	operators	operator	NOUN
ejpam-4553	327	12	:	:	PUNCT
ejpam-4553	327	13	a1(x	a1(x	NOUN
ejpam-4553	327	14	,	,	PUNCT
ejpam-4553	327	15	d)f	d)f	X
ejpam-4553	327	16	=	=	PUNCT
ejpam-4553	328	1	∞∑	∞∑	NUM
ejpam-4553	328	2	j=0	j=0	PROPN
ejpam-4553	328	3	(	(	PUNCT
ejpam-4553	328	4	j−4∑	j−4∑	ADV
ejpam-4553	328	5	k=0	k=0	PROPN
ejpam-4553	328	6	akjfj	akjfj	PROPN
ejpam-4553	328	7	)	)	PUNCT
ejpam-4553	328	8	,	,	PUNCT
ejpam-4553	328	9	a2(x	a2(x	PROPN
ejpam-4553	328	10	,	,	PUNCT
ejpam-4553	328	11	d)f	d)f	X
ejpam-4553	328	12	=	=	PUNCT
ejpam-4553	329	1	∞∑	∞∑	NUM
ejpam-4553	329	2	j=0	j=0	PRON
ejpam-4553	329	3			PROPN
ejpam-4553	329	4	j+3∑	j+3∑	PROPN
ejpam-4553	329	5	k	k	PROPN
ejpam-4553	329	6	=	=	PROPN
ejpam-4553	329	7	j−3	j−3	PROPN
ejpam-4553	329	8	akjfj	akjfj	NOUN
ejpam-4553	329	9			PROPN
ejpam-4553	329	10	,	,	PUNCT
ejpam-4553	329	11	a3(x	a3(x	PROPN
ejpam-4553	329	12	,	,	PUNCT
ejpam-4553	329	13	d)f	d)f	X
ejpam-4553	329	14	=	=	PUNCT
ejpam-4553	330	1	∞∑	∞∑	NUM
ejpam-4553	330	2	j=0	j=0	PRON
ejpam-4553	330	3			PROPN
ejpam-4553	330	4	∞∑	∞∑	ADJ
ejpam-4553	330	5	k	k	X
ejpam-4553	330	6	=	=	SYM
ejpam-4553	330	7	j+4	j+4	PROPN
ejpam-4553	330	8	akjfj	akjfj	NOUN
ejpam-4553	330	9	.	.	PROPN
ejpam-4553	330	10	(	(	PUNCT
ejpam-4553	330	11	ii	ii	NOUN
ejpam-4553	330	12	)	)	PUNCT
ejpam-4553	330	13	it	it	PRON
ejpam-4553	330	14	remains	remain	VERB
ejpam-4553	330	15	to	to	PART
ejpam-4553	330	16	estimate	estimate	VERB
ejpam-4553	330	17	each	each	PRON
ejpam-4553	330	18	of	of	ADP
ejpam-4553	330	19	these	these	DET
ejpam-4553	330	20	three	three	NUM
ejpam-4553	330	21	pseudo	pseudo	NOUN
ejpam-4553	330	22	-	-	ADJ
ejpam-4553	330	23	differential	differential	ADJ
ejpam-4553	330	24	operators	operator	NOUN
ejpam-4553	330	25	.	.	PUNCT
ejpam-4553	331	1	for	for	ADP
ejpam-4553	331	2	this	this	DET
ejpam-4553	331	3	purpose	purpose	NOUN
ejpam-4553	331	4	,	,	PUNCT
ejpam-4553	331	5	it	it	PRON
ejpam-4553	331	6	’s	’	VERB
ejpam-4553	331	7	necessary	necessary	ADJ
ejpam-4553	331	8	to	to	PART
ejpam-4553	331	9	estimate	estimate	VERB
ejpam-4553	331	10	∥akj∥l∞	∥akj∥l∞	PUNCT
ejpam-4553	331	11	.	.	PUNCT
ejpam-4553	332	1	let	let	VERB
ejpam-4553	332	2	us	we	PRON
ejpam-4553	332	3	recall	recall	VERB
ejpam-4553	332	4	the	the	DET
ejpam-4553	332	5	quasinorm	quasinorm	NOUN
ejpam-4553	332	6	of	of	ADP
ejpam-4553	332	7	cℓ	cℓ	ADP
ejpam-4553	332	8	∗	∗	NOUN
ejpam-4553	332	9	:	:	PUNCT
ejpam-4553	332	10	∥φk(d)σj∥cℓ	∥φk(d)σj∥cℓ	X
ejpam-4553	332	11	∗	∗	NOUN
ejpam-4553	332	12	=	=	PUNCT
ejpam-4553	332	13	supk	supk	PRON
ejpam-4553	332	14	2	2	NUM
ejpam-4553	332	15	kℓ	kℓ	NOUN
ejpam-4553	332	16	∥φk(d)σj∥l∞	∥φk(d)σj∥l∞	VERB
ejpam-4553	332	17	.	.	PUNCT
ejpam-4553	333	1	since	since	SCONJ
ejpam-4553	333	2	∥φk(d)σj∥cℓ	∥φk(d)σj∥cℓ	PROPN
ejpam-4553	333	3	∗	∗	NOUN
ejpam-4553	333	4	≤	≤	NUM
ejpam-4553	333	5	c	c	NOUN
ejpam-4553	333	6	∥σj∥cℓ	∥σj∥cℓ	PRON
ejpam-4553	333	7	∗	∗	NOUN
ejpam-4553	333	8	.	.	PUNCT
ejpam-4553	334	1	then	then	ADV
ejpam-4553	334	2	sup	sup	NOUN
ejpam-4553	334	3	k	k	PROPN
ejpam-4553	334	4	2kℓ	2kℓ	PROPN
ejpam-4553	334	5	∥φk(d)σj∥l∞	∥φk(d)σj∥l∞	PUNCT
ejpam-4553	334	6	≤	≤	PUNCT
ejpam-4553	334	7	c	c	NOUN
ejpam-4553	334	8	∥σj∥cℓ	∥σj∥cℓ	PRON
ejpam-4553	334	9	∗	∗	NOUN
ejpam-4553	334	10	.	.	PUNCT
ejpam-4553	335	1	mohamed	mohamed	PROPN
ejpam-4553	335	2	congo	congo	PROPN
ejpam-4553	335	3	,	,	PUNCT
ejpam-4553	335	4	m.	m.	PROPN
ejpam-4553	335	5	f.	f.	PROPN
ejpam-4553	335	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	335	7	/	/	SYM
ejpam-4553	335	8	eur	eur	PROPN
ejpam-4553	335	9	.	.	PUNCT
ejpam-4553	336	1	j.	j.	PROPN
ejpam-4553	336	2	pure	pure	PROPN
ejpam-4553	336	3	appl	appl	PROPN
ejpam-4553	336	4	.	.	PROPN
ejpam-4553	336	5	math	math	PROPN
ejpam-4553	336	6	,	,	PUNCT
ejpam-4553	336	7	15	15	NUM
ejpam-4553	336	8	(	(	PUNCT
ejpam-4553	336	9	4	4	NUM
ejpam-4553	336	10	)	)	PUNCT
ejpam-4553	336	11	(	(	PUNCT
ejpam-4553	336	12	2022	2022	NUM
ejpam-4553	336	13	)	)	PUNCT
ejpam-4553	336	14	,	,	PUNCT
ejpam-4553	336	15	1716	1716	NUM
ejpam-4553	336	16	-	-	SYM
ejpam-4553	336	17	1737	1737	NUM
ejpam-4553	336	18	1729	1729	NUM
ejpam-4553	336	19	using	use	VERB
ejpam-4553	336	20	(	(	PUNCT
ejpam-4553	336	21	9	9	NUM
ejpam-4553	336	22	)	)	PUNCT
ejpam-4553	336	23	,	,	PUNCT
ejpam-4553	336	24	we	we	PRON
ejpam-4553	336	25	obtain	obtain	VERB
ejpam-4553	336	26	∥akj∥l∞	∥akj∥l∞	PUNCT
ejpam-4553	336	27	≤	≤	NUM
ejpam-4553	336	28	c2jℓδ2−kℓ.	c2jℓδ2−kℓ.	X
ejpam-4553	336	29	(	(	PUNCT
ejpam-4553	336	30	12	12	NUM
ejpam-4553	336	31	)	)	PUNCT
ejpam-4553	336	32	we	we	PRON
ejpam-4553	336	33	are	be	AUX
ejpam-4553	336	34	ready	ready	ADJ
ejpam-4553	336	35	to	to	PART
ejpam-4553	336	36	estimate	estimate	VERB
ejpam-4553	336	37	the	the	DET
ejpam-4553	336	38	pseudo	pseudo	NOUN
ejpam-4553	336	39	-	-	NOUN
ejpam-4553	336	40	differential	differential	ADJ
ejpam-4553	336	41	operators	operator	NOUN
ejpam-4553	336	42	a1(x	a1(x	PRON
ejpam-4553	336	43	,	,	PUNCT
ejpam-4553	336	44	d	d	NOUN
ejpam-4553	336	45	)	)	PUNCT
ejpam-4553	336	46	,	,	PUNCT
ejpam-4553	336	47	a2(x	a2(x	PROPN
ejpam-4553	336	48	,	,	PUNCT
ejpam-4553	336	49	d	d	NOUN
ejpam-4553	336	50	)	)	PUNCT
ejpam-4553	336	51	and	and	CCONJ
ejpam-4553	336	52	a3(x	a3(x	PROPN
ejpam-4553	336	53	,	,	PUNCT
ejpam-4553	336	54	d	d	NOUN
ejpam-4553	336	55	)	)	PUNCT
ejpam-4553	336	56	.	.	PUNCT
ejpam-4553	337	1	•	•	NUM
ejpam-4553	337	2	the	the	DET
ejpam-4553	337	3	estimation	estimation	NOUN
ejpam-4553	337	4	of	of	ADP
ejpam-4553	337	5	a1(x	a1(x	PRON
ejpam-4553	337	6	,	,	PUNCT
ejpam-4553	337	7	d	d	NOUN
ejpam-4553	337	8	)	)	PUNCT
ejpam-4553	337	9	.	.	PUNCT
ejpam-4553	338	1	we	we	PRON
ejpam-4553	338	2	have	have	VERB
ejpam-4553	338	3	f	f	PROPN
ejpam-4553	338	4	(	(	PUNCT
ejpam-4553	338	5	j−4∑	j−4∑	ADV
ejpam-4553	338	6	k=0	k=0	PROPN
ejpam-4553	338	7	akjfj	akjfj	NOUN
ejpam-4553	338	8	)	)	PUNCT
ejpam-4553	339	1	=	=	PUNCT
ejpam-4553	339	2	j−4∑	j−4∑	X
ejpam-4553	339	3	k=0	k=0	PROPN
ejpam-4553	339	4	f	f	PROPN
ejpam-4553	339	5	(	(	PUNCT
ejpam-4553	339	6	φk(d)σj	φk(d)σj	ADJ
ejpam-4553	339	7	)	)	PUNCT
ejpam-4553	339	8	∗	∗	NOUN
ejpam-4553	339	9	f	f	PROPN
ejpam-4553	339	10	(	(	PUNCT
ejpam-4553	339	11	φj(d)f	φj(d)f	PROPN
ejpam-4553	339	12	)	)	PUNCT
ejpam-4553	339	13	=	=	PUNCT
ejpam-4553	340	1	j−4∑	j−4∑	NOUN
ejpam-4553	340	2	k=0	k=0	PROPN
ejpam-4553	340	3	(	(	PUNCT
ejpam-4553	340	4	ψkfσj	ψkfσj	NOUN
ejpam-4553	340	5	)	)	PUNCT
ejpam-4553	340	6	∗	∗	NOUN
ejpam-4553	340	7	(	(	PUNCT
ejpam-4553	340	8	ψjff	ψjff	PROPN
ejpam-4553	340	9	)	)	PUNCT
ejpam-4553	340	10	.	.	PUNCT
ejpam-4553	341	1	using	use	VERB
ejpam-4553	341	2	the	the	DET
ejpam-4553	341	3	fact	fact	NOUN
ejpam-4553	341	4	that	that	SCONJ
ejpam-4553	341	5	supp(f	supp(f	PROPN
ejpam-4553	341	6	∗	∗	VERB
ejpam-4553	341	7	g	g	NOUN
ejpam-4553	341	8	)	)	PUNCT
ejpam-4553	342	1	⊂	⊂	PROPN
ejpam-4553	342	2	suppf+suppg	suppf+suppg	PROPN
ejpam-4553	342	3	for	for	ADP
ejpam-4553	342	4	all	all	PRON
ejpam-4553	342	5	compactly	compactly	ADV
ejpam-4553	342	6	supported	support	VERB
ejpam-4553	342	7	distributions	distribution	NOUN
ejpam-4553	342	8	f	f	NOUN
ejpam-4553	342	9	,	,	PUNCT
ejpam-4553	342	10	g	g	PROPN
ejpam-4553	342	11	∈	∈	PROPN
ejpam-4553	342	12	s	s	PART
ejpam-4553	342	13	′	′	NOUN
ejpam-4553	342	14	,	,	PUNCT
ejpam-4553	342	15	we	we	PRON
ejpam-4553	342	16	have	have	VERB
ejpam-4553	342	17	suppf	suppf	NOUN
ejpam-4553	342	18	(	(	PUNCT
ejpam-4553	342	19	j−4∑	j−4∑	ADV
ejpam-4553	342	20	k=0	k=0	PROPN
ejpam-4553	342	21	akjfj	akjfj	PROPN
ejpam-4553	342	22	)	)	PUNCT
ejpam-4553	343	1	⊂	⊂	PROPN
ejpam-4553	343	2	{	{	PUNCT
ejpam-4553	343	3	ξ	ξ	X
ejpam-4553	343	4	∈	∈	PROPN
ejpam-4553	343	5	rn	rn	PROPN
ejpam-4553	343	6	:	:	PUNCT
ejpam-4553	343	7	|ξ|	|ξ|	AUX
ejpam-4553	343	8	∼	∼	VERB
ejpam-4553	343	9	2j+1	2j+1	NOUN
ejpam-4553	343	10	}	}	PUNCT
ejpam-4553	343	11	.	.	PUNCT
ejpam-4553	344	1	then	then	ADV
ejpam-4553	344	2	lemma	lemma	PROPN
ejpam-4553	344	3	7	7	NUM
ejpam-4553	344	4	yields	yield	NOUN
ejpam-4553	344	5	∥a1(x	∥a1(x	NOUN
ejpam-4553	344	6	,	,	PUNCT
ejpam-4553	344	7	d)f∥n	d)f∥n	PROPN
ejpam-4553	344	8	s	s	PART
ejpam-4553	344	9	(	(	PUNCT
ejpam-4553	344	10	·	·	PUNCT
ejpam-4553	344	11	)	)	PUNCT
ejpam-4553	344	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	344	13	(	(	PUNCT
ejpam-4553	344	14	·	·	PUNCT
ejpam-4553	344	15	)	)	PUNCT
ejpam-4553	344	16	=	=	SYM
ejpam-4553	344	17	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	345	1	∞∑	∞∑	NUM
ejpam-4553	345	2	j=0	j=0	PROPN
ejpam-4553	345	3	(	(	PUNCT
ejpam-4553	345	4	j−4∑	j−4∑	ADV
ejpam-4553	345	5	k=0	k=0	PROPN
ejpam-4553	345	6	akjfj	akjfj	PROPN
ejpam-4553	345	7	)	)	PUNCT
ejpam-4553	345	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	346	1	n	n	CCONJ
ejpam-4553	346	2	s	s	PROPN
ejpam-4553	346	3	(	(	PUNCT
ejpam-4553	346	4	·	·	PUNCT
ejpam-4553	346	5	)	)	PUNCT
ejpam-4553	346	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	346	7	(	(	PUNCT
ejpam-4553	346	8	·	·	PUNCT
ejpam-4553	346	9	)	)	PUNCT
ejpam-4553	347	1	≲	≲	PROPN
ejpam-4553	347	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	347	3	(	(	PUNCT
ejpam-4553	347	4	2js	2js	NOUN
ejpam-4553	347	5	(	(	PUNCT
ejpam-4553	347	6	·	·	PUNCT
ejpam-4553	347	7	)	)	PUNCT
ejpam-4553	347	8	j−4∑	j−4∑	X
ejpam-4553	348	1	k=0	k=0	PROPN
ejpam-4553	348	2	akjfj	akjfj	PROPN
ejpam-4553	348	3	)	)	PUNCT
ejpam-4553	348	4	j	j	PROPN
ejpam-4553	348	5	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	349	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	349	2	(	(	PUNCT
ejpam-4553	349	3	·	·	PUNCT
ejpam-4553	349	4	)	)	PUNCT
ejpam-4553	349	5	)	)	PUNCT
ejpam-4553	350	1	≲	≲	PROPN
ejpam-4553	350	2			PROPN
ejpam-4553	350	3	sup	sup	PROPN
ejpam-4553	350	4	j∈n0	j∈n0	VERB
ejpam-4553	350	5	max{j−4,0}∑	max{j−4,0}∑	PROPN
ejpam-4553	350	6	k=0	k=0	PROPN
ejpam-4553	350	7	∥akj∥l∞	∥akj∥l∞	CCONJ
ejpam-4553	350	8	∥∥∥∥(2js(·)φj(d)f	∥∥∥∥(2js(·)φj(d)f	PROPN
ejpam-4553	350	9	)	)	PUNCT
ejpam-4553	351	1	j	j	PROPN
ejpam-4553	351	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4553	351	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	351	4	(	(	PUNCT
ejpam-4553	351	5	·	·	PUNCT
ejpam-4553	351	6	)	)	PUNCT
ejpam-4553	351	7	)	)	PUNCT
ejpam-4553	352	1	≲	≲	PROPN
ejpam-4553	352	2	∥∥∥∥(2js(·)φj(d)f	∥∥∥∥(2js(·)φj(d)f	PROPN
ejpam-4553	352	3	)	)	PUNCT
ejpam-4553	353	1	j	j	PROPN
ejpam-4553	353	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4553	353	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	353	4	(	(	PUNCT
ejpam-4553	353	5	·	·	PUNCT
ejpam-4553	353	6	)	)	PUNCT
ejpam-4553	353	7	)	)	PUNCT
ejpam-4553	353	8	.	.	PUNCT
ejpam-4553	354	1	it	it	PRON
ejpam-4553	354	2	follows	follow	VERB
ejpam-4553	354	3	that	that	SCONJ
ejpam-4553	354	4	∥a1(x	∥a1(x	NOUN
ejpam-4553	354	5	,	,	PUNCT
ejpam-4553	354	6	d)f∥n	d)f∥n	PROPN
ejpam-4553	354	7	s	s	PART
ejpam-4553	354	8	(	(	PUNCT
ejpam-4553	354	9	·	·	PUNCT
ejpam-4553	354	10	)	)	PUNCT
ejpam-4553	354	11	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	354	12	(	(	PUNCT
ejpam-4553	354	13	·	·	PUNCT
ejpam-4553	354	14	)	)	PUNCT
ejpam-4553	354	15	≲	≲	PROPN
ejpam-4553	354	16	∥f∥n	∥f∥n	NUM
ejpam-4553	354	17	s	s	PART
ejpam-4553	354	18	(	(	PUNCT
ejpam-4553	354	19	·	·	PUNCT
ejpam-4553	354	20	)	)	PUNCT
ejpam-4553	354	21	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	354	22	(	(	PUNCT
ejpam-4553	354	23	·	·	PUNCT
ejpam-4553	354	24	)	)	PUNCT
ejpam-4553	354	25	.	.	PUNCT
ejpam-4553	355	1	•	•	NUM
ejpam-4553	355	2	estimation	estimation	NOUN
ejpam-4553	355	3	of	of	ADP
ejpam-4553	355	4	a2(x	a2(x	PROPN
ejpam-4553	355	5	,	,	PUNCT
ejpam-4553	355	6	d	d	NOUN
ejpam-4553	355	7	)	)	PUNCT
ejpam-4553	355	8	for	for	ADP
ejpam-4553	355	9	the	the	DET
ejpam-4553	355	10	second	second	ADJ
ejpam-4553	355	11	part	part	NOUN
ejpam-4553	355	12	∥a2(x	∥a2(x	PROPN
ejpam-4553	355	13	,	,	PUNCT
ejpam-4553	355	14	d)f∥n	d)f∥n	PROPN
ejpam-4553	355	15	s	s	PART
ejpam-4553	355	16	(	(	PUNCT
ejpam-4553	355	17	·	·	PUNCT
ejpam-4553	355	18	)	)	PUNCT
ejpam-4553	355	19	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	355	20	(	(	PUNCT
ejpam-4553	355	21	·	·	PUNCT
ejpam-4553	355	22	)	)	PUNCT
ejpam-4553	355	23	=	=	SYM
ejpam-4553	355	24	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	356	1	∞∑	∞∑	NUM
ejpam-4553	356	2	j=0	j=0	PRON
ejpam-4553	356	3			PROPN
ejpam-4553	356	4	j+3∑	j+3∑	PROPN
ejpam-4553	356	5	k	k	PROPN
ejpam-4553	356	6	=	=	NOUN
ejpam-4553	356	7	j−3	j−3	PROPN
ejpam-4553	356	8	akjfj	akjfj	NOUN
ejpam-4553	356	9	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	356	10	n	n	PRON
ejpam-4553	356	11	s	s	PROPN
ejpam-4553	356	12	(	(	PUNCT
ejpam-4553	356	13	·	·	PUNCT
ejpam-4553	356	14	)	)	PUNCT
ejpam-4553	356	15	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	356	16	(	(	PUNCT
ejpam-4553	356	17	·	·	PUNCT
ejpam-4553	356	18	)	)	PUNCT
ejpam-4553	356	19	,	,	PUNCT
ejpam-4553	356	20	let	let	VERB
ejpam-4553	356	21	us	we	PRON
ejpam-4553	356	22	first	first	ADV
ejpam-4553	356	23	observe	observe	VERB
ejpam-4553	356	24	that	that	SCONJ
ejpam-4553	356	25	f	f	PROPN
ejpam-4553	356	26			PROPN
ejpam-4553	356	27	j+3∑	j+3∑	PROPN
ejpam-4553	356	28	k	k	PROPN
ejpam-4553	356	29	=	=	ADJ
ejpam-4553	356	30	j−3	j−3	ADJ
ejpam-4553	356	31	akjfj	akjfj	NOUN
ejpam-4553	356	32			PROPN
ejpam-4553	356	33	=	=	SYM
ejpam-4553	356	34	j+3∑	j+3∑	PROPN
ejpam-4553	357	1	k	k	PROPN
ejpam-4553	358	1	=	=	PROPN
ejpam-4553	358	2	j−3	j−3	PROPN
ejpam-4553	358	3	f	f	X
ejpam-4553	358	4	(	(	PUNCT
ejpam-4553	358	5	φk(d)σj	φk(d)σj	ADJ
ejpam-4553	358	6	)	)	PUNCT
ejpam-4553	358	7	∗	∗	NOUN
ejpam-4553	358	8	f	f	PROPN
ejpam-4553	358	9	(	(	PUNCT
ejpam-4553	358	10	φj(d)f	φj(d)f	PROPN
ejpam-4553	358	11	)	)	PUNCT
ejpam-4553	358	12	mohamed	mohamed	PROPN
ejpam-4553	358	13	congo	congo	PROPN
ejpam-4553	358	14	,	,	PUNCT
ejpam-4553	358	15	m.	m.	PROPN
ejpam-4553	358	16	f.	f.	PROPN
ejpam-4553	358	17	ouedraogo	ouedraogo	PROPN
ejpam-4553	358	18	/	/	SYM
ejpam-4553	358	19	eur	eur	PROPN
ejpam-4553	358	20	.	.	PUNCT
ejpam-4553	359	1	j.	j.	PROPN
ejpam-4553	359	2	pure	pure	PROPN
ejpam-4553	359	3	appl	appl	PROPN
ejpam-4553	359	4	.	.	PROPN
ejpam-4553	359	5	math	math	PROPN
ejpam-4553	359	6	,	,	PUNCT
ejpam-4553	359	7	15	15	NUM
ejpam-4553	359	8	(	(	PUNCT
ejpam-4553	359	9	4	4	NUM
ejpam-4553	359	10	)	)	PUNCT
ejpam-4553	359	11	(	(	PUNCT
ejpam-4553	359	12	2022	2022	NUM
ejpam-4553	359	13	)	)	PUNCT
ejpam-4553	359	14	,	,	PUNCT
ejpam-4553	359	15	1716	1716	NUM
ejpam-4553	359	16	-	-	SYM
ejpam-4553	359	17	1737	1737	NUM
ejpam-4553	359	18	1730	1730	NUM
ejpam-4553	360	1	=	=	SYM
ejpam-4553	360	2	j+3∑	j+3∑	PROPN
ejpam-4553	360	3	k	k	X
ejpam-4553	360	4	=	=	X
ejpam-4553	360	5	j−3	j−3	X
ejpam-4553	360	6	(	(	PUNCT
ejpam-4553	360	7	φkfσj	φkfσj	NOUN
ejpam-4553	360	8	)	)	PUNCT
ejpam-4553	360	9	∗	∗	NOUN
ejpam-4553	360	10	(	(	PUNCT
ejpam-4553	360	11	φjff	φjff	VERB
ejpam-4553	360	12	)	)	PUNCT
ejpam-4553	360	13	.	.	PUNCT
ejpam-4553	361	1	therefore	therefore	ADV
ejpam-4553	361	2	f	f	PROPN
ejpam-4553	361	3			PROPN
ejpam-4553	361	4	j+3∑	j+3∑	PROPN
ejpam-4553	361	5	k	k	PROPN
ejpam-4553	361	6	=	=	ADJ
ejpam-4553	361	7	j−3	j−3	PROPN
ejpam-4553	361	8	akjfj	akjfj	NOUN
ejpam-4553	361	9			PROPN
ejpam-4553	361	10	is	be	AUX
ejpam-4553	361	11	supported	support	VERB
ejpam-4553	361	12	on	on	ADP
ejpam-4553	361	13	the	the	DET
ejpam-4553	361	14	ball	ball	NOUN
ejpam-4553	361	15	b(0	b(0	NOUN
ejpam-4553	361	16	,	,	PUNCT
ejpam-4553	361	17	2j+4	2j+4	NOUN
ejpam-4553	361	18	)	)	PUNCT
ejpam-4553	361	19	.	.	PUNCT
ejpam-4553	362	1	by	by	ADP
ejpam-4553	362	2	lemma	lemma	PROPN
ejpam-4553	362	3	8	8	NUM
ejpam-4553	362	4	,	,	PUNCT
ejpam-4553	362	5	∥a2(x	∥a2(x	PROPN
ejpam-4553	362	6	,	,	PUNCT
ejpam-4553	362	7	d)f∥n	d)f∥n	PROPN
ejpam-4553	362	8	s	s	PART
ejpam-4553	362	9	(	(	PUNCT
ejpam-4553	362	10	·	·	PUNCT
ejpam-4553	362	11	)	)	PUNCT
ejpam-4553	362	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	362	13	(	(	PUNCT
ejpam-4553	362	14	·	·	PUNCT
ejpam-4553	362	15	)	)	PUNCT
ejpam-4553	362	16	≲	≲	PROPN
ejpam-4553	362	17	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	362	18	2js	2js	ADP
ejpam-4553	362	19	(	(	PUNCT
ejpam-4553	362	20	·	·	PUNCT
ejpam-4553	362	21	)	)	PUNCT
ejpam-4553	362	22	j+3∑	j+3∑	PROPN
ejpam-4553	363	1	k	k	PROPN
ejpam-4553	363	2	=	=	PROPN
ejpam-4553	363	3	j−3	j−3	PROPN
ejpam-4553	363	4	akjfj	akjfj	NOUN
ejpam-4553	363	5			PROPN
ejpam-4553	363	6	j	j	PROPN
ejpam-4553	363	7	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	363	8	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	363	9	(	(	PUNCT
ejpam-4553	363	10	·	·	PUNCT
ejpam-4553	363	11	)	)	PUNCT
ejpam-4553	363	12	)	)	PUNCT
ejpam-4553	363	13	≤	≤	NUM
ejpam-4553	363	14	2−m	2−m	NUM
ejpam-4553	363	15	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4553	364	1			PROPN
ejpam-4553	364	2	j+3∑	j+3∑	PROPN
ejpam-4553	364	3	k	k	PROPN
ejpam-4553	364	4	=	=	PROPN
ejpam-4553	364	5	j−3	j−3	PROPN
ejpam-4553	364	6	∥akj∥l∞	∥akj∥l∞	PUNCT
ejpam-4553	364	7	2js(·)φj(d)f	2js(·)φj(d)f	NUM
ejpam-4553	364	8			PROPN
ejpam-4553	364	9	j	j	PROPN
ejpam-4553	364	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	365	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	365	2	(	(	PUNCT
ejpam-4553	365	3	·	·	PUNCT
ejpam-4553	365	4	)	)	PUNCT
ejpam-4553	365	5	)	)	PUNCT
ejpam-4553	365	6	.	.	PUNCT
ejpam-4553	366	1	now	now	ADV
ejpam-4553	366	2	using	use	VERB
ejpam-4553	366	3	(	(	PUNCT
ejpam-4553	366	4	12	12	NUM
ejpam-4553	366	5	)	)	PUNCT
ejpam-4553	366	6	one	one	NOUN
ejpam-4553	366	7	has	have	VERB
ejpam-4553	366	8	j+3∑	j+3∑	PROPN
ejpam-4553	366	9	k	k	PROPN
ejpam-4553	366	10	=	=	PROPN
ejpam-4553	366	11	j−3	j−3	NOUN
ejpam-4553	366	12	∥akj∥l∞	∥akj∥l∞	X
ejpam-4553	367	1	≲	≲	PROPN
ejpam-4553	367	2	3∑	3∑	PROPN
ejpam-4553	367	3	k=−3	k=−3	VERB
ejpam-4553	367	4	2−kℓ	2−kℓ	NUM
ejpam-4553	367	5	<	<	X
ejpam-4553	367	6	∞	∞	X
ejpam-4553	367	7	(	(	PUNCT
ejpam-4553	367	8	with	with	ADP
ejpam-4553	367	9	δ	δ	PROPN
ejpam-4553	367	10	=	=	SYM
ejpam-4553	367	11	1	1	NUM
ejpam-4553	367	12	)	)	PUNCT
ejpam-4553	367	13	and	and	CCONJ
ejpam-4553	367	14	then	then	ADV
ejpam-4553	367	15	∥a2(x	∥a2(x	ADV
ejpam-4553	367	16	,	,	PUNCT
ejpam-4553	367	17	d)f∥n	d)f∥n	PROPN
ejpam-4553	367	18	s	s	PART
ejpam-4553	367	19	(	(	PUNCT
ejpam-4553	367	20	·	·	PUNCT
ejpam-4553	367	21	)	)	PUNCT
ejpam-4553	367	22	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	367	23	(	(	PUNCT
ejpam-4553	367	24	·	·	PUNCT
ejpam-4553	367	25	)	)	PUNCT
ejpam-4553	367	26	≲	≲	PROPN
ejpam-4553	367	27	∥∥∥∥(2js(·)φj(d)f	∥∥∥∥(2js(·)φj(d)f	PROPN
ejpam-4553	367	28	)	)	PUNCT
ejpam-4553	367	29	j	j	PROPN
ejpam-4553	367	30	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4553	367	31	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	367	32	(	(	PUNCT
ejpam-4553	367	33	·	·	PUNCT
ejpam-4553	367	34	)	)	PUNCT
ejpam-4553	367	35	)	)	PUNCT
ejpam-4553	368	1	≲	≲	PROPN
ejpam-4553	368	2	∥f∥n	∥f∥n	NUM
ejpam-4553	368	3	s	s	PART
ejpam-4553	368	4	(	(	PUNCT
ejpam-4553	368	5	·	·	PUNCT
ejpam-4553	368	6	)	)	PUNCT
ejpam-4553	368	7	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	368	8	(	(	PUNCT
ejpam-4553	368	9	·	·	PUNCT
ejpam-4553	368	10	)	)	PUNCT
ejpam-4553	368	11	•	•	NUM
ejpam-4553	368	12	estimation	estimation	NOUN
ejpam-4553	368	13	of	of	ADP
ejpam-4553	368	14	a3(x	a3(x	PROPN
ejpam-4553	368	15	,	,	PUNCT
ejpam-4553	368	16	d	d	NOUN
ejpam-4553	368	17	)	)	PUNCT
ejpam-4553	368	18	since	since	SCONJ
ejpam-4553	368	19	f	f	PROPN
ejpam-4553	368	20			PROPN
ejpam-4553	368	21	∞∑	∞∑	PROPN
ejpam-4553	368	22	k	k	X
ejpam-4553	368	23	=	=	SYM
ejpam-4553	368	24	j+4	j+4	NUM
ejpam-4553	368	25	akjfj	akjfj	NOUN
ejpam-4553	368	26			PROPN
ejpam-4553	368	27	is	be	AUX
ejpam-4553	368	28	not	not	PART
ejpam-4553	368	29	supported	support	VERB
ejpam-4553	368	30	on	on	ADP
ejpam-4553	368	31	any	any	DET
ejpam-4553	368	32	ball	ball	NOUN
ejpam-4553	368	33	or	or	CCONJ
ejpam-4553	368	34	shell	shell	NOUN
ejpam-4553	368	35	,	,	PUNCT
ejpam-4553	368	36	we	we	PRON
ejpam-4553	368	37	can	can	AUX
ejpam-4553	368	38	not	not	PART
ejpam-4553	368	39	directly	directly	ADV
ejpam-4553	368	40	use	use	VERB
ejpam-4553	368	41	neither	neither	CCONJ
ejpam-4553	368	42	lemma	lemma	PROPN
ejpam-4553	368	43	7	7	NUM
ejpam-4553	368	44	nor	nor	CCONJ
ejpam-4553	368	45	lemma	lemma	PROPN
ejpam-4553	368	46	8	8	NUM
ejpam-4553	368	47	.	.	PUNCT
ejpam-4553	369	1	however	however	ADV
ejpam-4553	369	2	,	,	PUNCT
ejpam-4553	369	3	in	in	ADP
ejpam-4553	369	4	s	s	PRON
ejpam-4553	369	5	′	′	NOUN
ejpam-4553	369	6	we	we	PRON
ejpam-4553	369	7	can	can	AUX
ejpam-4553	369	8	write	write	VERB
ejpam-4553	369	9	∞∑	∞∑	NUM
ejpam-4553	369	10	j=0	j=0	PROPN
ejpam-4553	369	11	∞∑	∞∑	NUM
ejpam-4553	369	12	k	k	X
ejpam-4553	369	13	=	=	ADJ
ejpam-4553	369	14	j+4	j+4	NUM
ejpam-4553	369	15	akjfj	akjfj	NOUN
ejpam-4553	369	16	=	=	NOUN
ejpam-4553	370	1	∞∑	∞∑	NUM
ejpam-4553	370	2	k=4	k=4	PROPN
ejpam-4553	370	3	k−4∑	k−4∑	PROPN
ejpam-4553	370	4	j=0	j=0	PROPN
ejpam-4553	370	5	akjfj	akjfj	PROPN
ejpam-4553	370	6	.	.	PUNCT
ejpam-4553	371	1	we	we	PRON
ejpam-4553	371	2	have	have	VERB
ejpam-4553	371	3	f	f	PROPN
ejpam-4553	371	4	k−4∑	k−4∑	VERB
ejpam-4553	371	5	j=0	j=0	PROPN
ejpam-4553	371	6	akjfj	akjfj	VERB
ejpam-4553	371	7			PROPN
ejpam-4553	371	8	=	=	SYM
ejpam-4553	371	9	k−4∑	k−4∑	PROPN
ejpam-4553	371	10	j=0	j=0	PROPN
ejpam-4553	371	11	(	(	PUNCT
ejpam-4553	371	12	ψkfaj	ψkfaj	NOUN
ejpam-4553	371	13	)	)	PUNCT
ejpam-4553	371	14	∗	∗	NOUN
ejpam-4553	371	15	(	(	PUNCT
ejpam-4553	371	16	ψjff	ψjff	PROPN
ejpam-4553	371	17	)	)	PUNCT
ejpam-4553	371	18	then	then	ADV
ejpam-4553	371	19	suppf	suppf	PROPN
ejpam-4553	371	20	k−4∑	k−4∑	VERB
ejpam-4553	371	21	j=0	j=0	PROPN
ejpam-4553	371	22	akjfj	akjfj	PROPN
ejpam-4553	371	23			PROPN
ejpam-4553	371	24	⊂	⊂	PROPN
ejpam-4553	371	25	{	{	PUNCT
ejpam-4553	371	26	ξ	ξ	PROPN
ejpam-4553	371	27	∈	∈	PROPN
ejpam-4553	371	28	rn	rn	PROPN
ejpam-4553	371	29	:	:	PUNCT
ejpam-4553	371	30	|ξ|	|ξ|	VERB
ejpam-4553	371	31	∼	∼	NOUN
ejpam-4553	371	32	2k+1	2k+1	PROPN
ejpam-4553	371	33	}	}	PUNCT
ejpam-4553	371	34	.	.	PUNCT
ejpam-4553	372	1	mohamed	mohamed	PROPN
ejpam-4553	372	2	congo	congo	PROPN
ejpam-4553	372	3	,	,	PUNCT
ejpam-4553	372	4	m.	m.	PROPN
ejpam-4553	372	5	f.	f.	PROPN
ejpam-4553	372	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	372	7	/	/	SYM
ejpam-4553	372	8	eur	eur	PROPN
ejpam-4553	372	9	.	.	PUNCT
ejpam-4553	373	1	j.	j.	PROPN
ejpam-4553	373	2	pure	pure	PROPN
ejpam-4553	373	3	appl	appl	PROPN
ejpam-4553	373	4	.	.	PROPN
ejpam-4553	373	5	math	math	PROPN
ejpam-4553	373	6	,	,	PUNCT
ejpam-4553	373	7	15	15	NUM
ejpam-4553	373	8	(	(	PUNCT
ejpam-4553	373	9	4	4	NUM
ejpam-4553	373	10	)	)	PUNCT
ejpam-4553	373	11	(	(	PUNCT
ejpam-4553	373	12	2022	2022	NUM
ejpam-4553	373	13	)	)	PUNCT
ejpam-4553	373	14	,	,	PUNCT
ejpam-4553	373	15	1716	1716	NUM
ejpam-4553	373	16	-	-	SYM
ejpam-4553	373	17	1737	1737	NUM
ejpam-4553	373	18	1731	1731	NUM
ejpam-4553	373	19	then	then	ADV
ejpam-4553	373	20	lemma	lemma	PROPN
ejpam-4553	373	21	7	7	NUM
ejpam-4553	373	22	yields	yield	NOUN
ejpam-4553	373	23	∥a3(x	∥a3(x	PROPN
ejpam-4553	373	24	,	,	PUNCT
ejpam-4553	373	25	d)f∥n	d)f∥n	PROPN
ejpam-4553	373	26	s	s	PART
ejpam-4553	373	27	(	(	PUNCT
ejpam-4553	373	28	·	·	PUNCT
ejpam-4553	373	29	)	)	PUNCT
ejpam-4553	373	30	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	373	31	(	(	PUNCT
ejpam-4553	373	32	·	·	PUNCT
ejpam-4553	373	33	)	)	PUNCT
ejpam-4553	373	34	=	=	SYM
ejpam-4553	373	35	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	374	1	∞∑	∞∑	X
ejpam-4553	374	2	k=4	k=4	PROPN
ejpam-4553	374	3	k−4∑	k−4∑	VERB
ejpam-4553	374	4	j=0	j=0	PROPN
ejpam-4553	374	5	akjfj	akjfj	PROPN
ejpam-4553	374	6	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	375	1	n	n	PRON
ejpam-4553	375	2	s	s	PROPN
ejpam-4553	375	3	(	(	PUNCT
ejpam-4553	375	4	·	·	PUNCT
ejpam-4553	375	5	)	)	PUNCT
ejpam-4553	375	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	375	7	(	(	PUNCT
ejpam-4553	375	8	·	·	PUNCT
ejpam-4553	375	9	)	)	PUNCT
ejpam-4553	376	1	≲	≲	PROPN
ejpam-4553	376	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	376	3	2ks	2ks	X
ejpam-4553	376	4	(	(	PUNCT
ejpam-4553	376	5	·	·	PUNCT
ejpam-4553	376	6	)	)	PUNCT
ejpam-4553	376	7	k−4∑	k−4∑	PROPN
ejpam-4553	376	8	j=0	j=0	PROPN
ejpam-4553	376	9	akjfj	akjfj	NOUN
ejpam-4553	376	10			PROPN
ejpam-4553	376	11	k	k	X
ejpam-4553	376	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	376	13	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	376	14	(	(	PUNCT
ejpam-4553	376	15	·	·	PUNCT
ejpam-4553	376	16	)	)	PUNCT
ejpam-4553	376	17	)	)	PUNCT
ejpam-4553	377	1	≲	≲	PROPN
ejpam-4553	377	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	377	3	k−4∑	k−4∑	VERB
ejpam-4553	377	4	j=0	j=0	PROPN
ejpam-4553	377	5	∥akj∥l∞	∥akj∥l∞	PUNCT
ejpam-4553	378	1	2ks(·)φj(d)f	2ks(·)φj(d)f	NUM
ejpam-4553	378	2			PROPN
ejpam-4553	378	3	k	k	X
ejpam-4553	378	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	379	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	379	2	(	(	PUNCT
ejpam-4553	379	3	·	·	PUNCT
ejpam-4553	379	4	)	)	PUNCT
ejpam-4553	379	5	)	)	PUNCT
ejpam-4553	379	6	.	.	PUNCT
ejpam-4553	380	1	if	if	SCONJ
ejpam-4553	380	2	we	we	PRON
ejpam-4553	380	3	use	use	VERB
ejpam-4553	380	4	(	(	PUNCT
ejpam-4553	380	5	12	12	NUM
ejpam-4553	380	6	)	)	PUNCT
ejpam-4553	380	7	with	with	ADP
ejpam-4553	380	8	δ	δ	PROPN
ejpam-4553	380	9	=	=	SYM
ejpam-4553	380	10	1	1	NUM
ejpam-4553	380	11	,	,	PUNCT
ejpam-4553	380	12	we	we	PRON
ejpam-4553	380	13	have	have	VERB
ejpam-4553	380	14	∥a3(x	∥a3(x	PROPN
ejpam-4553	380	15	,	,	PUNCT
ejpam-4553	380	16	d)f∥n	d)f∥n	PROPN
ejpam-4553	380	17	s	s	PART
ejpam-4553	380	18	(	(	PUNCT
ejpam-4553	380	19	·	·	PUNCT
ejpam-4553	380	20	)	)	PUNCT
ejpam-4553	380	21	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	380	22	(	(	PUNCT
ejpam-4553	380	23	·	·	PUNCT
ejpam-4553	380	24	)	)	PUNCT
ejpam-4553	381	1	≲	≲	PROPN
ejpam-4553	381	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	381	3	k−4∑	k−4∑	VERB
ejpam-4553	381	4	j=0	j=0	PROPN
ejpam-4553	381	5	2jℓ2−kℓ2ks(·)φj(d)f	2jℓ2−kℓ2ks(·)φj(d)f	PROPN
ejpam-4553	381	6			PROPN
ejpam-4553	381	7	k	k	X
ejpam-4553	381	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	381	9	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	381	10	(	(	PUNCT
ejpam-4553	381	11	·	·	PUNCT
ejpam-4553	381	12	)	)	PUNCT
ejpam-4553	381	13	)	)	PUNCT
ejpam-4553	382	1	=	=	SYM
ejpam-4553	382	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	382	3	k−4∑	k−4∑	VERB
ejpam-4553	382	4	j=0	j=0	PROPN
ejpam-4553	382	5	2(k−j)(s(·)−ℓ)2js(·)φj(d)f	2(k−j)(s(·)−ℓ)2js(·)φj(d)f	NUM
ejpam-4553	383	1			PROPN
ejpam-4553	383	2	k	k	X
ejpam-4553	383	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	383	4	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	383	5	(	(	PUNCT
ejpam-4553	383	6	·	·	PUNCT
ejpam-4553	383	7	)	)	PUNCT
ejpam-4553	383	8	)	)	PUNCT
ejpam-4553	383	9	≤	≤	NOUN
ejpam-4553	383	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4553	383	11	k−4∑	k−4∑	VERB
ejpam-4553	383	12	j=0	j=0	PROPN
ejpam-4553	383	13	2−|k−j||s−−ℓ|2js(·)φj(d)f	2−|k−j||s−−ℓ|2js(·)φj(d)f	NUM
ejpam-4553	383	14			PROPN
ejpam-4553	383	15	k	k	X
ejpam-4553	383	16	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	384	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	384	2	(	(	PUNCT
ejpam-4553	384	3	·	·	PUNCT
ejpam-4553	384	4	)	)	PUNCT
ejpam-4553	384	5	)	)	PUNCT
ejpam-4553	385	1	≤	≤	NUM
ejpam-4553	385	2	∥∥∥∥∥∥	∥∥∥∥∥∥	X
ejpam-4553	386	1			PROPN
ejpam-4553	386	2	∞∑	∞∑	NUM
ejpam-4553	386	3	j=0	j=0	PROPN
ejpam-4553	386	4	2−|k−j||s−−ℓ|2js(·)φj(d)f	2−|k−j||s−−ℓ|2js(·)φj(d)f	NUM
ejpam-4553	386	5			PROPN
ejpam-4553	386	6	k	k	X
ejpam-4553	386	7	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	386	8	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	386	9	(	(	PUNCT
ejpam-4553	386	10	·	·	PUNCT
ejpam-4553	386	11	)	)	PUNCT
ejpam-4553	386	12	)	)	PUNCT
ejpam-4553	386	13	.	.	PUNCT
ejpam-4553	387	1	by	by	ADP
ejpam-4553	387	2	hypothesis	hypothesis	NOUN
ejpam-4553	387	3	we	we	PRON
ejpam-4553	387	4	have	have	AUX
ejpam-4553	387	5	|s−	|s−	VERB
ejpam-4553	387	6	−	−	ADP
ejpam-4553	387	7	ℓ|	ℓ|	PROPN
ejpam-4553	387	8	>	>	X
ejpam-4553	387	9	0	0	X
ejpam-4553	387	10	.	.	PUNCT
ejpam-4553	388	1	therefore	therefore	ADV
ejpam-4553	388	2	,	,	PUNCT
ejpam-4553	388	3	by	by	ADP
ejpam-4553	388	4	lemma	lemma	PROPN
ejpam-4553	388	5	5∥∥∥∥∥∥	5∥∥∥∥∥∥	NUM
ejpam-4553	388	6	k−4∑	k−4∑	ADJ
ejpam-4553	388	7	j=0	j=0	PROPN
ejpam-4553	388	8	2−|k−j||s−−ℓ|2js(·)φj(d)f	2−|k−j||s−−ℓ|2js(·)φj(d)f	NUM
ejpam-4553	388	9			PROPN
ejpam-4553	388	10	j	j	PROPN
ejpam-4553	388	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	388	12	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	388	13	(	(	PUNCT
ejpam-4553	388	14	·	·	PUNCT
ejpam-4553	388	15	)	)	PUNCT
ejpam-4553	388	16	)	)	PUNCT
ejpam-4553	389	1	≲	≲	PROPN
ejpam-4553	389	2	∥∥∥(2js(·)φj(d)f	∥∥∥(2js(·)φj(d)f	NUM
ejpam-4553	389	3	)	)	PUNCT
ejpam-4553	390	1	k	k	PROPN
ejpam-4553	390	2	∥∥∥	∥∥∥	PROPN
ejpam-4553	390	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	390	4	(	(	PUNCT
ejpam-4553	390	5	·	·	PUNCT
ejpam-4553	390	6	)	)	PUNCT
ejpam-4553	390	7	)	)	PUNCT
ejpam-4553	390	8	.	.	PUNCT
ejpam-4553	391	1	then	then	ADV
ejpam-4553	391	2	∥a3(x	∥a3(x	PROPN
ejpam-4553	391	3	,	,	PUNCT
ejpam-4553	391	4	d)f∥n	d)f∥n	PROPN
ejpam-4553	391	5	s	s	PART
ejpam-4553	391	6	(	(	PUNCT
ejpam-4553	391	7	·	·	PUNCT
ejpam-4553	391	8	)	)	PUNCT
ejpam-4553	391	9	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	391	10	(	(	PUNCT
ejpam-4553	391	11	·	·	PUNCT
ejpam-4553	391	12	)	)	PUNCT
ejpam-4553	391	13	≲	≲	PROPN
ejpam-4553	391	14	∥f∥n	∥f∥n	NUM
ejpam-4553	391	15	s	s	PART
ejpam-4553	391	16	(	(	PUNCT
ejpam-4553	391	17	·	·	PUNCT
ejpam-4553	391	18	)	)	PUNCT
ejpam-4553	391	19	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	391	20	(	(	PUNCT
ejpam-4553	391	21	·	·	PUNCT
ejpam-4553	391	22	)	)	PUNCT
ejpam-4553	391	23	.	.	PUNCT
ejpam-4553	392	1	the	the	DET
ejpam-4553	392	2	proof	proof	NOUN
ejpam-4553	392	3	is	be	AUX
ejpam-4553	392	4	completed	complete	VERB
ejpam-4553	392	5	.	.	PUNCT
ejpam-4553	393	1	□	□	PUNCT
ejpam-4553	393	2	4.2	4.2	NUM
ejpam-4553	393	3	.	.	PUNCT
ejpam-4553	393	4	thet	thet	PROPN
ejpam-4553	393	5	adjoint	adjoint	PROPN
ejpam-4553	393	6	operator	operator	NOUN
ejpam-4553	393	7	estimate	estimate	NOUN
ejpam-4553	393	8	in	in	ADP
ejpam-4553	393	9	this	this	DET
ejpam-4553	393	10	subsection	subsection	NOUN
ejpam-4553	393	11	,	,	PUNCT
ejpam-4553	393	12	let	let	VERB
ejpam-4553	393	13	us	we	PRON
ejpam-4553	393	14	go	go	VERB
ejpam-4553	393	15	further	far	ADV
ejpam-4553	393	16	by	by	ADP
ejpam-4553	393	17	studying	study	VERB
ejpam-4553	393	18	the	the	DET
ejpam-4553	393	19	boundedness	boundedness	NOUN
ejpam-4553	393	20	of	of	ADP
ejpam-4553	393	21	the	the	DET
ejpam-4553	393	22	adjoint	adjoint	NOUN
ejpam-4553	393	23	operator	operator	NOUN
ejpam-4553	393	24	.	.	PUNCT
ejpam-4553	394	1	let	let	VERB
ejpam-4553	394	2	the	the	DET
ejpam-4553	394	3	adjoint	adjoint	NOUN
ejpam-4553	394	4	operator	operator	NOUN
ejpam-4553	394	5	a∗	a∗	NOUN
ejpam-4553	394	6	of	of	ADP
ejpam-4553	394	7	the	the	DET
ejpam-4553	394	8	operator	operator	NOUN
ejpam-4553	394	9	a	a	DET
ejpam-4553	394	10	defined	define	VERB
ejpam-4553	394	11	by∫	by∫	NOUN
ejpam-4553	394	12	(	(	PUNCT
ejpam-4553	394	13	af)gdx	af)gdx	X
ejpam-4553	394	14	=	=	SYM
ejpam-4553	394	15	∫	∫	PROPN
ejpam-4553	394	16	fa∗gdx	fa∗gdx	PROPN
ejpam-4553	394	17	f	f	PROPN
ejpam-4553	394	18	,	,	PUNCT
ejpam-4553	394	19	g	g	PROPN
ejpam-4553	394	20	∈	∈	PROPN
ejpam-4553	394	21	s.	s.	PROPN
ejpam-4553	394	22	(	(	PUNCT
ejpam-4553	394	23	13	13	NUM
ejpam-4553	394	24	)	)	PUNCT
ejpam-4553	394	25	mohamed	mohamed	PROPN
ejpam-4553	394	26	congo	congo	PROPN
ejpam-4553	394	27	,	,	PUNCT
ejpam-4553	394	28	m.	m.	PROPN
ejpam-4553	394	29	f.	f.	PROPN
ejpam-4553	394	30	ouedraogo	ouedraogo	PROPN
ejpam-4553	394	31	/	/	SYM
ejpam-4553	394	32	eur	eur	PROPN
ejpam-4553	394	33	.	.	PUNCT
ejpam-4553	395	1	j.	j.	PROPN
ejpam-4553	395	2	pure	pure	PROPN
ejpam-4553	395	3	appl	appl	PROPN
ejpam-4553	395	4	.	.	PROPN
ejpam-4553	395	5	math	math	PROPN
ejpam-4553	395	6	,	,	PUNCT
ejpam-4553	395	7	15	15	NUM
ejpam-4553	395	8	(	(	PUNCT
ejpam-4553	395	9	4	4	NUM
ejpam-4553	395	10	)	)	PUNCT
ejpam-4553	395	11	(	(	PUNCT
ejpam-4553	395	12	2022	2022	NUM
ejpam-4553	395	13	)	)	PUNCT
ejpam-4553	395	14	,	,	PUNCT
ejpam-4553	395	15	1716	1716	NUM
ejpam-4553	395	16	-	-	SYM
ejpam-4553	395	17	1737	1737	NUM
ejpam-4553	395	18	1732	1732	NUM
ejpam-4553	395	19	since	since	SCONJ
ejpam-4553	395	20	an	an	DET
ejpam-4553	395	21	operator	operator	NOUN
ejpam-4553	395	22	a(x	a(x	NOUN
ejpam-4553	395	23	,	,	PUNCT
ejpam-4553	395	24	d	d	NOUN
ejpam-4553	395	25	)	)	PUNCT
ejpam-4553	395	26	with	with	ADP
ejpam-4553	395	27	symbol	symbol	NOUN
ejpam-4553	395	28	a(x	a(x	NOUN
ejpam-4553	395	29	,	,	PUNCT
ejpam-4553	395	30	ξ	ξ	NOUN
ejpam-4553	395	31	)	)	PUNCT
ejpam-4553	395	32	∈	∈	NOUN
ejpam-4553	395	33	cℓ	cℓ	ADP
ejpam-4553	395	34	∗s	∗s	PROPN
ejpam-4553	395	35	0	0	NUM
ejpam-4553	395	36	1,δ	1,δ	NUM
ejpam-4553	395	37	can	can	AUX
ejpam-4553	395	38	be	be	AUX
ejpam-4553	395	39	decomposed	decompose	VERB
ejpam-4553	395	40	in	in	ADP
ejpam-4553	395	41	the	the	DET
ejpam-4553	395	42	form	form	NOUN
ejpam-4553	395	43	a(x	a(x	NOUN
ejpam-4553	395	44	,	,	PUNCT
ejpam-4553	395	45	d	d	NOUN
ejpam-4553	395	46	)	)	PUNCT
ejpam-4553	395	47	=	=	SYM
ejpam-4553	396	1	a1(x	a1(x	NOUN
ejpam-4553	396	2	,	,	PUNCT
ejpam-4553	396	3	d	d	NOUN
ejpam-4553	396	4	)	)	PUNCT
ejpam-4553	396	5	+	+	CCONJ
ejpam-4553	396	6	a2(x	a2(x	PROPN
ejpam-4553	396	7	,	,	PUNCT
ejpam-4553	396	8	d	d	NOUN
ejpam-4553	396	9	)	)	PUNCT
ejpam-4553	396	10	+	+	CCONJ
ejpam-4553	396	11	a3(x	a3(x	PROPN
ejpam-4553	396	12	,	,	PUNCT
ejpam-4553	396	13	d	d	NOUN
ejpam-4553	396	14	)	)	PUNCT
ejpam-4553	396	15	,	,	PUNCT
ejpam-4553	396	16	then	then	ADV
ejpam-4553	396	17	its	its	PRON
ejpam-4553	396	18	adjoint	adjoint	NOUN
ejpam-4553	396	19	a(x	a(x	NOUN
ejpam-4553	396	20	,	,	PUNCT
ejpam-4553	396	21	d)∗	d)∗	PROPN
ejpam-4553	396	22	can	can	AUX
ejpam-4553	396	23	be	be	AUX
ejpam-4553	396	24	written	write	VERB
ejpam-4553	396	25	as	as	ADP
ejpam-4553	396	26	follow	follow	VERB
ejpam-4553	396	27	a(x	a(x	NOUN
ejpam-4553	396	28	,	,	PUNCT
ejpam-4553	396	29	d)∗	d)∗	PROPN
ejpam-4553	396	30	=	=	SYM
ejpam-4553	396	31	a1(x	a1(x	PROPN
ejpam-4553	396	32	,	,	PUNCT
ejpam-4553	396	33	d)∗	d)∗	PROPN
ejpam-4553	396	34	+	+	CCONJ
ejpam-4553	396	35	a2(x	a2(x	PROPN
ejpam-4553	396	36	,	,	PUNCT
ejpam-4553	396	37	d)∗	d)∗	PROPN
ejpam-4553	396	38	+	+	CCONJ
ejpam-4553	396	39	a3(x	a3(x	PROPN
ejpam-4553	396	40	,	,	PUNCT
ejpam-4553	396	41	d)∗.	d)∗.	NOUN
ejpam-4553	396	42	this	this	DET
ejpam-4553	396	43	method	method	NOUN
ejpam-4553	396	44	has	have	AUX
ejpam-4553	396	45	already	already	ADV
ejpam-4553	396	46	been	be	AUX
ejpam-4553	396	47	used	use	VERB
ejpam-4553	396	48	by	by	ADP
ejpam-4553	396	49	marschall	marschall	NOUN
ejpam-4553	396	50	in	in	ADP
ejpam-4553	396	51	[	[	X
ejpam-4553	396	52	11	11	NUM
ejpam-4553	396	53	]	]	PUNCT
ejpam-4553	396	54	and	and	CCONJ
ejpam-4553	396	55	[	[	X
ejpam-4553	396	56	12	12	NUM
ejpam-4553	396	57	]	]	PUNCT
ejpam-4553	396	58	.	.	PUNCT
ejpam-4553	397	1	let	let	VERB
ejpam-4553	397	2	’s	’s	NOUN
ejpam-4553	397	3	calculate	calculate	VERB
ejpam-4553	397	4	aλ(x	aλ(x	PUNCT
ejpam-4553	397	5	,	,	PUNCT
ejpam-4553	397	6	d)∗	d)∗	PROPN
ejpam-4553	397	7	for	for	ADP
ejpam-4553	397	8	λ	λ	PROPN
ejpam-4553	397	9	=	=	SYM
ejpam-4553	397	10	1	1	NUM
ejpam-4553	397	11	,	,	PUNCT
ejpam-4553	397	12	2	2	NUM
ejpam-4553	397	13	,	,	PUNCT
ejpam-4553	397	14	3	3	NUM
ejpam-4553	397	15	.	.	X
ejpam-4553	398	1	for	for	ADP
ejpam-4553	398	2	that	that	PRON
ejpam-4553	398	3	,	,	PUNCT
ejpam-4553	398	4	let	let	VERB
ejpam-4553	398	5	aλ(x	aλ(x	ADV
ejpam-4553	398	6	,	,	PUNCT
ejpam-4553	398	7	d)f	d)f	X
ejpam-4553	398	8	=	=	PUNCT
ejpam-4553	398	9	∑	∑	PUNCT
ejpam-4553	398	10	j∈iλ	j∈iλ	PROPN
ejpam-4553	398	11	∑	∑	PROPN
ejpam-4553	398	12	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	398	13	akjfj	akjfj	PROPN
ejpam-4553	398	14	where	where	SCONJ
ejpam-4553	398	15	iλ	iλ	PROPN
ejpam-4553	398	16	⊂	⊂	PROPN
ejpam-4553	398	17	n0	n0	PROPN
ejpam-4553	398	18	,	,	PUNCT
ejpam-4553	398	19	i	i	PRON
ejpam-4553	398	20	′	′	VERB
ejpam-4553	399	1	λ	λ	PROPN
ejpam-4553	399	2	⊂	⊂	PROPN
ejpam-4553	399	3	n0	n0	PROPN
ejpam-4553	399	4	.	.	PUNCT
ejpam-4553	400	1	using	use	VERB
ejpam-4553	400	2	(	(	PUNCT
ejpam-4553	400	3	13),∫	13),∫	NUM
ejpam-4553	400	4	(	(	PUNCT
ejpam-4553	400	5	aλ(x	aλ(x	X
ejpam-4553	400	6	,	,	PUNCT
ejpam-4553	400	7	d)f(x	d)f(x	NOUN
ejpam-4553	400	8	)	)	PUNCT
ejpam-4553	400	9	)	)	PUNCT
ejpam-4553	401	1	ḡ(x)dx	ḡ(x)dx	PROPN
ejpam-4553	401	2	=	=	SYM
ejpam-4553	401	3	∫	∫	PROPN
ejpam-4553	401	4	∑	∑	PUNCT
ejpam-4553	401	5	j∈iλ	j∈iλ	PROPN
ejpam-4553	401	6	∑	∑	PUNCT
ejpam-4553	401	7	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	401	8	akjφj(d)f(x)g(x)dx	akjφj(d)f(x)g(x)dx	NOUN
ejpam-4553	401	9	=	=	SYM
ejpam-4553	401	10	∫	∫	PROPN
ejpam-4553	401	11	∑	∑	NOUN
ejpam-4553	401	12	j∈iλ	j∈iλ	PROPN
ejpam-4553	401	13	∑	∑	PUNCT
ejpam-4553	401	14	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	401	15	f−1(φjff)akjg	f−1(φjff)akjg	PRON
ejpam-4553	401	16			PROPN
ejpam-4553	401	17	(	(	PUNCT
ejpam-4553	401	18	x)dx	x)dx	PROPN
ejpam-4553	401	19	.	.	PUNCT
ejpam-4553	402	1	plancherel	plancherel	PROPN
ejpam-4553	402	2	’s	’s	PART
ejpam-4553	402	3	theorem	theorem	ADJ
ejpam-4553	402	4	yields	yield	NOUN
ejpam-4553	402	5	∫	∫	PROPN
ejpam-4553	402	6	(	(	PUNCT
ejpam-4553	402	7	aλ(x	aλ(x	X
ejpam-4553	402	8	,	,	PUNCT
ejpam-4553	402	9	d)f(x	d)f(x	NOUN
ejpam-4553	402	10	)	)	PUNCT
ejpam-4553	402	11	)	)	PUNCT
ejpam-4553	403	1	ḡ(x)dx	ḡ(x)dx	PROPN
ejpam-4553	403	2	=	=	SYM
ejpam-4553	403	3	∫	∫	PROPN
ejpam-4553	403	4	f(x	f(x	PROPN
ejpam-4553	403	5	)	)	PUNCT
ejpam-4553	403	6	∑	∑	NOUN
ejpam-4553	403	7	j∈iλ	j∈iλ	PROPN
ejpam-4553	403	8	∑	∑	PROPN
ejpam-4553	403	9	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	403	10	f−1	f−1	PROPN
ejpam-4553	403	11	(	(	PUNCT
ejpam-4553	403	12	φjf(akjg	φjf(akjg	NOUN
ejpam-4553	403	13	)	)	PUNCT
ejpam-4553	403	14	)	)	PUNCT
ejpam-4553	403	15	(x)dx	(x)dx	VERB
ejpam-4553	403	16	.	.	PUNCT
ejpam-4553	404	1	then	then	ADV
ejpam-4553	404	2	,	,	PUNCT
ejpam-4553	404	3	the	the	DET
ejpam-4553	404	4	adjoint	adjoint	NOUN
ejpam-4553	404	5	of	of	ADP
ejpam-4553	404	6	aλ(x	aλ(x	ADJ
ejpam-4553	404	7	,	,	PUNCT
ejpam-4553	404	8	d	d	X
ejpam-4553	404	9	)	)	PUNCT
ejpam-4553	404	10	is	be	AUX
ejpam-4553	404	11	aλ(x	aλ(x	ADJ
ejpam-4553	404	12	,	,	PUNCT
ejpam-4553	404	13	d)∗f	d)∗f	X
ejpam-4553	404	14	=	=	PUNCT
ejpam-4553	404	15	∑	∑	PUNCT
ejpam-4553	404	16	j∈iλ	j∈iλ	PROPN
ejpam-4553	404	17	∑	∑	PROPN
ejpam-4553	404	18	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	404	19	φj(d	φj(d	PUNCT
ejpam-4553	404	20	)	)	PUNCT
ejpam-4553	404	21	(	(	PUNCT
ejpam-4553	404	22	akjf	akjf	PROPN
ejpam-4553	404	23	)	)	PUNCT
ejpam-4553	404	24	=	=	SYM
ejpam-4553	404	25	∑	∑	PUNCT
ejpam-4553	404	26	j∈iλ	j∈iλ	PROPN
ejpam-4553	404	27	∑	∑	PROPN
ejpam-4553	404	28	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	404	29	φj(d	φj(d	PUNCT
ejpam-4553	404	30	)	)	PUNCT
ejpam-4553	404	31	(	(	PUNCT
ejpam-4553	404	32	akj	akj	PROPN
ejpam-4553	404	33	∞∑	∞∑	PROPN
ejpam-4553	404	34	k′=0	k′=0	PROPN
ejpam-4553	404	35	φk′(d)f	φk′(d)f	PROPN
ejpam-4553	404	36	)	)	PUNCT
ejpam-4553	404	37	.	.	PUNCT
ejpam-4553	405	1	thus	thus	ADV
ejpam-4553	405	2	aλ(x	aλ(x	X
ejpam-4553	405	3	,	,	PUNCT
ejpam-4553	405	4	d)∗f	d)∗f	X
ejpam-4553	405	5	=	=	PUNCT
ejpam-4553	405	6	∑	∑	PUNCT
ejpam-4553	405	7	j∈iλ	j∈iλ	PROPN
ejpam-4553	405	8	∑	∑	PROPN
ejpam-4553	405	9	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	405	10	φj(d	φj(d	PUNCT
ejpam-4553	405	11	)	)	PUNCT
ejpam-4553	405	12	(	(	PUNCT
ejpam-4553	405	13	akj	akj	PROPN
ejpam-4553	405	14	∞∑	∞∑	DET
ejpam-4553	405	15	k′=0	k′=0	PROPN
ejpam-4553	405	16	fk′	fk′	NOUN
ejpam-4553	405	17	)	)	PUNCT
ejpam-4553	405	18	=	=	SYM
ejpam-4553	405	19	∑	∑	PUNCT
ejpam-4553	405	20	j∈iλ	j∈iλ	PROPN
ejpam-4553	405	21	∑	∑	PROPN
ejpam-4553	405	22	k∈i′λ	k∈i′λ	PROPN
ejpam-4553	405	23	∞∑	∞∑	PROPN
ejpam-4553	405	24	k′=0	k′=0	PROPN
ejpam-4553	405	25	φj(d	φj(d	PUNCT
ejpam-4553	405	26	)	)	PUNCT
ejpam-4553	405	27	(	(	PUNCT
ejpam-4553	405	28	akjfk′	akjfk′	NUM
ejpam-4553	405	29	)	)	PUNCT
ejpam-4553	405	30	for	for	ADP
ejpam-4553	405	31	λ	λ	NOUN
ejpam-4553	405	32	=	=	SYM
ejpam-4553	405	33	1	1	NUM
ejpam-4553	405	34	,	,	PUNCT
ejpam-4553	405	35	2	2	NUM
ejpam-4553	405	36	,	,	PUNCT
ejpam-4553	405	37	3	3	NUM
ejpam-4553	405	38	(	(	PUNCT
ejpam-4553	405	39	14	14	NUM
ejpam-4553	405	40	)	)	PUNCT
ejpam-4553	405	41	one	one	NOUN
ejpam-4553	405	42	has	have	VERB
ejpam-4553	405	43	f	f	X
ejpam-4553	405	44	{	{	PUNCT
ejpam-4553	405	45	φj(d	φj(d	NOUN
ejpam-4553	405	46	)	)	PUNCT
ejpam-4553	405	47	(	(	PUNCT
ejpam-4553	405	48	akjfk′	akjfk′	NOUN
ejpam-4553	405	49	)	)	PUNCT
ejpam-4553	405	50	}	}	PUNCT
ejpam-4553	406	1	=	=	SYM
ejpam-4553	406	2	φjf	φjf	X
ejpam-4553	406	3	{	{	PUNCT
ejpam-4553	406	4	f−1(φkfσj	f−1(φkfσj	NOUN
ejpam-4553	406	5	)	)	PUNCT
ejpam-4553	406	6	·	·	PUNCT
ejpam-4553	406	7	f−1(φk′ff	f−1(φk′ff	X
ejpam-4553	406	8	)	)	PUNCT
ejpam-4553	406	9	}	}	PUNCT
ejpam-4553	406	10	.	.	PUNCT
ejpam-4553	407	1	the	the	DET
ejpam-4553	407	2	intersection	intersection	NOUN
ejpam-4553	407	3	of	of	ADP
ejpam-4553	407	4	the	the	DET
ejpam-4553	407	5	supports	support	NOUN
ejpam-4553	407	6	of	of	ADP
ejpam-4553	407	7	φj	φj	NOUN
ejpam-4553	407	8	and	and	CCONJ
ejpam-4553	407	9	f	f	PROPN
ejpam-4553	407	10	{	{	PUNCT
ejpam-4553	407	11	f−1(φkfσj	f−1(φkfσj	PROPN
ejpam-4553	407	12	)	)	PUNCT
ejpam-4553	407	13	·	·	PUNCT
ejpam-4553	407	14	f−1(φk′ff	f−1(φk′ff	X
ejpam-4553	407	15	)	)	PUNCT
ejpam-4553	407	16	}	}	PUNCT
ejpam-4553	407	17	is	be	AUX
ejpam-4553	407	18	empty	empty	ADJ
ejpam-4553	407	19	if	if	SCONJ
ejpam-4553	407	20	the	the	DET
ejpam-4553	407	21	non	non	ADJ
ejpam-4553	407	22	-	-	ADJ
ejpam-4553	407	23	negative	negative	ADJ
ejpam-4553	407	24	integer	integer	NOUN
ejpam-4553	407	25	k′	k′	PROPN
ejpam-4553	407	26	dœs	dœs	PROPN
ejpam-4553	407	27	not	not	PART
ejpam-4553	407	28	verify	verify	VERB
ejpam-4553	407	29	the	the	DET
ejpam-4553	407	30	following	follow	VERB
ejpam-4553	407	31	cases	case	NOUN
ejpam-4553	407	32	(	(	PUNCT
ejpam-4553	407	33	see	see	VERB
ejpam-4553	407	34	[	[	X
ejpam-4553	407	35	14	14	NUM
ejpam-4553	407	36	]	]	PUNCT
ejpam-4553	407	37	and	and	CCONJ
ejpam-4553	407	38	[	[	X
ejpam-4553	407	39	11]):	11]):	NUM
ejpam-4553	407	40	j	j	NOUN
ejpam-4553	407	41	−	−	NOUN
ejpam-4553	408	1	3	3	NUM
ejpam-4553	408	2	≤	≤	PROPN
ejpam-4553	408	3	k′	k′	PROPN
ejpam-4553	408	4	≤	≤	NUM
ejpam-4553	408	5	j	j	PROPN
ejpam-4553	408	6	+	+	CCONJ
ejpam-4553	408	7	3	3	NUM
ejpam-4553	408	8	and	and	CCONJ
ejpam-4553	408	9	k	k	NOUN
ejpam-4553	408	10	=	=	SYM
ejpam-4553	408	11	0	0	PROPN
ejpam-4553	408	12	,	,	PUNCT
ejpam-4553	408	13	.	.	PUNCT
ejpam-4553	408	14	.	.	PUNCT
ejpam-4553	408	15	.	.	PUNCT
ejpam-4553	409	1	,	,	PUNCT
ejpam-4553	409	2	j	j	PROPN
ejpam-4553	409	3	+	+	CCONJ
ejpam-4553	409	4	3	3	NUM
ejpam-4553	409	5	j	j	NOUN
ejpam-4553	409	6	−	−	PROPN
ejpam-4553	409	7	3	3	NUM
ejpam-4553	409	8	≤	≤	NUM
ejpam-4553	409	9	k	k	PROPN
ejpam-4553	409	10	≤	≤	PROPN
ejpam-4553	409	11	j	j	PROPN
ejpam-4553	410	1	+	+	CCONJ
ejpam-4553	410	2	3	3	NUM
ejpam-4553	410	3	and	and	CCONJ
ejpam-4553	410	4	k′	k′	PROPN
ejpam-4553	410	5	=	=	SYM
ejpam-4553	410	6	0	0	PROPN
ejpam-4553	410	7	,	,	PUNCT
ejpam-4553	410	8	.	.	PUNCT
ejpam-4553	410	9	.	.	PUNCT
ejpam-4553	411	1	.	.	PUNCT
ejpam-4553	412	1	,	,	PUNCT
ejpam-4553	412	2	j	j	PROPN
ejpam-4553	413	1	+	+	CCONJ
ejpam-4553	413	2	3	3	NUM
ejpam-4553	413	3	k	k	PROPN
ejpam-4553	413	4	≥	≥	X
ejpam-4553	413	5	j	j	NOUN
ejpam-4553	413	6	+	+	CCONJ
ejpam-4553	413	7	4	4	NUM
ejpam-4553	413	8	,	,	PUNCT
ejpam-4553	413	9	k′	k′	PROPN
ejpam-4553	413	10	≥	≥	PROPN
ejpam-4553	413	11	j	j	NOUN
ejpam-4553	413	12	+	+	CCONJ
ejpam-4553	413	13	4	4	NUM
ejpam-4553	413	14	and	and	CCONJ
ejpam-4553	413	15	|k′	|k′	NOUN
ejpam-4553	413	16	−	−	NOUN
ejpam-4553	413	17	k|	k|	NOUN
ejpam-4553	413	18	≤	≤	ADJ
ejpam-4553	413	19	3	3	NUM
ejpam-4553	413	20	.	.	PUNCT
ejpam-4553	413	21	.	.	PUNCT
ejpam-4553	414	1	mohamed	mohamed	PROPN
ejpam-4553	414	2	congo	congo	PROPN
ejpam-4553	414	3	,	,	PUNCT
ejpam-4553	414	4	m.	m.	PROPN
ejpam-4553	414	5	f.	f.	PROPN
ejpam-4553	414	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	414	7	/	/	SYM
ejpam-4553	414	8	eur	eur	PROPN
ejpam-4553	414	9	.	.	PUNCT
ejpam-4553	415	1	j.	j.	PROPN
ejpam-4553	415	2	pure	pure	PROPN
ejpam-4553	415	3	appl	appl	PROPN
ejpam-4553	415	4	.	.	PROPN
ejpam-4553	415	5	math	math	PROPN
ejpam-4553	415	6	,	,	PUNCT
ejpam-4553	415	7	15	15	NUM
ejpam-4553	415	8	(	(	PUNCT
ejpam-4553	415	9	4	4	NUM
ejpam-4553	415	10	)	)	PUNCT
ejpam-4553	415	11	(	(	PUNCT
ejpam-4553	415	12	2022	2022	NUM
ejpam-4553	415	13	)	)	PUNCT
ejpam-4553	415	14	,	,	PUNCT
ejpam-4553	415	15	1716	1716	NUM
ejpam-4553	415	16	-	-	SYM
ejpam-4553	415	17	1737	1737	NUM
ejpam-4553	415	18	1733	1733	NUM
ejpam-4553	415	19	it	it	PRON
ejpam-4553	415	20	follows	follow	VERB
ejpam-4553	415	21	that	that	SCONJ
ejpam-4553	415	22	a1(x	a1(x	NOUN
ejpam-4553	415	23	,	,	PUNCT
ejpam-4553	415	24	d)∗f	d)∗f	NOUN
ejpam-4553	415	25	=	=	NOUN
ejpam-4553	416	1	∞∑	∞∑	NUM
ejpam-4553	416	2	j=0	j=0	PROPN
ejpam-4553	416	3	j−4∑	j−4∑	X
ejpam-4553	416	4	k=0	k=0	PROPN
ejpam-4553	416	5	φj(d	φj(d	PUNCT
ejpam-4553	416	6	)	)	PUNCT
ejpam-4553	416	7	akj	akj	PROPN
ejpam-4553	416	8	j+3∑	j+3∑	PROPN
ejpam-4553	416	9	k′=j−3	k′=j−3	NOUN
ejpam-4553	416	10	fk′	fk′	VERB
ejpam-4553	416	11			PROPN
ejpam-4553	416	12	,	,	PUNCT
ejpam-4553	416	13	a2(x	a2(x	PROPN
ejpam-4553	416	14	,	,	PUNCT
ejpam-4553	416	15	d)∗f	d)∗f	NOUN
ejpam-4553	416	16	=	=	NOUN
ejpam-4553	417	1	∞∑	∞∑	NUM
ejpam-4553	417	2	j=0	j=0	PROPN
ejpam-4553	417	3	j+3∑	j+3∑	PROPN
ejpam-4553	417	4	k	k	PROPN
ejpam-4553	417	5	=	=	PROPN
ejpam-4553	417	6	j−3	j−3	NOUN
ejpam-4553	417	7	φj(d	φj(d	NOUN
ejpam-4553	417	8	)	)	PUNCT
ejpam-4553	417	9	(	(	PUNCT
ejpam-4553	417	10	akj	akj	PROPN
ejpam-4553	417	11	j+6∑	j+6∑	PROPN
ejpam-4553	417	12	k′=0	k′=0	PROPN
ejpam-4553	417	13	fk′	fk′	PROPN
ejpam-4553	417	14	)	)	PUNCT
ejpam-4553	417	15	,	,	PUNCT
ejpam-4553	417	16	a3(x	a3(x	PROPN
ejpam-4553	417	17	,	,	PUNCT
ejpam-4553	417	18	d)∗f	d)∗f	NOUN
ejpam-4553	417	19	=	=	NOUN
ejpam-4553	418	1	∞∑	∞∑	NUM
ejpam-4553	418	2	j=0	j=0	PROPN
ejpam-4553	418	3	∞∑	∞∑	NUM
ejpam-4553	418	4	k	k	X
ejpam-4553	418	5	=	=	NOUN
ejpam-4553	418	6	j+4	j+4	NOUN
ejpam-4553	418	7	φj(d	φj(d	NOUN
ejpam-4553	418	8	)	)	PUNCT
ejpam-4553	418	9	(	(	PUNCT
ejpam-4553	418	10	akj	akj	PROPN
ejpam-4553	418	11	k+3∑	k+3∑	PROPN
ejpam-4553	418	12	k′=k−3	k′=k−3	NOUN
ejpam-4553	418	13	fk′	fk′	PROPN
ejpam-4553	418	14	)	)	PUNCT
ejpam-4553	418	15	.	.	PUNCT
ejpam-4553	419	1	theorem	theorem	NOUN
ejpam-4553	419	2	3	3	X
ejpam-4553	419	3	.	.	PUNCT
ejpam-4553	420	1	let	let	VERB
ejpam-4553	420	2	a(x	a(x	NOUN
ejpam-4553	420	3	,	,	PUNCT
ejpam-4553	420	4	ξ	ξ	NOUN
ejpam-4553	420	5	)	)	PUNCT
ejpam-4553	420	6	∈	∈	NOUN
ejpam-4553	420	7	cℓ	cℓ	ADP
ejpam-4553	420	8	∗s	∗s	PROPN
ejpam-4553	420	9	m	m	PROPN
ejpam-4553	420	10	1,δ	1,δ	NUM
ejpam-4553	420	11	where	where	SCONJ
ejpam-4553	420	12	m	m	VERB
ejpam-4553	420	13	∈	∈	PROPN
ejpam-4553	420	14	r	r	NOUN
ejpam-4553	420	15	,	,	PUNCT
ejpam-4553	420	16	δ	δ	PROPN
ejpam-4553	420	17	∈	∈	PROPN
ejpam-4553	421	1	[	[	X
ejpam-4553	421	2	0	0	NUM
ejpam-4553	421	3	,	,	PUNCT
ejpam-4553	421	4	1	1	NUM
ejpam-4553	421	5	]	]	PUNCT
ejpam-4553	421	6	and	and	CCONJ
ejpam-4553	421	7	ℓ	ℓ	INTJ
ejpam-4553	421	8	>	>	X
ejpam-4553	421	9	0	0	X
ejpam-4553	421	10	.	.	PUNCT
ejpam-4553	422	1	let	let	VERB
ejpam-4553	422	2	p	p	PRON
ejpam-4553	422	3	∈	∈	PROPN
ejpam-4553	422	4	p	p	NOUN
ejpam-4553	422	5	log(rn	log(rn	PROPN
ejpam-4553	422	6	)	)	PUNCT
ejpam-4553	422	7	and	and	CCONJ
ejpam-4553	422	8	u	u	NOUN
ejpam-4553	422	9	,	,	PUNCT
ejpam-4553	422	10	q	q	PROPN
ejpam-4553	422	11	∈	∈	PROPN
ejpam-4553	422	12	p	p	NOUN
ejpam-4553	422	13	such	such	ADJ
ejpam-4553	422	14	that	that	SCONJ
ejpam-4553	422	15	1	1	NUM
ejpam-4553	422	16	q	q	NOUN
ejpam-4553	422	17	∈	∈	PROPN
ejpam-4553	422	18	c	c	PROPN
ejpam-4553	422	19	log	log	PROPN
ejpam-4553	422	20	loc	loc	NOUN
ejpam-4553	422	21	with	with	ADP
ejpam-4553	422	22	1	1	NUM
ejpam-4553	422	23	≤	≤	NOUN
ejpam-4553	422	24	p−	p−	NOUN
ejpam-4553	422	25	≤	≤	NUM
ejpam-4553	422	26	p(x	p(x	PROPN
ejpam-4553	422	27	)	)	PUNCT
ejpam-4553	422	28	≤	≤	NUM
ejpam-4553	422	29	u(x	u(x	NOUN
ejpam-4553	422	30	)	)	PUNCT
ejpam-4553	422	31	≤	≤	NOUN
ejpam-4553	422	32	∞.	∞.	PROPN
ejpam-4553	422	33	let	let	VERB
ejpam-4553	422	34	s	s	PRON
ejpam-4553	422	35	∈	∈	VERB
ejpam-4553	422	36	c	c	PROPN
ejpam-4553	422	37	log	log	PROPN
ejpam-4553	422	38	loc	loc	PROPN
ejpam-4553	422	39	such	such	ADJ
ejpam-4553	422	40	that	that	SCONJ
ejpam-4553	422	41	0	0	NUM
ejpam-4553	422	42	<	<	X
ejpam-4553	422	43	s−	s−	PROPN
ejpam-4553	422	44	≤	≤	NUM
ejpam-4553	422	45	s(x	s(x	PROPN
ejpam-4553	422	46	)	)	PUNCT
ejpam-4553	422	47	<	<	X
ejpam-4553	422	48	ℓ.	ℓ.	NOUN
ejpam-4553	422	49	then	then	ADV
ejpam-4553	422	50	a(x	a(x	NOUN
ejpam-4553	422	51	,	,	PUNCT
ejpam-4553	422	52	d)∗	d)∗	PROPN
ejpam-4553	422	53	:	:	PUNCT
ejpam-4553	422	54	n	n	PROPN
ejpam-4553	422	55	s	s	PROPN
ejpam-4553	422	56	(	(	PUNCT
ejpam-4553	422	57	·	·	PUNCT
ejpam-4553	422	58	)	)	PUNCT
ejpam-4553	422	59	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	422	60	(	(	PUNCT
ejpam-4553	422	61	·	·	PUNCT
ejpam-4553	422	62	)	)	PUNCT
ejpam-4553	423	1	−→	−→	NOUN
ejpam-4553	423	2	n	n	CCONJ
ejpam-4553	423	3	s(·)−m	s(·)−m	NOUN
ejpam-4553	423	4	p(·),u()·,q	p(·),u()·,q	NOUN
ejpam-4553	423	5	(	(	PUNCT
ejpam-4553	423	6	·	·	PUNCT
ejpam-4553	423	7	)	)	PUNCT
ejpam-4553	423	8	is	be	AUX
ejpam-4553	423	9	bounded	bound	VERB
ejpam-4553	423	10	.	.	PUNCT
ejpam-4553	424	1	proof	proof	NOUN
ejpam-4553	424	2	.	.	PUNCT
ejpam-4553	425	1	as	as	ADP
ejpam-4553	425	2	for	for	ADP
ejpam-4553	425	3	the	the	DET
ejpam-4553	425	4	proof	proof	NOUN
ejpam-4553	425	5	of	of	ADP
ejpam-4553	425	6	theorem	theorem	NOUN
ejpam-4553	425	7	2	2	NUM
ejpam-4553	425	8	,	,	PUNCT
ejpam-4553	425	9	we	we	PRON
ejpam-4553	425	10	will	will	AUX
ejpam-4553	425	11	proceed	proceed	VERB
ejpam-4553	425	12	by	by	ADP
ejpam-4553	425	13	estimating	estimate	VERB
ejpam-4553	425	14	the	the	DET
ejpam-4553	425	15	three	three	NUM
ejpam-4553	425	16	above	above	ADP
ejpam-4553	425	17	operators	operator	NOUN
ejpam-4553	425	18	.	.	PUNCT
ejpam-4553	426	1	let	let	VERB
ejpam-4553	426	2	m	m	VERB
ejpam-4553	426	3	=	=	NOUN
ejpam-4553	426	4	0	0	NUM
ejpam-4553	426	5	.	.	NOUN
ejpam-4553	426	6	•	•	NUM
ejpam-4553	427	1	the	the	DET
ejpam-4553	427	2	estimation	estimation	NOUN
ejpam-4553	427	3	of	of	ADP
ejpam-4553	427	4	a1(x	a1(x	PRON
ejpam-4553	427	5	,	,	PUNCT
ejpam-4553	427	6	d)∗	d)∗	PROPN
ejpam-4553	427	7	∥a1(x	∥a1(x	NOUN
ejpam-4553	427	8	,	,	PUNCT
ejpam-4553	427	9	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	427	10	s	s	PROPN
ejpam-4553	427	11	(	(	PUNCT
ejpam-4553	427	12	·	·	PUNCT
ejpam-4553	427	13	)	)	PUNCT
ejpam-4553	427	14	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	427	15	(	(	PUNCT
ejpam-4553	427	16	·	·	PUNCT
ejpam-4553	427	17	)	)	PUNCT
ejpam-4553	427	18	=	=	SYM
ejpam-4553	427	19	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	428	1	∞∑	∞∑	NUM
ejpam-4553	428	2	j=0	j=0	PROPN
ejpam-4553	428	3	j−4∑	j−4∑	X
ejpam-4553	428	4	k=0	k=0	PROPN
ejpam-4553	428	5	φj(d	φj(d	PUNCT
ejpam-4553	428	6	)	)	PUNCT
ejpam-4553	428	7	akj	akj	PROPN
ejpam-4553	428	8	j+3∑	j+3∑	PROPN
ejpam-4553	428	9	k′=j−3	k′=j−3	NOUN
ejpam-4553	428	10	fk′	fk′	PROPN
ejpam-4553	428	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	429	1	n	n	PROPN
ejpam-4553	429	2	s	s	PROPN
ejpam-4553	429	3	(	(	PUNCT
ejpam-4553	429	4	·	·	PUNCT
ejpam-4553	429	5	)	)	PUNCT
ejpam-4553	429	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	429	7	(	(	PUNCT
ejpam-4553	429	8	·	·	PUNCT
ejpam-4553	429	9	)	)	PUNCT
ejpam-4553	429	10	=	=	SYM
ejpam-4553	429	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	430	1	∞∑	∞∑	NUM
ejpam-4553	430	2	j=0	j=0	PROPN
ejpam-4553	430	3	j−4∑	j−4∑	X
ejpam-4553	430	4	k=0	k=0	PROPN
ejpam-4553	430	5	φj(d	φj(d	X
ejpam-4553	430	6	)	)	PUNCT
ejpam-4553	430	7	(	(	PUNCT
ejpam-4553	430	8	akjfj	akjfj	NOUN
ejpam-4553	430	9	)	)	PUNCT
ejpam-4553	430	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	431	1	n	n	CCONJ
ejpam-4553	431	2	s	s	PROPN
ejpam-4553	431	3	(	(	PUNCT
ejpam-4553	431	4	·	·	PUNCT
ejpam-4553	431	5	)	)	PUNCT
ejpam-4553	431	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	431	7	(	(	PUNCT
ejpam-4553	431	8	·	·	PUNCT
ejpam-4553	431	9	)	)	PUNCT
ejpam-4553	431	10	.	.	PUNCT
ejpam-4553	432	1	here	here	ADV
ejpam-4553	432	2	fj	fj	X
ejpam-4553	432	3	:	:	PUNCT
ejpam-4553	432	4	=	=	SYM
ejpam-4553	432	5	φ′	φ′	PUNCT
ejpam-4553	432	6	jf	jf	INTJ
ejpam-4553	432	7	where	where	SCONJ
ejpam-4553	432	8	φ′	φ′	NUM
ejpam-4553	432	9	j	j	PROPN
ejpam-4553	432	10	is	be	AUX
ejpam-4553	432	11	a	a	DET
ejpam-4553	432	12	suitably	suitably	ADV
ejpam-4553	432	13	chosen	choose	VERB
ejpam-4553	432	14	smooth	smooth	ADJ
ejpam-4553	432	15	function	function	NOUN
ejpam-4553	432	16	supported	support	VERB
ejpam-4553	432	17	in	in	ADP
ejpam-4553	432	18	the	the	DET
ejpam-4553	432	19	annulus	annulus	NOUN
ejpam-4553	432	20	|ξ|	|ξ|	PROPN
ejpam-4553	432	21	∼	∼	NOUN
ejpam-4553	432	22	2j	2j	NOUN
ejpam-4553	432	23	.	.	PUNCT
ejpam-4553	433	1	moreover	moreover	ADV
ejpam-4553	433	2	we	we	PRON
ejpam-4553	433	3	have	have	VERB
ejpam-4553	433	4	suppf	suppf	NOUN
ejpam-4553	433	5	{	{	PUNCT
ejpam-4553	433	6	j−4∑	j−4∑	ADV
ejpam-4553	433	7	k=0	k=0	PROPN
ejpam-4553	433	8	φj(d	φj(d	X
ejpam-4553	433	9	)	)	PUNCT
ejpam-4553	433	10	(	(	PUNCT
ejpam-4553	433	11	akjfj	akjfj	NOUN
ejpam-4553	433	12	)	)	PUNCT
ejpam-4553	433	13	}	}	PUNCT
ejpam-4553	434	1	⊂	⊂	PRON
ejpam-4553	434	2	{	{	PUNCT
ejpam-4553	434	3	ξ	ξ	PROPN
ejpam-4553	434	4	∈	∈	PROPN
ejpam-4553	434	5	rn	rn	PROPN
ejpam-4553	434	6	:	:	PUNCT
ejpam-4553	434	7	|ξ|	|ξ|	VERB
ejpam-4553	434	8	∼	∼	NOUN
ejpam-4553	434	9	2j	2j	NUM
ejpam-4553	434	10	}	}	PUNCT
ejpam-4553	434	11	.	.	PUNCT
ejpam-4553	435	1	by	by	ADP
ejpam-4553	435	2	applying	apply	VERB
ejpam-4553	435	3	lemma	lemma	PROPN
ejpam-4553	435	4	7	7	NUM
ejpam-4553	435	5	and	and	CCONJ
ejpam-4553	435	6	lemma	lemma	PROPN
ejpam-4553	435	7	1	1	NUM
ejpam-4553	435	8	we	we	PRON
ejpam-4553	435	9	obtain	obtain	VERB
ejpam-4553	435	10	,	,	PUNCT
ejpam-4553	435	11	∥a1(x	∥a1(x	NOUN
ejpam-4553	435	12	,	,	PUNCT
ejpam-4553	435	13	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	435	14	s	s	PROPN
ejpam-4553	435	15	(	(	PUNCT
ejpam-4553	435	16	·	·	PUNCT
ejpam-4553	435	17	)	)	PUNCT
ejpam-4553	435	18	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	435	19	(	(	PUNCT
ejpam-4553	435	20	·	·	PUNCT
ejpam-4553	435	21	)	)	PUNCT
ejpam-4553	435	22	≲	≲	PROPN
ejpam-4553	435	23	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	435	24	(	(	PUNCT
ejpam-4553	435	25	2js(·)φ̌j	2js(·)φ̌j	NUM
ejpam-4553	435	26	∗	∗	NOUN
ejpam-4553	435	27	j−4∑	j−4∑	X
ejpam-4553	435	28	k=0	k=0	PROPN
ejpam-4553	435	29	akjfj	akjfj	PROPN
ejpam-4553	435	30	)	)	PUNCT
ejpam-4553	435	31	j	j	PROPN
ejpam-4553	435	32	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	436	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	436	2	(	(	PUNCT
ejpam-4553	436	3	·	·	PUNCT
ejpam-4553	436	4	)	)	PUNCT
ejpam-4553	436	5	)	)	PUNCT
ejpam-4553	437	1	mohamed	mohamed	PROPN
ejpam-4553	437	2	congo	congo	PROPN
ejpam-4553	437	3	,	,	PUNCT
ejpam-4553	437	4	m.	m.	PROPN
ejpam-4553	437	5	f.	f.	PROPN
ejpam-4553	437	6	ouedraogo	ouedraogo	PROPN
ejpam-4553	437	7	/	/	SYM
ejpam-4553	437	8	eur	eur	PROPN
ejpam-4553	437	9	.	.	PUNCT
ejpam-4553	438	1	j.	j.	PROPN
ejpam-4553	438	2	pure	pure	PROPN
ejpam-4553	438	3	appl	appl	PROPN
ejpam-4553	438	4	.	.	PROPN
ejpam-4553	438	5	math	math	PROPN
ejpam-4553	438	6	,	,	PUNCT
ejpam-4553	438	7	15	15	NUM
ejpam-4553	438	8	(	(	PUNCT
ejpam-4553	438	9	4	4	NUM
ejpam-4553	438	10	)	)	PUNCT
ejpam-4553	438	11	(	(	PUNCT
ejpam-4553	438	12	2022	2022	NUM
ejpam-4553	438	13	)	)	PUNCT
ejpam-4553	438	14	,	,	PUNCT
ejpam-4553	438	15	1716	1716	NUM
ejpam-4553	438	16	-	-	SYM
ejpam-4553	438	17	1737	1737	NUM
ejpam-4553	438	18	1734	1734	NUM
ejpam-4553	438	19	≲	≲	PROPN
ejpam-4553	438	20	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	438	21	(	(	PUNCT
ejpam-4553	438	22	2js(·)ηj	2js(·)ηj	NUM
ejpam-4553	438	23	,	,	PUNCT
ejpam-4553	438	24	m	m	NOUN
ejpam-4553	438	25	∗	∗	NOUN
ejpam-4553	438	26	∣∣∣∣∣	∣∣∣∣∣	VERB
ejpam-4553	438	27	j−4∑	j−4∑	X
ejpam-4553	438	28	k=0	k=0	PROPN
ejpam-4553	438	29	akjfj	akjfj	PROPN
ejpam-4553	438	30	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4553	438	31	)	)	PUNCT
ejpam-4553	439	1	j	j	PROPN
ejpam-4553	439	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	439	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	439	4	(	(	PUNCT
ejpam-4553	439	5	·	·	PUNCT
ejpam-4553	439	6	)	)	PUNCT
ejpam-4553	439	7	)	)	PUNCT
ejpam-4553	440	1	for	for	ADP
ejpam-4553	440	2	any	any	DET
ejpam-4553	440	3	m	m	NOUN
ejpam-4553	440	4	>	>	X
ejpam-4553	440	5	n+	n+	NUM
ejpam-4553	440	6	clog(s	clog(s	NOUN
ejpam-4553	440	7	)	)	PUNCT
ejpam-4553	440	8	+	+	CCONJ
ejpam-4553	440	9	clog	clog	PROPN
ejpam-4553	440	10	(	(	PUNCT
ejpam-4553	440	11	1	1	NUM
ejpam-4553	440	12	q	q	NOUN
ejpam-4553	440	13	)	)	PUNCT
ejpam-4553	440	14	+	+	CCONJ
ejpam-4553	440	15	nmax	nmax	ADJ
ejpam-4553	440	16	{	{	PUNCT
ejpam-4553	440	17	0	0	NUM
ejpam-4553	440	18	,	,	PUNCT
ejpam-4553	440	19	supx∈rn	supx∈rn	PUNCT
ejpam-4553	440	20	(	(	PUNCT
ejpam-4553	440	21	1	1	NUM
ejpam-4553	440	22	p(x	p(x	NOUN
ejpam-4553	440	23	)	)	PUNCT
ejpam-4553	440	24	−	−	PROPN
ejpam-4553	440	25	1	1	NUM
ejpam-4553	440	26	u(x	u(x	NOUN
ejpam-4553	440	27	)	)	PUNCT
ejpam-4553	440	28	)	)	PUNCT
ejpam-4553	440	29	−	−	PROPN
ejpam-4553	440	30	1	1	NUM
ejpam-4553	440	31	p∞	p∞	PROPN
ejpam-4553	440	32	}	}	PUNCT
ejpam-4553	440	33	thus	thus	ADV
ejpam-4553	440	34	,	,	PUNCT
ejpam-4553	440	35	by	by	ADP
ejpam-4553	440	36	lemmas	lemmas	PROPN
ejpam-4553	440	37	2	2	NUM
ejpam-4553	440	38	,	,	PUNCT
ejpam-4553	440	39	∥a1(x	∥a1(x	NOUN
ejpam-4553	440	40	,	,	PUNCT
ejpam-4553	440	41	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	440	42	s	s	PROPN
ejpam-4553	440	43	(	(	PUNCT
ejpam-4553	440	44	·	·	PUNCT
ejpam-4553	440	45	)	)	PUNCT
ejpam-4553	440	46	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	440	47	(	(	PUNCT
ejpam-4553	440	48	·	·	PUNCT
ejpam-4553	440	49	)	)	PUNCT
ejpam-4553	441	1	≲	≲	PROPN
ejpam-4553	441	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	441	3	(	(	PUNCT
ejpam-4553	441	4	ηj	ηj	NOUN
ejpam-4553	441	5	,	,	PUNCT
ejpam-4553	441	6	m−clog(s	m−clog(s	PROPN
ejpam-4553	441	7	)	)	PUNCT
ejpam-4553	441	8	∗	∗	NOUN
ejpam-4553	441	9	j−4∑	j−4∑	X
ejpam-4553	441	10	k=0	k=0	PROPN
ejpam-4553	441	11	∣∣∣akj2js(·)fj∣∣∣	∣∣∣akj2js(·)fj∣∣∣	PROPN
ejpam-4553	441	12	)	)	PUNCT
ejpam-4553	441	13	j	j	PROPN
ejpam-4553	441	14	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	441	15	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	441	16	(	(	PUNCT
ejpam-4553	441	17	·	·	PUNCT
ejpam-4553	441	18	)	)	PUNCT
ejpam-4553	441	19	)	)	PUNCT
ejpam-4553	441	20	then	then	ADV
ejpam-4553	441	21	by	by	ADP
ejpam-4553	441	22	lemma	lemma	PROPN
ejpam-4553	441	23	3	3	NUM
ejpam-4553	441	24	,	,	PUNCT
ejpam-4553	441	25	∥a1(x	∥a1(x	NOUN
ejpam-4553	441	26	,	,	PUNCT
ejpam-4553	441	27	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	441	28	s	s	PROPN
ejpam-4553	441	29	(	(	PUNCT
ejpam-4553	441	30	·	·	PUNCT
ejpam-4553	441	31	)	)	PUNCT
ejpam-4553	441	32	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	441	33	(	(	PUNCT
ejpam-4553	441	34	·	·	PUNCT
ejpam-4553	441	35	)	)	PUNCT
ejpam-4553	442	1	≲	≲	PROPN
ejpam-4553	442	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	443	1	(	(	PUNCT
ejpam-4553	443	2	j−4∑	j−4∑	NUM
ejpam-4553	443	3	k=0	k=0	PRON
ejpam-4553	443	4	∣∣∣∥akj∥l∞	∣∣∣∥akj∥l∞	ADP
ejpam-4553	443	5	2js(·)φ′	2js(·)φ′	NUM
ejpam-4553	443	6	j(d)f	j(d)f	PROPN
ejpam-4553	443	7	∣∣∣	∣∣∣	ADJ
ejpam-4553	443	8	)	)	PUNCT
ejpam-4553	443	9	j	j	PROPN
ejpam-4553	443	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	443	11	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	443	12	(	(	PUNCT
ejpam-4553	443	13	·	·	PUNCT
ejpam-4553	443	14	)	)	PUNCT
ejpam-4553	443	15	)	)	PUNCT
ejpam-4553	443	16	.	.	PUNCT
ejpam-4553	444	1	therefore	therefore	ADV
ejpam-4553	444	2	∥a1(x	∥a1(x	VERB
ejpam-4553	444	3	,	,	PUNCT
ejpam-4553	444	4	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	444	5	s	s	PROPN
ejpam-4553	444	6	(	(	PUNCT
ejpam-4553	444	7	·	·	PUNCT
ejpam-4553	444	8	)	)	PUNCT
ejpam-4553	444	9	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	444	10	(	(	PUNCT
ejpam-4553	444	11	·	·	PUNCT
ejpam-4553	444	12	)	)	PUNCT
ejpam-4553	445	1	≲	≲	PROPN
ejpam-4553	445	2	∥f∥n	∥f∥n	NUM
ejpam-4553	445	3	s	s	PART
ejpam-4553	445	4	(	(	PUNCT
ejpam-4553	445	5	·	·	PUNCT
ejpam-4553	445	6	)	)	PUNCT
ejpam-4553	445	7	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	445	8	(	(	PUNCT
ejpam-4553	445	9	·	·	PUNCT
ejpam-4553	445	10	)	)	PUNCT
ejpam-4553	445	11	.	.	PUNCT
ejpam-4553	446	1	(	(	PUNCT
ejpam-4553	446	2	15	15	NUM
ejpam-4553	446	3	)	)	PUNCT
ejpam-4553	446	4	•	•	ADP
ejpam-4553	446	5	the	the	DET
ejpam-4553	446	6	estimation	estimation	NOUN
ejpam-4553	446	7	of	of	ADP
ejpam-4553	446	8	a2(x	a2(x	PROPN
ejpam-4553	446	9	,	,	PUNCT
ejpam-4553	446	10	d)∗	d)∗	PROPN
ejpam-4553	446	11	∥a2(x	∥a2(x	PROPN
ejpam-4553	446	12	,	,	PUNCT
ejpam-4553	446	13	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	446	14	s	s	PROPN
ejpam-4553	446	15	(	(	PUNCT
ejpam-4553	446	16	·	·	PUNCT
ejpam-4553	446	17	)	)	PUNCT
ejpam-4553	446	18	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	446	19	(	(	PUNCT
ejpam-4553	446	20	·	·	PUNCT
ejpam-4553	446	21	)	)	PUNCT
ejpam-4553	446	22	=	=	SYM
ejpam-4553	446	23	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	447	1	∞∑	∞∑	NUM
ejpam-4553	447	2	j=0	j=0	PROPN
ejpam-4553	447	3	j+3∑	j+3∑	PROPN
ejpam-4553	447	4	k	k	PROPN
ejpam-4553	447	5	=	=	PROPN
ejpam-4553	447	6	j−3	j−3	NOUN
ejpam-4553	447	7	φj(d	φj(d	NOUN
ejpam-4553	447	8	)	)	PUNCT
ejpam-4553	447	9	(	(	PUNCT
ejpam-4553	447	10	akj	akj	PROPN
ejpam-4553	447	11	j+6∑	j+6∑	PROPN
ejpam-4553	447	12	k′=0	k′=0	PROPN
ejpam-4553	447	13	fk′	fk′	PROPN
ejpam-4553	447	14	)	)	PUNCT
ejpam-4553	447	15	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	448	1	n	n	CCONJ
ejpam-4553	448	2	s	s	PROPN
ejpam-4553	448	3	(	(	PUNCT
ejpam-4553	448	4	·	·	PUNCT
ejpam-4553	448	5	)	)	PUNCT
ejpam-4553	448	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	448	7	(	(	PUNCT
ejpam-4553	448	8	·	·	PUNCT
ejpam-4553	448	9	)	)	PUNCT
ejpam-4553	448	10	=	=	SYM
ejpam-4553	448	11	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	449	1	3∑	3∑	NUM
ejpam-4553	449	2	k=−3	k=−3	VERB
ejpam-4553	449	3	∞∑	∞∑	NUM
ejpam-4553	449	4	j=0	j=0	PROPN
ejpam-4553	449	5	φj(d	φj(d	NOUN
ejpam-4553	449	6	)	)	PUNCT
ejpam-4553	449	7	(	(	PUNCT
ejpam-4553	449	8	a(k+j)j	a(k+j)j	VERB
ejpam-4553	449	9	j+6∑	j+6∑	PROPN
ejpam-4553	449	10	k′=0	k′=0	PROPN
ejpam-4553	449	11	fk′	fk′	PROPN
ejpam-4553	449	12	)	)	PUNCT
ejpam-4553	449	13	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	449	14	n	n	CCONJ
ejpam-4553	449	15	s	s	PROPN
ejpam-4553	449	16	(	(	PUNCT
ejpam-4553	449	17	·	·	PUNCT
ejpam-4553	449	18	)	)	PUNCT
ejpam-4553	449	19	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	449	20	(	(	PUNCT
ejpam-4553	449	21	·	·	PUNCT
ejpam-4553	449	22	)	)	PUNCT
ejpam-4553	450	1	≲	≲	PROPN
ejpam-4553	450	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	451	1	∞∑	∞∑	DET
ejpam-4553	451	2	j=0	j=0	PROPN
ejpam-4553	451	3	φj(d	φj(d	NOUN
ejpam-4553	451	4	)	)	PUNCT
ejpam-4553	451	5	(	(	PUNCT
ejpam-4553	451	6	a(k+j)j	a(k+j)j	VERB
ejpam-4553	451	7	j+6∑	j+6∑	PROPN
ejpam-4553	451	8	k′=0	k′=0	PROPN
ejpam-4553	451	9	fk′	fk′	PROPN
ejpam-4553	451	10	)	)	PUNCT
ejpam-4553	451	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	451	12	n	n	CCONJ
ejpam-4553	451	13	s	s	PROPN
ejpam-4553	451	14	(	(	PUNCT
ejpam-4553	451	15	·	·	PUNCT
ejpam-4553	451	16	)	)	PUNCT
ejpam-4553	451	17	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	451	18	(	(	PUNCT
ejpam-4553	451	19	·	·	PUNCT
ejpam-4553	451	20	)	)	PUNCT
ejpam-4553	451	21	one	one	NOUN
ejpam-4553	451	22	has	have	VERB
ejpam-4553	451	23	supp	supp	PROPN
ejpam-4553	451	24	f	f	PROPN
ejpam-4553	451	25	{	{	PUNCT
ejpam-4553	451	26	φj(d	φj(d	NOUN
ejpam-4553	451	27	)	)	PUNCT
ejpam-4553	451	28	(	(	PUNCT
ejpam-4553	451	29	a(k+j)j	a(k+j)j	VERB
ejpam-4553	451	30	j+6∑	j+6∑	PROPN
ejpam-4553	451	31	k′=0	k′=0	PROPN
ejpam-4553	451	32	fk′	fk′	NOUN
ejpam-4553	451	33	)	)	PUNCT
ejpam-4553	451	34	}	}	PUNCT
ejpam-4553	451	35	⊂	⊂	PROPN
ejpam-4553	452	1	b(0	b(0	NOUN
ejpam-4553	452	2	,	,	PUNCT
ejpam-4553	452	3	c2j+1	c2j+1	PROPN
ejpam-4553	452	4	)	)	PUNCT
ejpam-4553	452	5	.	.	PUNCT
ejpam-4553	453	1	by	by	ADP
ejpam-4553	453	2	lemma	lemma	PROPN
ejpam-4553	453	3	8	8	NUM
ejpam-4553	453	4	,	,	PUNCT
ejpam-4553	453	5	∥a2(x	∥a2(x	PROPN
ejpam-4553	453	6	,	,	PUNCT
ejpam-4553	453	7	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	453	8	s	s	PROPN
ejpam-4553	453	9	(	(	PUNCT
ejpam-4553	453	10	·	·	PUNCT
ejpam-4553	453	11	)	)	PUNCT
ejpam-4553	453	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	453	13	(	(	PUNCT
ejpam-4553	453	14	·	·	PUNCT
ejpam-4553	453	15	)	)	PUNCT
ejpam-4553	454	1	≲	≲	PROPN
ejpam-4553	454	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	454	3	(	(	PUNCT
ejpam-4553	454	4	2js(·)φj(d	2js(·)φj(d	NUM
ejpam-4553	454	5	)	)	PUNCT
ejpam-4553	454	6	(	(	PUNCT
ejpam-4553	454	7	a(k+j)j	a(k+j)j	VERB
ejpam-4553	454	8	j+6∑	j+6∑	PROPN
ejpam-4553	454	9	k′=0	k′=0	PROPN
ejpam-4553	454	10	fk′	fk′	PROPN
ejpam-4553	454	11	)	)	PUNCT
ejpam-4553	454	12	)	)	PUNCT
ejpam-4553	455	1	j	j	PROPN
ejpam-4553	455	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	455	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	455	4	(	(	PUNCT
ejpam-4553	455	5	·	·	PUNCT
ejpam-4553	455	6	)	)	PUNCT
ejpam-4553	455	7	)	)	PUNCT
ejpam-4553	456	1	≲	≲	PROPN
ejpam-4553	456	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	456	3	(	(	PUNCT
ejpam-4553	456	4	∥∥a(k+j)j	∥∥a(k+j)j	ADJ
ejpam-4553	456	5	∥∥	∥∥	PRON
ejpam-4553	456	6	l∞	l∞	NOUN
ejpam-4553	456	7	2js(·)ηj	2js(·)ηj	NUM
ejpam-4553	456	8	,	,	PUNCT
ejpam-4553	456	9	m−clog(s	m−clog(s	PROPN
ejpam-4553	456	10	)	)	PUNCT
ejpam-4553	456	11	∗	∗	NOUN
ejpam-4553	456	12	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-4553	456	13	j+6∑	j+6∑	PROPN
ejpam-4553	456	14	k′=0	k′=0	PROPN
ejpam-4553	456	15	fk′	fk′	PROPN
ejpam-4553	456	16	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4553	456	17	)	)	PUNCT
ejpam-4553	456	18	j	j	PROPN
ejpam-4553	456	19	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	456	20	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	456	21	(	(	PUNCT
ejpam-4553	456	22	·	·	PUNCT
ejpam-4553	456	23	)	)	PUNCT
ejpam-4553	456	24	)	)	PUNCT
ejpam-4553	456	25	mohamed	mohamed	PROPN
ejpam-4553	456	26	congo	congo	PROPN
ejpam-4553	456	27	,	,	PUNCT
ejpam-4553	456	28	m.	m.	PROPN
ejpam-4553	456	29	f.	f.	PROPN
ejpam-4553	456	30	ouedraogo	ouedraogo	PROPN
ejpam-4553	456	31	/	/	SYM
ejpam-4553	456	32	eur	eur	PROPN
ejpam-4553	456	33	.	.	PUNCT
ejpam-4553	457	1	j.	j.	PROPN
ejpam-4553	457	2	pure	pure	PROPN
ejpam-4553	457	3	appl	appl	PROPN
ejpam-4553	457	4	.	.	PROPN
ejpam-4553	457	5	math	math	PROPN
ejpam-4553	457	6	,	,	PUNCT
ejpam-4553	457	7	15	15	NUM
ejpam-4553	457	8	(	(	PUNCT
ejpam-4553	457	9	4	4	NUM
ejpam-4553	457	10	)	)	PUNCT
ejpam-4553	457	11	(	(	PUNCT
ejpam-4553	457	12	2022	2022	NUM
ejpam-4553	457	13	)	)	PUNCT
ejpam-4553	457	14	,	,	PUNCT
ejpam-4553	457	15	1716	1716	NUM
ejpam-4553	457	16	-	-	SYM
ejpam-4553	457	17	1737	1737	NUM
ejpam-4553	457	18	1735	1735	NUM
ejpam-4553	457	19	for	for	ADP
ejpam-4553	457	20	any	any	DET
ejpam-4553	457	21	m	m	NOUN
ejpam-4553	457	22	>	>	X
ejpam-4553	457	23	n+	n+	NUM
ejpam-4553	457	24	clog(s	clog(s	NOUN
ejpam-4553	457	25	)	)	PUNCT
ejpam-4553	457	26	+	+	CCONJ
ejpam-4553	457	27	clog	clog	PROPN
ejpam-4553	457	28	(	(	PUNCT
ejpam-4553	457	29	1	1	NUM
ejpam-4553	457	30	q	q	NOUN
ejpam-4553	457	31	)	)	PUNCT
ejpam-4553	458	1	+	+	CCONJ
ejpam-4553	458	2	nmax	nmax	ADJ
ejpam-4553	458	3	{	{	PUNCT
ejpam-4553	458	4	0	0	NUM
ejpam-4553	458	5	,	,	PUNCT
ejpam-4553	458	6	supx∈rn	supx∈rn	PUNCT
ejpam-4553	458	7	(	(	PUNCT
ejpam-4553	458	8	1	1	NUM
ejpam-4553	458	9	p(x	p(x	NOUN
ejpam-4553	458	10	)	)	PUNCT
ejpam-4553	458	11	−	−	PROPN
ejpam-4553	458	12	1	1	NUM
ejpam-4553	458	13	u(x	u(x	NOUN
ejpam-4553	458	14	)	)	PUNCT
ejpam-4553	458	15	)	)	PUNCT
ejpam-4553	459	1	−	−	PROPN
ejpam-4553	459	2	1	1	NUM
ejpam-4553	459	3	p∞	p∞	PROPN
ejpam-4553	459	4	}	}	PUNCT
ejpam-4553	459	5	.	.	PUNCT
ejpam-4553	460	1	then	then	ADV
ejpam-4553	460	2	by	by	ADP
ejpam-4553	460	3	lemma	lemma	PROPN
ejpam-4553	460	4	3	3	NUM
ejpam-4553	460	5	∥a2(x	∥a2(x	NOUN
ejpam-4553	460	6	,	,	PUNCT
ejpam-4553	460	7	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	460	8	s	s	PROPN
ejpam-4553	460	9	(	(	PUNCT
ejpam-4553	460	10	·	·	PUNCT
ejpam-4553	460	11	)	)	PUNCT
ejpam-4553	460	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	460	13	(	(	PUNCT
ejpam-4553	460	14	·	·	PUNCT
ejpam-4553	460	15	)	)	PUNCT
ejpam-4553	460	16	≲	≲	PROPN
ejpam-4553	460	17	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	460	18	(	(	PUNCT
ejpam-4553	460	19	2js	2js	ADJ
ejpam-4553	460	20	(	(	PUNCT
ejpam-4553	460	21	·	·	PUNCT
ejpam-4553	460	22	)	)	PUNCT
ejpam-4553	460	23	j+6∑	j+6∑	PROPN
ejpam-4553	460	24	k′=0	k′=0	PROPN
ejpam-4553	460	25	φk′(d)f	φk′(d)f	PROPN
ejpam-4553	460	26	)	)	PUNCT
ejpam-4553	461	1	j	j	PROPN
ejpam-4553	461	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	461	3	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	461	4	(	(	PUNCT
ejpam-4553	461	5	·	·	PUNCT
ejpam-4553	461	6	)	)	PUNCT
ejpam-4553	461	7	)	)	PUNCT
ejpam-4553	461	8	then	then	ADV
ejpam-4553	461	9	∥a2(x	∥a2(x	PROPN
ejpam-4553	461	10	,	,	PUNCT
ejpam-4553	461	11	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	461	12	s	s	PROPN
ejpam-4553	461	13	(	(	PUNCT
ejpam-4553	461	14	·	·	PUNCT
ejpam-4553	461	15	)	)	PUNCT
ejpam-4553	461	16	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	461	17	(	(	PUNCT
ejpam-4553	461	18	·	·	PUNCT
ejpam-4553	461	19	)	)	PUNCT
ejpam-4553	461	20	≲	≲	PROPN
ejpam-4553	461	21	∥f∥n	∥f∥n	NUM
ejpam-4553	461	22	s	s	PART
ejpam-4553	461	23	(	(	PUNCT
ejpam-4553	461	24	·	·	PUNCT
ejpam-4553	461	25	)	)	PUNCT
ejpam-4553	461	26	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	461	27	(	(	PUNCT
ejpam-4553	461	28	·	·	PUNCT
ejpam-4553	461	29	)	)	PUNCT
ejpam-4553	461	30	.	.	PUNCT
ejpam-4553	462	1	(	(	PUNCT
ejpam-4553	462	2	16	16	NUM
ejpam-4553	462	3	)	)	PUNCT
ejpam-4553	462	4	•	•	ADP
ejpam-4553	462	5	the	the	DET
ejpam-4553	462	6	estimation	estimation	NOUN
ejpam-4553	462	7	of	of	ADP
ejpam-4553	462	8	a3(x	a3(x	PROPN
ejpam-4553	462	9	,	,	PUNCT
ejpam-4553	462	10	d)∗	d)∗	PROPN
ejpam-4553	462	11	∥a3(x	∥a3(x	PROPN
ejpam-4553	462	12	,	,	PUNCT
ejpam-4553	463	1	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	463	2	s	s	PROPN
ejpam-4553	463	3	(	(	PUNCT
ejpam-4553	463	4	·	·	PUNCT
ejpam-4553	463	5	)	)	PUNCT
ejpam-4553	463	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	463	7	(	(	PUNCT
ejpam-4553	463	8	·	·	PUNCT
ejpam-4553	463	9	)	)	PUNCT
ejpam-4553	463	10	=	=	SYM
ejpam-4553	463	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	464	1	∞∑	∞∑	NUM
ejpam-4553	464	2	j=0	j=0	PROPN
ejpam-4553	464	3	∞∑	∞∑	NUM
ejpam-4553	464	4	k	k	X
ejpam-4553	464	5	=	=	NOUN
ejpam-4553	464	6	j+4	j+4	NOUN
ejpam-4553	464	7	φj(d	φj(d	NOUN
ejpam-4553	464	8	)	)	PUNCT
ejpam-4553	464	9	(	(	PUNCT
ejpam-4553	464	10	akj	akj	PROPN
ejpam-4553	464	11	k+3∑	k+3∑	PROPN
ejpam-4553	464	12	k′=k−3	k′=k−3	NOUN
ejpam-4553	464	13	fk′	fk′	PROPN
ejpam-4553	464	14	)	)	PUNCT
ejpam-4553	464	15	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	464	16	n	n	CCONJ
ejpam-4553	464	17	s	s	PROPN
ejpam-4553	464	18	(	(	PUNCT
ejpam-4553	464	19	·	·	PUNCT
ejpam-4553	464	20	)	)	PUNCT
ejpam-4553	464	21	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	464	22	(	(	PUNCT
ejpam-4553	464	23	·	·	PUNCT
ejpam-4553	464	24	)	)	PUNCT
ejpam-4553	464	25	=	=	SYM
ejpam-4553	464	26	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	465	1	∞∑	∞∑	NUM
ejpam-4553	465	2	k=4	k=4	PROPN
ejpam-4553	465	3	k−4∑	k−4∑	PROPN
ejpam-4553	465	4	j=0	j=0	PROPN
ejpam-4553	465	5	φj(d	φj(d	ADV
ejpam-4553	465	6	)	)	PUNCT
ejpam-4553	465	7	(	(	PUNCT
ejpam-4553	465	8	akjfj	akjfj	NOUN
ejpam-4553	465	9	)	)	PUNCT
ejpam-4553	465	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	466	1	n	n	CCONJ
ejpam-4553	466	2	s	s	PROPN
ejpam-4553	466	3	(	(	PUNCT
ejpam-4553	466	4	·	·	PUNCT
ejpam-4553	466	5	)	)	PUNCT
ejpam-4553	466	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	466	7	(	(	PUNCT
ejpam-4553	466	8	·	·	PUNCT
ejpam-4553	466	9	)	)	PUNCT
ejpam-4553	466	10	.	.	PUNCT
ejpam-4553	467	1	here	here	ADV
ejpam-4553	467	2	fj	fj	X
ejpam-4553	467	3	:	:	PUNCT
ejpam-4553	467	4	=	=	SYM
ejpam-4553	467	5	φ′	φ′	PUNCT
ejpam-4553	467	6	jf	jf	INTJ
ejpam-4553	467	7	where	where	SCONJ
ejpam-4553	467	8	φ′	φ′	NUM
ejpam-4553	467	9	j	j	PROPN
ejpam-4553	467	10	is	be	AUX
ejpam-4553	467	11	a	a	DET
ejpam-4553	467	12	suitably	suitably	ADV
ejpam-4553	467	13	chosen	choose	VERB
ejpam-4553	467	14	smooth	smooth	ADJ
ejpam-4553	467	15	function	function	NOUN
ejpam-4553	467	16	supported	support	VERB
ejpam-4553	467	17	in	in	ADP
ejpam-4553	467	18	the	the	DET
ejpam-4553	467	19	annulus	annulus	NOUN
ejpam-4553	467	20	|ξ|	|ξ|	PROPN
ejpam-4553	467	21	∼	∼	NOUN
ejpam-4553	467	22	2j	2j	NOUN
ejpam-4553	467	23	.	.	PUNCT
ejpam-4553	468	1	moreover	moreover	ADV
ejpam-4553	468	2	we	we	PRON
ejpam-4553	468	3	have	have	VERB
ejpam-4553	468	4	suppf	suppf	NOUN
ejpam-4553	468	5			PUNCT
ejpam-4553	468	6	k−4∑	k−4∑	PROPN
ejpam-4553	468	7	j=0	j=0	PROPN
ejpam-4553	468	8	φj(d	φj(d	ADV
ejpam-4553	468	9	)	)	PUNCT
ejpam-4553	468	10	(	(	PUNCT
ejpam-4553	468	11	akjfj	akjfj	NOUN
ejpam-4553	468	12	)	)	PUNCT
ejpam-4553	469	1			PROPN
ejpam-4553	469	2	⊂	⊂	X
ejpam-4553	469	3	{	{	PUNCT
ejpam-4553	469	4	ξ	ξ	PROPN
ejpam-4553	469	5	∈	∈	PROPN
ejpam-4553	469	6	rn	rn	PROPN
ejpam-4553	469	7	:	:	PUNCT
ejpam-4553	469	8	|ξ|	|ξ|	VERB
ejpam-4553	469	9	∼	∼	NOUN
ejpam-4553	469	10	2k	2k	NUM
ejpam-4553	469	11	}	}	PUNCT
ejpam-4553	469	12	.	.	PUNCT
ejpam-4553	470	1	then	then	ADV
ejpam-4553	470	2	by	by	ADP
ejpam-4553	470	3	lemma	lemma	PROPN
ejpam-4553	470	4	7	7	NUM
ejpam-4553	470	5	,	,	PUNCT
ejpam-4553	470	6	∥a3(x	∥a3(x	PROPN
ejpam-4553	470	7	,	,	PUNCT
ejpam-4553	470	8	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	470	9	s	s	PROPN
ejpam-4553	470	10	(	(	PUNCT
ejpam-4553	470	11	·	·	PUNCT
ejpam-4553	470	12	)	)	PUNCT
ejpam-4553	470	13	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	470	14	(	(	PUNCT
ejpam-4553	470	15	·	·	PUNCT
ejpam-4553	470	16	)	)	PUNCT
ejpam-4553	470	17	=	=	SYM
ejpam-4553	470	18	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4553	470	19	2ks	2ks	X
ejpam-4553	470	20	(	(	PUNCT
ejpam-4553	470	21	·	·	PUNCT
ejpam-4553	470	22	)	)	PUNCT
ejpam-4553	470	23	k−4∑	k−4∑	PROPN
ejpam-4553	470	24	j=0	j=0	PROPN
ejpam-4553	470	25	φj(d	φj(d	ADV
ejpam-4553	470	26	)	)	PUNCT
ejpam-4553	470	27	(	(	PUNCT
ejpam-4553	470	28	akjfj	akjfj	NOUN
ejpam-4553	470	29	)	)	PUNCT
ejpam-4553	470	30			PROPN
ejpam-4553	470	31	k	k	X
ejpam-4553	470	32	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	470	33	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	470	34	(	(	PUNCT
ejpam-4553	470	35	·	·	PUNCT
ejpam-4553	470	36	)	)	PUNCT
ejpam-4553	470	37	)	)	PUNCT
ejpam-4553	470	38	.	.	PUNCT
ejpam-4553	471	1	for	for	ADP
ejpam-4553	471	2	any	any	DET
ejpam-4553	471	3	m	m	NOUN
ejpam-4553	471	4	>	>	X
ejpam-4553	471	5	n+	n+	NUM
ejpam-4553	471	6	clog(s	clog(s	NOUN
ejpam-4553	471	7	)	)	PUNCT
ejpam-4553	471	8	+	+	CCONJ
ejpam-4553	471	9	clog	clog	PROPN
ejpam-4553	471	10	(	(	PUNCT
ejpam-4553	471	11	1	1	NUM
ejpam-4553	471	12	q	q	NOUN
ejpam-4553	471	13	)	)	PUNCT
ejpam-4553	471	14	+	+	CCONJ
ejpam-4553	471	15	nmax	nmax	ADJ
ejpam-4553	471	16	{	{	PUNCT
ejpam-4553	471	17	0	0	NUM
ejpam-4553	471	18	,	,	PUNCT
ejpam-4553	471	19	supx∈rn	supx∈rn	PUNCT
ejpam-4553	471	20	(	(	PUNCT
ejpam-4553	471	21	1	1	NUM
ejpam-4553	471	22	p(x	p(x	NOUN
ejpam-4553	471	23	)	)	PUNCT
ejpam-4553	471	24	−	−	PROPN
ejpam-4553	471	25	1	1	NUM
ejpam-4553	471	26	u(x	u(x	NOUN
ejpam-4553	471	27	)	)	PUNCT
ejpam-4553	471	28	)	)	PUNCT
ejpam-4553	471	29	−	−	PROPN
ejpam-4553	471	30	1	1	NUM
ejpam-4553	471	31	p∞	p∞	PROPN
ejpam-4553	471	32	}	}	PUNCT
ejpam-4553	471	33	we	we	PRON
ejpam-4553	471	34	have	have	VERB
ejpam-4553	471	35	∥a3(x	∥a3(x	ADP
ejpam-4553	471	36	,	,	PUNCT
ejpam-4553	471	37	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	471	38	s	s	PROPN
ejpam-4553	471	39	(	(	PUNCT
ejpam-4553	471	40	·	·	PUNCT
ejpam-4553	471	41	)	)	PUNCT
ejpam-4553	471	42	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	471	43	(	(	PUNCT
ejpam-4553	471	44	·	·	PUNCT
ejpam-4553	471	45	)	)	PUNCT
ejpam-4553	472	1	≲	≲	PROPN
ejpam-4553	472	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	472	3	k−4∑	k−4∑	VERB
ejpam-4553	472	4	j=0	j=0	PROPN
ejpam-4553	472	5	ηj	ηj	PROPN
ejpam-4553	472	6	,	,	PUNCT
ejpam-4553	472	7	m−clog(s	m−clog(s	PROPN
ejpam-4553	472	8	)	)	PUNCT
ejpam-4553	472	9	∗	∗	NOUN
ejpam-4553	472	10	∣∣∣akj2ks(·)φ′	∣∣∣akj2ks(·)φ′	NUM
ejpam-4553	472	11	j(d)f	j(d)f	PROPN
ejpam-4553	472	12	∣∣∣	∣∣∣	NOUN
ejpam-4553	472	13			PROPN
ejpam-4553	472	14	k	k	X
ejpam-4553	472	15	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	473	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	473	2	(	(	PUNCT
ejpam-4553	473	3	·	·	PUNCT
ejpam-4553	473	4	)	)	PUNCT
ejpam-4553	473	5	)	)	PUNCT
ejpam-4553	474	1	≲	≲	PROPN
ejpam-4553	474	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	474	3	k−4∑	k−4∑	VERB
ejpam-4553	474	4	j=0	j=0	PROPN
ejpam-4553	474	5	∣∣∣akj2ks(·)φ′	∣∣∣akj2ks(·)φ′	NUM
ejpam-4553	474	6	j(d)f	j(d)f	PROPN
ejpam-4553	474	7	∣∣∣	∣∣∣	X
ejpam-4553	474	8			PROPN
ejpam-4553	474	9	k	k	X
ejpam-4553	474	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	474	11	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	474	12	(	(	PUNCT
ejpam-4553	474	13	·	·	PUNCT
ejpam-4553	474	14	)	)	PUNCT
ejpam-4553	474	15	)	)	PUNCT
ejpam-4553	475	1	references	reference	VERB
ejpam-4553	475	2	1736	1736	NUM
ejpam-4553	475	3	≲	≲	PROPN
ejpam-4553	475	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	475	5	k−4∑	k−4∑	VERB
ejpam-4553	475	6	j=0	j=0	PROPN
ejpam-4553	475	7	∥akj∥l∞	∥akj∥l∞	CCONJ
ejpam-4553	475	8	∣∣∣2ks(·)φ′	∣∣∣2ks(·)φ′	PROPN
ejpam-4553	475	9	j(d)f	j(d)f	PROPN
ejpam-4553	475	10	∣∣∣	∣∣∣	ADJ
ejpam-4553	475	11			PROPN
ejpam-4553	475	12	k	k	X
ejpam-4553	475	13	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4553	475	14	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4553	475	15	(	(	PUNCT
ejpam-4553	475	16	·	·	PUNCT
ejpam-4553	475	17	)	)	PUNCT
ejpam-4553	475	18	)	)	PUNCT
ejpam-4553	475	19	.	.	PUNCT
ejpam-4553	476	1	the	the	DET
ejpam-4553	476	2	rest	rest	NOUN
ejpam-4553	476	3	is	be	AUX
ejpam-4553	476	4	the	the	DET
ejpam-4553	476	5	same	same	ADJ
ejpam-4553	476	6	as	as	ADP
ejpam-4553	476	7	that	that	PRON
ejpam-4553	476	8	of	of	ADP
ejpam-4553	476	9	a3(x	a3(x	PROPN
ejpam-4553	476	10	,	,	PUNCT
ejpam-4553	476	11	d	d	NOUN
ejpam-4553	476	12	)	)	PUNCT
ejpam-4553	476	13	in	in	ADP
ejpam-4553	476	14	the	the	DET
ejpam-4553	476	15	proof	proof	NOUN
ejpam-4553	476	16	of	of	ADP
ejpam-4553	476	17	theorem	theorem	NOUN
ejpam-4553	476	18	2	2	X
ejpam-4553	476	19	.	.	X
ejpam-4553	476	20	we	we	PRON
ejpam-4553	476	21	obtain	obtain	VERB
ejpam-4553	476	22	∥a3(x	∥a3(x	ADP
ejpam-4553	476	23	,	,	PUNCT
ejpam-4553	476	24	d)∗f∥n	d)∗f∥n	PROPN
ejpam-4553	476	25	s	s	PROPN
ejpam-4553	476	26	(	(	PUNCT
ejpam-4553	476	27	·	·	PUNCT
ejpam-4553	476	28	)	)	PUNCT
ejpam-4553	476	29	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	476	30	(	(	PUNCT
ejpam-4553	476	31	·	·	PUNCT
ejpam-4553	476	32	)	)	PUNCT
ejpam-4553	477	1	≲	≲	PROPN
ejpam-4553	477	2	∥f∥n	∥f∥n	NUM
ejpam-4553	477	3	s	s	PART
ejpam-4553	477	4	(	(	PUNCT
ejpam-4553	477	5	·	·	PUNCT
ejpam-4553	477	6	)	)	PUNCT
ejpam-4553	477	7	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4553	477	8	(	(	PUNCT
ejpam-4553	477	9	·	·	PUNCT
ejpam-4553	477	10	)	)	PUNCT
ejpam-4553	477	11	(	(	PUNCT
ejpam-4553	477	12	17	17	NUM
ejpam-4553	477	13	)	)	PUNCT
ejpam-4553	477	14	the	the	DET
ejpam-4553	477	15	three	three	NUM
ejpam-4553	477	16	estimates	estimate	NOUN
ejpam-4553	477	17	(	(	PUNCT
ejpam-4553	477	18	15	15	NUM
ejpam-4553	477	19	)	)	PUNCT
ejpam-4553	477	20	,	,	PUNCT
ejpam-4553	477	21	(	(	PUNCT
ejpam-4553	477	22	16	16	NUM
ejpam-4553	477	23	)	)	PUNCT
ejpam-4553	477	24	and	and	CCONJ
ejpam-4553	477	25	(	(	PUNCT
ejpam-4553	477	26	17	17	NUM
ejpam-4553	477	27	)	)	PUNCT
ejpam-4553	477	28	yield	yield	NOUN
ejpam-4553	477	29	the	the	DET
ejpam-4553	477	30	desired	desire	VERB
ejpam-4553	477	31	estimate	estimate	NOUN
ejpam-4553	477	32	.	.	PUNCT
ejpam-4553	478	1	□	□	PUNCT
ejpam-4553	478	2	references	reference	NOUN
ejpam-4553	478	3	[	[	X
ejpam-4553	478	4	1	1	NUM
ejpam-4553	478	5	]	]	PUNCT
ejpam-4553	478	6	a.	a.	PROPN
ejpam-4553	478	7	almeida	almeida	PROPN
ejpam-4553	478	8	and	and	CCONJ
ejpam-4553	478	9	a.	a.	PROPN
ejpam-4553	478	10	caetano	caetano	PROPN
ejpam-4553	478	11	.	.	PUNCT
ejpam-4553	479	1	variable	variable	ADJ
ejpam-4553	479	2	exponent	exponent	PROPN
ejpam-4553	479	3	besov	besov	PROPN
ejpam-4553	479	4	-	-	PUNCT
ejpam-4553	479	5	morrey	morrey	NOUN
ejpam-4553	479	6	spaces	space	NOUN
ejpam-4553	479	7	.	.	PUNCT
ejpam-4553	480	1	journal	journal	NOUN
ejpam-4553	480	2	of	of	ADP
ejpam-4553	480	3	fourier	fourier	ADJ
ejpam-4553	480	4	analysis	analysis	NOUN
ejpam-4553	480	5	and	and	CCONJ
ejpam-4553	480	6	applications	application	NOUN
ejpam-4553	480	7	,	,	PUNCT
ejpam-4553	480	8	2020	2020	NUM
ejpam-4553	480	9	.	.	PUNCT
ejpam-4553	481	1	[	[	X
ejpam-4553	481	2	2	2	NUM
ejpam-4553	481	3	]	]	X
ejpam-4553	481	4	g.	g.	PROPN
ejpam-4553	481	5	bourdaud	bourdaud	PROPN
ejpam-4553	481	6	.	.	PUNCT
ejpam-4553	482	1	une	une	AUX
ejpam-4553	482	2	algèbre	algèbre	PROPN
ejpam-4553	482	3	maximale	maximale	PROPN
ejpam-4553	482	4	d’opérateurs	d’opérateur	VERB
ejpam-4553	482	5	pseudo	pseudo	NOUN
ejpam-4553	482	6	-	-	PUNCT
ejpam-4553	482	7	différentiels	différentiel	NOUN
ejpam-4553	482	8	.	.	PUNCT
ejpam-4553	482	9	comm	comm	NOUN
ejpam-4553	482	10	.	.	PUNCT
ejpam-4553	483	1	partial	partial	ADJ
ejpam-4553	483	2	differential	differential	NOUN
ejpam-4553	483	3	equations	equation	NOUN
ejpam-4553	483	4	,	,	PUNCT
ejpam-4553	483	5	13(9):1059–1083	13(9):1059–1083	NUM
ejpam-4553	483	6	,	,	PUNCT
ejpam-4553	483	7	1988	1988	NUM
ejpam-4553	483	8	.	.	PUNCT
ejpam-4553	484	1	[	[	X
ejpam-4553	484	2	3	3	X
ejpam-4553	484	3	]	]	X
ejpam-4553	484	4	r.	r.	PROPN
ejpam-4553	484	5	coifman	coifman	PROPN
ejpam-4553	484	6	and	and	CCONJ
ejpam-4553	484	7	y.	y.	PROPN
ejpam-4553	484	8	meyer	meyer	PROPN
ejpam-4553	484	9	.	.	PROPN
ejpam-4553	484	10	au	au	PROPN
ejpam-4553	484	11	delà	delà	PROPN
ejpam-4553	484	12	des	des	X
ejpam-4553	484	13	opérateurs	opérateurs	X
ejpam-4553	484	14	pseudo	pseudo	NOUN
ejpam-4553	484	15	-	-	NOUN
ejpam-4553	484	16	différentiels	différentiel	NOUN
ejpam-4553	484	17	.	.	PUNCT
ejpam-4553	485	1	société	société	PROPN
ejpam-4553	485	2	mathématique	mathématique	PROPN
ejpam-4553	485	3	de	de	X
ejpam-4553	485	4	france	france	PROPN
ejpam-4553	485	5	,	,	PUNCT
ejpam-4553	485	6	paris	paris	PROPN
ejpam-4553	485	7	.	.	PUNCT
ejpam-4553	485	8	,	,	PUNCT
ejpam-4553	485	9	1978	1978	NUM
ejpam-4553	485	10	.	.	PUNCT
ejpam-4553	486	1	[	[	X
ejpam-4553	486	2	4	4	NUM
ejpam-4553	486	3	]	]	PUNCT
ejpam-4553	486	4	m.	m.	NOUN
ejpam-4553	486	5	congo	congo	PROPN
ejpam-4553	486	6	and	and	CCONJ
ejpam-4553	486	7	m.	m.	PROPN
ejpam-4553	486	8	f.	f.	PROPN
ejpam-4553	486	9	ouedraogo	ouedraogo	PROPN
ejpam-4553	486	10	.	.	PUNCT
ejpam-4553	487	1	boundedness	boundedness	NOUN
ejpam-4553	487	2	of	of	ADP
ejpam-4553	487	3	nonregular	nonregular	ADJ
ejpam-4553	487	4	pseudo	pseudo	NOUN
ejpam-4553	487	5	-	-	NOUN
ejpam-4553	487	6	differential	differential	ADJ
ejpam-4553	487	7	operators	operator	NOUN
ejpam-4553	487	8	on	on	ADP
ejpam-4553	487	9	variable	variable	ADJ
ejpam-4553	487	10	exponent	exponent	NOUN
ejpam-4553	487	11	triebel	triebel	NOUN
ejpam-4553	487	12	-	-	PUNCT
ejpam-4553	487	13	lizorkin	lizorkin	NOUN
ejpam-4553	487	14	-	-	PUNCT
ejpam-4553	487	15	morrey	morrey	NOUN
ejpam-4553	487	16	spaces	space	NOUN
ejpam-4553	487	17	.	.	PUNCT
ejpam-4553	488	1	ejpam	ejpam	NOUN
ejpam-4553	488	2	,	,	PUNCT
ejpam-4553	488	3	15(1):47–63	15(1):47–63	NUM
ejpam-4553	488	4	,	,	PUNCT
ejpam-4553	488	5	2022	2022	NUM
ejpam-4553	488	6	.	.	PUNCT
ejpam-4553	489	1	[	[	X
ejpam-4553	489	2	5	5	X
ejpam-4553	489	3	]	]	PUNCT
ejpam-4553	489	4	d.	d.	PROPN
ejpam-4553	489	5	cruz	cruz	PROPN
ejpam-4553	489	6	-	-	PUNCT
ejpam-4553	489	7	uribe	uribe	PROPN
ejpam-4553	489	8	and	and	CCONJ
ejpam-4553	489	9	a.	a.	NOUN
ejpam-4553	489	10	fiorenza	fiorenza	PROPN
ejpam-4553	489	11	.	.	PUNCT
ejpam-4553	490	1	variable	variable	ADJ
ejpam-4553	490	2	lebesgue	lebesgue	PROPN
ejpam-4553	490	3	spaces	space	NOUN
ejpam-4553	490	4	.	.	PUNCT
ejpam-4553	491	1	birkhäuser	birkhäuser	NOUN
ejpam-4553	491	2	,	,	PUNCT
ejpam-4553	491	3	basel	basel	PROPN
ejpam-4553	491	4	.	.	PROPN
ejpam-4553	491	5	,	,	PUNCT
ejpam-4553	491	6	2013	2013	NUM
ejpam-4553	491	7	.	.	PUNCT
ejpam-4553	492	1	[	[	X
ejpam-4553	492	2	6	6	NUM
ejpam-4553	492	3	]	]	PUNCT
ejpam-4553	492	4	j.	j.	PROPN
ejpam-4553	492	5	xu	xu	PROPN
ejpam-4553	492	6	j.	j.	PROPN
ejpam-4553	492	7	fu	fu	PROPN
ejpam-4553	492	8	.	.	PUNCT
ejpam-4553	493	1	characterizations	characterization	NOUN
ejpam-4553	493	2	of	of	ADP
ejpam-4553	493	3	morrey	morrey	PROPN
ejpam-4553	493	4	type	type	NOUN
ejpam-4553	493	5	besov	besov	NOUN
ejpam-4553	493	6	and	and	CCONJ
ejpam-4553	493	7	triebel	triebel	NOUN
ejpam-4553	493	8	-	-	PUNCT
ejpam-4553	493	9	lizorkin	lizorkin	NOUN
ejpam-4553	493	10	spaces	space	NOUN
ejpam-4553	493	11	with	with	ADP
ejpam-4553	493	12	variable	variable	ADJ
ejpam-4553	493	13	exponents	exponent	NOUN
ejpam-4553	493	14	.	.	PUNCT
ejpam-4553	494	1	j.	j.	PROPN
ejpam-4553	494	2	math	math	PROPN
ejpam-4553	494	3	.	.	PUNCT
ejpam-4553	495	1	anal	anal	PROPN
ejpam-4553	495	2	.	.	PUNCT
ejpam-4553	496	1	appl	appl	PROPN
ejpam-4553	496	2	.	.	PROPN
ejpam-4553	496	3	,	,	PUNCT
ejpam-4553	496	4	381:280–298	381:280–298	NUM
ejpam-4553	496	5	,	,	PUNCT
ejpam-4553	496	6	2011	2011	NUM
ejpam-4553	496	7	.	.	PUNCT
ejpam-4553	497	1	[	[	X
ejpam-4553	497	2	7	7	X
ejpam-4553	497	3	]	]	X
ejpam-4553	497	4	h.	h.	PROPN
ejpam-4553	497	5	kempka	kempka	PROPN
ejpam-4553	497	6	and	and	CCONJ
ejpam-4553	497	7	j.	j.	PROPN
ejpam-4553	497	8	vyb́ıral	vyb́ıral	PROPN
ejpam-4553	497	9	.	.	PUNCT
ejpam-4553	498	1	spaces	space	NOUN
ejpam-4553	498	2	of	of	ADP
ejpam-4553	498	3	variable	variable	ADJ
ejpam-4553	498	4	smoothness	smoothness	NOUN
ejpam-4553	498	5	and	and	CCONJ
ejpam-4553	498	6	integrability	integrability	NOUN
ejpam-4553	498	7	:	:	PUNCT
ejpam-4553	498	8	characterizations	characterization	NOUN
ejpam-4553	498	9	by	by	ADP
ejpam-4553	498	10	local	local	ADJ
ejpam-4553	498	11	means	mean	NOUN
ejpam-4553	498	12	and	and	CCONJ
ejpam-4553	498	13	ball	ball	NOUN
ejpam-4553	498	14	means	mean	NOUN
ejpam-4553	498	15	of	of	ADP
ejpam-4553	498	16	differences	difference	NOUN
ejpam-4553	498	17	.	.	PUNCT
ejpam-4553	499	1	fourier	fouri	ADJ
ejpam-4553	499	2	anal	anal	PROPN
ejpam-4553	499	3	.	.	PUNCT
ejpam-4553	500	1	appl	appl	PROPN
ejpam-4553	500	2	.	.	PROPN
ejpam-4553	500	3	,	,	PUNCT
ejpam-4553	500	4	18(4):852–891	18(4):852–891	PROPN
ejpam-4553	500	5	,	,	PUNCT
ejpam-4553	500	6	2012	2012	NUM
ejpam-4553	500	7	.	.	PUNCT
ejpam-4553	501	1	[	[	X
ejpam-4553	501	2	8	8	NUM
ejpam-4553	501	3	]	]	X
ejpam-4553	501	4	h.	h.	PROPN
ejpam-4553	501	5	kozono	kozono	PROPN
ejpam-4553	501	6	and	and	CCONJ
ejpam-4553	501	7	m.	m.	PROPN
ejpam-4553	501	8	yamazaki	yamazaki	PROPN
ejpam-4553	501	9	.	.	PUNCT
ejpam-4553	502	1	semilinear	semilinear	PROPN
ejpam-4553	502	2	heat	heat	NOUN
ejpam-4553	502	3	equations	equation	NOUN
ejpam-4553	502	4	and	and	CCONJ
ejpam-4553	502	5	the	the	DET
ejpam-4553	502	6	navier	navier	NOUN
ejpam-4553	502	7	-	-	PUNCT
ejpam-4553	502	8	stokes	stoke	NOUN
ejpam-4553	502	9	equation	equation	NOUN
ejpam-4553	502	10	with	with	ADP
ejpam-4553	502	11	distributions	distribution	NOUN
ejpam-4553	502	12	in	in	ADP
ejpam-4553	502	13	new	new	ADJ
ejpam-4553	502	14	function	function	NOUN
ejpam-4553	502	15	spaces	space	NOUN
ejpam-4553	502	16	as	as	ADP
ejpam-4553	502	17	initial	initial	ADJ
ejpam-4553	502	18	data	datum	NOUN
ejpam-4553	502	19	.	.	PUNCT
ejpam-4553	503	1	comm	comm	NOUN
ejpam-4553	503	2	.	.	PUNCT
ejpam-4553	504	1	partial	partial	ADJ
ejpam-4553	504	2	differential	differential	NOUN
ejpam-4553	504	3	equations	equation	NOUN
ejpam-4553	504	4	,	,	PUNCT
ejpam-4553	504	5	19:959–1014	19:959–1014	NUM
ejpam-4553	504	6	,	,	PUNCT
ejpam-4553	504	7	1994	1994	NUM
ejpam-4553	504	8	.	.	PUNCT
ejpam-4553	505	1	[	[	X
ejpam-4553	505	2	9	9	NUM
ejpam-4553	505	3	]	]	PUNCT
ejpam-4553	505	4	p.	p.	NOUN
ejpam-4553	505	5	hästö	hästö	VERB
ejpam-4553	505	6	l.	l.	PROPN
ejpam-4553	505	7	diening	diening	PROPN
ejpam-4553	505	8	and	and	CCONJ
ejpam-4553	505	9	s.	s.	PROPN
ejpam-4553	505	10	roudenko	roudenko	PROPN
ejpam-4553	505	11	.	.	PUNCT
ejpam-4553	506	1	function	function	NOUN
ejpam-4553	506	2	spaces	space	NOUN
ejpam-4553	506	3	of	of	ADP
ejpam-4553	506	4	variable	variable	ADJ
ejpam-4553	506	5	smoothness	smoothness	NOUN
ejpam-4553	506	6	and	and	CCONJ
ejpam-4553	506	7	integrability	integrability	NOUN
ejpam-4553	506	8	.	.	PUNCT
ejpam-4553	507	1	funct	funct	PROPN
ejpam-4553	507	2	.	.	PUNCT
ejpam-4553	508	1	anal	anal	PROPN
ejpam-4553	508	2	.	.	PUNCT
ejpam-4553	508	3	,	,	PUNCT
ejpam-4553	508	4	256(6):1731–1768	256(6):1731–1768	NOUN
ejpam-4553	508	5	,	,	PUNCT
ejpam-4553	508	6	2009	2009	NUM
ejpam-4553	508	7	.	.	PUNCT
ejpam-4553	509	1	[	[	X
ejpam-4553	509	2	10	10	NUM
ejpam-4553	509	3	]	]	PUNCT
ejpam-4553	509	4	p.	p.	NOUN
ejpam-4553	509	5	hästö	hästö	VERB
ejpam-4553	509	6	l.	l.	PROPN
ejpam-4553	509	7	diening	diening	PROPN
ejpam-4553	509	8	,	,	PUNCT
ejpam-4553	509	9	p.	p.	NOUN
ejpam-4553	509	10	harjulehto	harjulehto	NOUN
ejpam-4553	509	11	and	and	CCONJ
ejpam-4553	509	12	m.	m.	PROPN
ejpam-4553	509	13	ruzicka	ruzicka	PROPN
ejpam-4553	509	14	.	.	PUNCT
ejpam-4553	510	1	lebesgue	lebesgue	PROPN
ejpam-4553	510	2	and	and	CCONJ
ejpam-4553	510	3	sobolev	sobolev	NOUN
ejpam-4553	510	4	spaces	space	NOUN
ejpam-4553	510	5	with	with	ADP
ejpam-4553	510	6	variable	variable	ADJ
ejpam-4553	510	7	exponents	exponent	NOUN
ejpam-4553	510	8	.	.	PUNCT
ejpam-4553	510	9	,	,	PUNCT
ejpam-4553	510	10	volume	volume	NOUN
ejpam-4553	510	11	2017	2017	NUM
ejpam-4553	510	12	.	.	PUNCT
ejpam-4553	511	1	springer	springer	NOUN
ejpam-4553	511	2	-	-	PUNCT
ejpam-4553	511	3	verlag	verlag	PROPN
ejpam-4553	511	4	,	,	PUNCT
ejpam-4553	511	5	berlin	berlin	PROPN
ejpam-4553	511	6	,	,	PUNCT
ejpam-4553	511	7	2011	2011	NUM
ejpam-4553	511	8	.	.	PUNCT
ejpam-4553	512	1	[	[	X
ejpam-4553	512	2	11	11	NUM
ejpam-4553	512	3	]	]	PUNCT
ejpam-4553	512	4	j.	j.	PROPN
ejpam-4553	512	5	marschall	marschall	PROPN
ejpam-4553	512	6	.	.	PUNCT
ejpam-4553	513	1	pseudodifferential	pseudodifferential	ADJ
ejpam-4553	513	2	operators	operator	NOUN
ejpam-4553	513	3	with	with	ADP
ejpam-4553	513	4	coefficients	coefficient	NOUN
ejpam-4553	513	5	in	in	ADP
ejpam-4553	513	6	sobolev	sobolev	NOUN
ejpam-4553	513	7	spaces	space	NOUN
ejpam-4553	513	8	.	.	PUNCT
ejpam-4553	514	1	trans	trans	PROPN
ejpam-4553	514	2	.	.	PUNCT
ejpam-4553	515	1	amer	amer	PROPN
ejpam-4553	515	2	.	.	PUNCT
ejpam-4553	515	3	math	math	PROPN
ejpam-4553	515	4	.	.	PUNCT
ejpam-4553	516	1	soc	soc	PROPN
ejpam-4553	516	2	.	.	PUNCT
ejpam-4553	516	3	,	,	PUNCT
ejpam-4553	516	4	307(1):335–361	307(1):335–361	NUM
ejpam-4553	516	5	,	,	PUNCT
ejpam-4553	516	6	1988	1988	NUM
ejpam-4553	516	7	.	.	PUNCT
ejpam-4553	517	1	references	reference	NOUN
ejpam-4553	517	2	1737	1737	NUM
ejpam-4553	517	3	[	[	X
ejpam-4553	517	4	12	12	NUM
ejpam-4553	517	5	]	]	PUNCT
ejpam-4553	517	6	j.	j.	PROPN
ejpam-4553	517	7	marschall	marschall	PROPN
ejpam-4553	517	8	.	.	PUNCT
ejpam-4553	518	1	nonregular	nonregular	ADJ
ejpam-4553	518	2	pseudo	pseudo	NOUN
ejpam-4553	518	3	-	-	ADJ
ejpam-4553	518	4	differential	differential	ADJ
ejpam-4553	518	5	operators	operator	NOUN
ejpam-4553	518	6	.	.	PUNCT
ejpam-4553	519	1	z.	z.	PROPN
ejpam-4553	519	2	anal	anal	PROPN
ejpam-4553	519	3	.	.	PUNCT
ejpam-4553	520	1	anwend	anwend	PROPN
ejpam-4553	520	2	,	,	PUNCT
ejpam-4553	520	3	15(1):109	15(1):109	NUM
ejpam-4553	520	4	–	–	PUNCT
ejpam-4553	520	5	148	148	NUM
ejpam-4553	520	6	,	,	PUNCT
ejpam-4553	520	7	1996	1996	NUM
ejpam-4553	520	8	.	.	PUNCT
ejpam-4553	521	1	[	[	X
ejpam-4553	521	2	13	13	NUM
ejpam-4553	521	3	]	]	PUNCT
ejpam-4553	521	4	a.	a.	NOUN
ejpam-4553	521	5	mazzucato	mazzucato	PROPN
ejpam-4553	521	6	.	.	PUNCT
ejpam-4553	522	1	besov	besov	NOUN
ejpam-4553	522	2	-	-	PUNCT
ejpam-4553	522	3	morrey	morrey	NOUN
ejpam-4553	522	4	spaces	space	NOUN
ejpam-4553	522	5	:	:	PUNCT
ejpam-4553	522	6	function	function	NOUN
ejpam-4553	522	7	space	space	NOUN
ejpam-4553	522	8	theory	theory	NOUN
ejpam-4553	522	9	and	and	CCONJ
ejpam-4553	522	10	applications	application	NOUN
ejpam-4553	522	11	to	to	ADP
ejpam-4553	522	12	nonlinear	nonlinear	ADJ
ejpam-4553	522	13	pde	pde	NOUN
ejpam-4553	522	14	.	.	PUNCT
ejpam-4553	523	1	trans	trans	PROPN
ejpam-4553	523	2	.	.	PUNCT
ejpam-4553	524	1	amer	amer	PROPN
ejpam-4553	524	2	.	.	PUNCT
ejpam-4553	524	3	math	math	PROPN
ejpam-4553	524	4	.	.	PUNCT
ejpam-4553	525	1	soc	soc	PROPN
ejpam-4553	525	2	.	.	PUNCT
ejpam-4553	525	3	,	,	PUNCT
ejpam-4553	525	4	355:1297–1364	355:1297–1364	NUM
ejpam-4553	525	5	,	,	PUNCT
ejpam-4553	525	6	2003	2003	NUM
ejpam-4553	525	7	.	.	PUNCT
ejpam-4553	526	1	[	[	X
ejpam-4553	526	2	14	14	NUM
ejpam-4553	526	3	]	]	X
ejpam-4553	526	4	t.	t.	NOUN
ejpam-4553	526	5	runst	runst	PROPN
ejpam-4553	526	6	.	.	PUNCT
ejpam-4553	527	1	para	para	NOUN
ejpam-4553	527	2	-	-	PUNCT
ejpam-4553	527	3	differential	differential	NOUN
ejpam-4553	527	4	operators	operator	NOUN
ejpam-4553	527	5	in	in	ADP
ejpam-4553	527	6	spaces	space	NOUN
ejpam-4553	527	7	of	of	ADP
ejpam-4553	527	8	triebel	triebel	NOUN
ejpam-4553	527	9	-	-	PUNCT
ejpam-4553	527	10	lizorkin	lizorkin	NOUN
ejpam-4553	527	11	and	and	CCONJ
ejpam-4553	527	12	besov	besov	PROPN
ejpam-4553	527	13	typee	typee	PROPN
ejpam-4553	527	14	.	.	PUNCT
ejpam-4553	528	1	z.	z.	PROPN
ejpam-4553	528	2	anal	anal	PROPN
ejpam-4553	528	3	.	.	PUNCT
ejpam-4553	529	1	anwendungen	anwendungen	PROPN
ejpam-4553	529	2	.	.	PROPN
ejpam-4553	529	3	,	,	PUNCT
ejpam-4553	529	4	4:557–573	4:557–573	NOUN
ejpam-4553	529	5	,	,	PUNCT
ejpam-4553	529	6	1985	1985	NUM
ejpam-4553	529	7	.	.	PUNCT
ejpam-4553	530	1	[	[	X
ejpam-4553	530	2	15	15	NUM
ejpam-4553	530	3	]	]	X
ejpam-4553	530	4	y.	y.	PROPN
ejpam-4553	530	5	sawano	sawano	PROPN
ejpam-4553	530	6	.	.	PUNCT
ejpam-4553	531	1	a	a	DET
ejpam-4553	531	2	note	note	NOUN
ejpam-4553	531	3	on	on	ADP
ejpam-4553	531	4	besov	besov	NOUN
ejpam-4553	531	5	-	-	PUNCT
ejpam-4553	531	6	morrey	morrey	NOUN
ejpam-4553	531	7	spaces	space	NOUN
ejpam-4553	531	8	and	and	CCONJ
ejpam-4553	531	9	triebel	triebel	NOUN
ejpam-4553	531	10	-	-	PUNCT
ejpam-4553	531	11	lizorkin	lizorkin	NOUN
ejpam-4553	531	12	-	-	PUNCT
ejpam-4553	531	13	morrey	morrey	NOUN
ejpam-4553	531	14	spaces	space	NOUN
ejpam-4553	531	15	.	.	PUNCT
ejpam-4553	532	1	acta	acta	PROPN
ejpam-4553	532	2	math	math	PROPN
ejpam-4553	532	3	.	.	PUNCT
ejpam-4553	533	1	sin	sin	NOUN
ejpam-4553	533	2	.	.	PUNCT
ejpam-4553	533	3	,	,	PUNCT
ejpam-4553	533	4	25:1223–1242	25:1223–1242	PROPN
ejpam-4553	533	5	,	,	PUNCT
ejpam-4553	533	6	2009	2009	NUM
ejpam-4553	533	7	.	.	PUNCT
ejpam-4553	534	1	[	[	X
ejpam-4553	534	2	16	16	NUM
ejpam-4553	534	3	]	]	PUNCT
ejpam-4553	534	4	m.	m.	PROPN
ejpam-4553	534	5	e.	e.	PROPN
ejpam-4553	534	6	taylor	taylor	PROPN
ejpam-4553	534	7	.	.	PUNCT
ejpam-4553	535	1	partial	partial	ADJ
ejpam-4553	535	2	differential	differential	PROPN
ejpam-4553	535	3	equations	equations	PROPN
ejpam-4553	535	4	iii	iii	PROPN
ejpam-4553	535	5	.	.	PUNCT
ejpam-4553	535	6	springer	springer	NOUN
ejpam-4553	535	7	-	-	PUNCT
ejpam-4553	535	8	verlag	verlag	PROPN
ejpam-4553	535	9	new	new	PROPN
ejpam-4553	535	10	york	york	PROPN
ejpam-4553	535	11	,	,	PUNCT
ejpam-4553	535	12	inc	inc	PROPN
ejpam-4553	535	13	,	,	PUNCT
ejpam-4553	535	14	1996	1996	NUM
ejpam-4553	535	15	.	.	PUNCT
ejpam-4553	536	1	[	[	X
ejpam-4553	536	2	17	17	NUM
ejpam-4553	536	3	]	]	X
ejpam-4553	536	4	h.	h.	PROPN
ejpam-4553	536	5	triebel	triebel	PROPN
ejpam-4553	536	6	.	.	PUNCT
ejpam-4553	537	1	besov	besov	NOUN
ejpam-4553	537	2	spaces	space	NOUN
ejpam-4553	537	3	with	with	ADP
ejpam-4553	537	4	variable	variable	ADJ
ejpam-4553	537	5	smoothness	smoothness	NOUN
ejpam-4553	537	6	and	and	CCONJ
ejpam-4553	537	7	integrability	integrability	NOUN
ejpam-4553	537	8	.	.	PUNCT
ejpam-4553	538	1	birkhauser	birkhauser	PROPN
ejpam-4553	538	2	verlag	verlag	PROPN
ejpam-4553	538	3	,	,	PUNCT
ejpam-4553	538	4	basel	basel	PROPN
ejpam-4553	538	5	and	and	CCONJ
ejpam-4553	538	6	al	al	PROPN
ejpam-4553	538	7	.	.	PROPN
ejpam-4553	538	8	,	,	PUNCT
ejpam-4553	538	9	1983	1983	NUM
ejpam-4553	538	10	.	.	PUNCT
ejpam-4553	539	1	[	[	X
ejpam-4553	539	2	18	18	NUM
ejpam-4553	539	3	]	]	PUNCT
ejpam-4553	539	4	w.	w.	PROPN
ejpam-4553	539	5	sickel	sickel	PROPN
ejpam-4553	539	6	w.	w.	PROPN
ejpam-4553	539	7	yuan	yuan	PROPN
ejpam-4553	539	8	and	and	CCONJ
ejpam-4553	539	9	d.	d.	PROPN
ejpam-4553	539	10	yang	yang	PROPN
ejpam-4553	539	11	.	.	PUNCT
ejpam-4553	540	1	morrey	morrey	PROPN
ejpam-4553	540	2	and	and	CCONJ
ejpam-4553	540	3	campanato	campanato	PROPN
ejpam-4553	540	4	meet	meet	NOUN
ejpam-4553	540	5	besov	besov	NOUN
ejpam-4553	540	6	,	,	PUNCT
ejpam-4553	540	7	lizorkin	lizorkin	NOUN
ejpam-4553	540	8	and	and	CCONJ
ejpam-4553	540	9	triebel	triebel	NOUN
ejpam-4553	540	10	.	.	PUNCT
ejpam-4553	541	1	lecture	lecture	NOUN
ejpam-4553	541	2	notes	note	NOUN
ejpam-4553	541	3	in	in	ADP
ejpam-4553	541	4	mathematics	mathematic	NOUN
ejpam-4553	541	5	.	.	PUNCT
ejpam-4553	542	1	springer	springer	PROPN
ejpam-4553	542	2	,	,	PUNCT
ejpam-4553	542	3	berlin	berlin	PROPN
ejpam-4553	542	4	.	.	PROPN
ejpam-4553	542	5	,	,	PUNCT
ejpam-4553	542	6	2005	2005	NUM
ejpam-4553	542	7	,	,	PUNCT
ejpam-4553	542	8	2010	2010	NUM
ejpam-4553	542	9	.	.	PUNCT