id	sid	tid	token	lemma	pos
ejpam-4200	1	1	european	european	PROPN
ejpam-4200	1	2	journal	journal	PROPN
ejpam-4200	1	3	of	of	ADP
ejpam-4200	1	4	pure	pure	ADJ
ejpam-4200	1	5	and	and	CCONJ
ejpam-4200	1	6	applied	apply	VERB
ejpam-4200	1	7	mathematics	mathematic	NOUN
ejpam-4200	1	8	vol	vol	NOUN
ejpam-4200	1	9	.	.	PROPN
ejpam-4200	2	1	15	15	NUM
ejpam-4200	2	2	,	,	PUNCT
ejpam-4200	2	3	no	no	INTJ
ejpam-4200	2	4	.	.	NOUN
ejpam-4200	2	5	1	1	NUM
ejpam-4200	2	6	,	,	PUNCT
ejpam-4200	2	7	2022	2022	NUM
ejpam-4200	2	8	,	,	PUNCT
ejpam-4200	2	9	47	47	NUM
ejpam-4200	2	10	-	-	SYM
ejpam-4200	2	11	63	63	NUM
ejpam-4200	2	12	issn	issn	PROPN
ejpam-4200	2	13	1307	1307	NUM
ejpam-4200	2	14	-	-	SYM
ejpam-4200	2	15	5543	5543	NUM
ejpam-4200	2	16	–	–	PUNCT
ejpam-4200	2	17	ejpam.com	ejpam.com	X
ejpam-4200	2	18	published	publish	VERB
ejpam-4200	2	19	by	by	ADP
ejpam-4200	2	20	new	new	PROPN
ejpam-4200	2	21	york	york	PROPN
ejpam-4200	2	22	business	business	PROPN
ejpam-4200	2	23	global	global	PROPN
ejpam-4200	2	24	boundedness	boundedness	NOUN
ejpam-4200	2	25	of	of	ADP
ejpam-4200	2	26	non	non	ADJ
ejpam-4200	2	27	regular	regular	ADJ
ejpam-4200	2	28	pseudo	pseudo	NOUN
ejpam-4200	2	29	-	-	ADJ
ejpam-4200	2	30	differential	differential	ADJ
ejpam-4200	2	31	operators	operator	NOUN
ejpam-4200	2	32	on	on	ADP
ejpam-4200	2	33	variable	variable	ADJ
ejpam-4200	2	34	exponent	exponent	NOUN
ejpam-4200	2	35	triebel	triebel	NOUN
ejpam-4200	2	36	-	-	PUNCT
ejpam-4200	2	37	lizorkin	lizorkin	NOUN
ejpam-4200	2	38	-	-	PUNCT
ejpam-4200	2	39	morrey	morrey	NOUN
ejpam-4200	2	40	spaces	space	NOUN
ejpam-4200	2	41	mohamed	mohamed	PROPN
ejpam-4200	2	42	congo1,∗	congo1,∗	PROPN
ejpam-4200	2	43	,	,	PUNCT
ejpam-4200	2	44	marie	marie	PROPN
ejpam-4200	2	45	françoise	françoise	PROPN
ejpam-4200	2	46	ouedraogo1	ouedraogo1	PROPN
ejpam-4200	2	47	1	1	NUM
ejpam-4200	2	48	laboratoire	laboratoire	PROPN
ejpam-4200	2	49	de	de	X
ejpam-4200	2	50	théorie	théorie	PROPN
ejpam-4200	2	51	des	des	PROPN
ejpam-4200	2	52	nombres	nombres	PROPN
ejpam-4200	2	53	,	,	PUNCT
ejpam-4200	2	54	algèbre	algèbre	PROPN
ejpam-4200	2	55	,	,	PUNCT
ejpam-4200	2	56	géométrie	géométrie	PROPN
ejpam-4200	2	57	algébrique	algébrique	NOUN
ejpam-4200	2	58	,	,	PUNCT
ejpam-4200	2	59	topologie	topologie	NOUN
ejpam-4200	2	60	algébrique	algébrique	NOUN
ejpam-4200	2	61	et	et	PROPN
ejpam-4200	2	62	applications(tn	applications(tn	PROPN
ejpam-4200	2	63	-	-	PUNCT
ejpam-4200	2	64	agata	agata	PROPN
ejpam-4200	2	65	)	)	PUNCT
ejpam-4200	2	66	.	.	PUNCT
ejpam-4200	3	1	ufr	ufr	PROPN
ejpam-4200	3	2	sciences	sciences	PROPN
ejpam-4200	3	3	exactes	exact	VERB
ejpam-4200	3	4	et	et	NOUN
ejpam-4200	3	5	appliquées/	appliquées/	PROPN
ejpam-4200	3	6	université	université	NOUN
ejpam-4200	3	7	joseph	joseph	PROPN
ejpam-4200	3	8	ki	ki	PROPN
ejpam-4200	3	9	-	-	PUNCT
ejpam-4200	3	10	zerbo	zerbo	PROPN
ejpam-4200	3	11	,	,	PUNCT
ejpam-4200	3	12	03	03	NUM
ejpam-4200	3	13	bp	bp	PROPN
ejpam-4200	3	14	7021	7021	NUM
ejpam-4200	3	15	ouaga	ouaga	NOUN
ejpam-4200	3	16	03	03	NUM
ejpam-4200	3	17	,	,	PUNCT
ejpam-4200	3	18	ouagadougou	ouagadougou	PROPN
ejpam-4200	3	19	,	,	PUNCT
ejpam-4200	3	20	burkina	burkina	PROPN
ejpam-4200	3	21	faso	faso	PROPN
ejpam-4200	3	22	abstract	abstract	NOUN
ejpam-4200	3	23	.	.	PUNCT
ejpam-4200	4	1	in	in	ADP
ejpam-4200	4	2	this	this	DET
ejpam-4200	4	3	paper	paper	NOUN
ejpam-4200	4	4	,	,	PUNCT
ejpam-4200	4	5	we	we	PRON
ejpam-4200	4	6	study	study	VERB
ejpam-4200	4	7	the	the	DET
ejpam-4200	4	8	boundedness	boundedness	NOUN
ejpam-4200	4	9	of	of	ADP
ejpam-4200	4	10	non	non	ADJ
ejpam-4200	4	11	regular	regular	ADJ
ejpam-4200	4	12	pseudo	pseudo	NOUN
ejpam-4200	4	13	-	-	ADJ
ejpam-4200	4	14	differential	differential	ADJ
ejpam-4200	4	15	operators	operator	NOUN
ejpam-4200	4	16	on	on	ADP
ejpam-4200	4	17	variable	variable	ADJ
ejpam-4200	4	18	exponent	exponent	NOUN
ejpam-4200	4	19	besov	besov	NOUN
ejpam-4200	4	20	-	-	PUNCT
ejpam-4200	4	21	morrey	morrey	PROPN
ejpam-4200	4	22	spaces	space	NOUN
ejpam-4200	4	23	es	es	VERB
ejpam-4200	4	24	(	(	PUNCT
ejpam-4200	4	25	·	·	PUNCT
ejpam-4200	4	26	)	)	PUNCT
ejpam-4200	4	27	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	4	28	(	(	PUNCT
ejpam-4200	4	29	·	·	PUNCT
ejpam-4200	4	30	)	)	PUNCT
ejpam-4200	4	31	with	with	ADP
ejpam-4200	4	32	symbols	symbol	NOUN
ejpam-4200	4	33	a(x	a(x	PROPN
ejpam-4200	4	34	,	,	PUNCT
ejpam-4200	4	35	ξ	ξ	X
ejpam-4200	4	36	)	)	PUNCT
ejpam-4200	4	37	belonging	belong	VERB
ejpam-4200	4	38	to	to	ADP
ejpam-4200	4	39	cℓ	cℓ	ADP
ejpam-4200	4	40	∗s	∗s	PROPN
ejpam-4200	4	41	m	m	NOUN
ejpam-4200	4	42	1,δ	1,δ	NUM
ejpam-4200	4	43	.	.	PUNCT
ejpam-4200	5	1	for	for	ADP
ejpam-4200	5	2	these	these	DET
ejpam-4200	5	3	symbols	symbol	NOUN
ejpam-4200	5	4	x	x	NOUN
ejpam-4200	5	5	-	-	NOUN
ejpam-4200	5	6	regularity	regularity	NOUN
ejpam-4200	5	7	is	be	AUX
ejpam-4200	5	8	measured	measure	VERB
ejpam-4200	5	9	in	in	ADP
ejpam-4200	5	10	hölder	hölder	NOUN
ejpam-4200	5	11	-	-	PUNCT
ejpam-4200	5	12	zygmund	zygmund	NOUN
ejpam-4200	5	13	spaces	space	NOUN
ejpam-4200	5	14	.	.	PUNCT
ejpam-4200	6	1	2020	2020	NUM
ejpam-4200	6	2	mathematics	mathematic	NOUN
ejpam-4200	6	3	subject	subject	NOUN
ejpam-4200	6	4	classifications	classification	NOUN
ejpam-4200	6	5	:	:	PUNCT
ejpam-4200	6	6	42b35,46e30,35s05	42b35,46e30,35s05	NUM
ejpam-4200	6	7	key	key	ADJ
ejpam-4200	6	8	words	word	NOUN
ejpam-4200	6	9	and	and	CCONJ
ejpam-4200	6	10	phrases	phrase	NOUN
ejpam-4200	6	11	:	:	PUNCT
ejpam-4200	6	12	pseudo	pseudo	NOUN
ejpam-4200	6	13	-	-	NOUN
ejpam-4200	6	14	differential	differential	ADJ
ejpam-4200	6	15	operators	operator	NOUN
ejpam-4200	6	16	,	,	PUNCT
ejpam-4200	6	17	non	non	X
ejpam-4200	6	18	regular	regular	ADJ
ejpam-4200	6	19	symbols	symbol	NOUN
ejpam-4200	6	20	,	,	PUNCT
ejpam-4200	6	21	variable	variable	ADJ
ejpam-4200	6	22	exponent	exponent	NOUN
ejpam-4200	6	23	triebel	triebel	NOUN
ejpam-4200	6	24	-	-	PUNCT
ejpam-4200	6	25	lizorkin	lizorkin	NOUN
ejpam-4200	6	26	-	-	PUNCT
ejpam-4200	6	27	morrey	morrey	NOUN
ejpam-4200	6	28	spaces	space	VERB
ejpam-4200	6	29	1	1	NUM
ejpam-4200	6	30	.	.	PUNCT
ejpam-4200	7	1	introduction	introduction	NOUN
ejpam-4200	7	2	pseudo	pseudo	NOUN
ejpam-4200	7	3	-	-	NOUN
ejpam-4200	7	4	differential	differential	ADJ
ejpam-4200	7	5	calculus	calculus	NOUN
ejpam-4200	7	6	is	be	AUX
ejpam-4200	7	7	a	a	DET
ejpam-4200	7	8	well	well	ADV
ejpam-4200	7	9	-	-	PUNCT
ejpam-4200	7	10	established	establish	VERB
ejpam-4200	7	11	tool	tool	NOUN
ejpam-4200	7	12	for	for	ADP
ejpam-4200	7	13	the	the	DET
ejpam-4200	7	14	analysis	analysis	NOUN
ejpam-4200	7	15	of	of	ADP
ejpam-4200	7	16	partial	partial	ADJ
ejpam-4200	7	17	differential	differential	NOUN
ejpam-4200	7	18	equations	equation	NOUN
ejpam-4200	7	19	,	,	PUNCT
ejpam-4200	7	20	especially	especially	ADV
ejpam-4200	7	21	non	non	ADJ
ejpam-4200	7	22	-	-	ADJ
ejpam-4200	7	23	linear	linear	ADJ
ejpam-4200	7	24	ones	one	NOUN
ejpam-4200	7	25	.	.	PUNCT
ejpam-4200	8	1	indeed	indeed	ADV
ejpam-4200	8	2	,	,	PUNCT
ejpam-4200	8	3	in	in	ADP
ejpam-4200	8	4	[	[	PUNCT
ejpam-4200	8	5	16	16	NUM
ejpam-4200	8	6	]	]	X
ejpam-4200	8	7	one	one	PRON
ejpam-4200	8	8	can	can	AUX
ejpam-4200	8	9	find	find	VERB
ejpam-4200	8	10	many	many	ADJ
ejpam-4200	8	11	applications	application	NOUN
ejpam-4200	8	12	of	of	ADP
ejpam-4200	8	13	the	the	DET
ejpam-4200	8	14	calculus	calculus	NOUN
ejpam-4200	8	15	of	of	ADP
ejpam-4200	8	16	non	non	ADJ
ejpam-4200	8	17	regular	regular	ADJ
ejpam-4200	8	18	pseudo	pseudo	NOUN
ejpam-4200	8	19	-	-	ADJ
ejpam-4200	8	20	differential	differential	ADJ
ejpam-4200	8	21	operators	operator	NOUN
ejpam-4200	8	22	to	to	ADP
ejpam-4200	8	23	non	non	ADJ
ejpam-4200	8	24	-	-	ADJ
ejpam-4200	8	25	linear	linear	ADJ
ejpam-4200	8	26	differential	differential	ADJ
ejpam-4200	8	27	equations	equation	NOUN
ejpam-4200	8	28	.	.	PUNCT
ejpam-4200	9	1	the	the	DET
ejpam-4200	9	2	boundedness	boundedness	NOUN
ejpam-4200	9	3	of	of	ADP
ejpam-4200	9	4	these	these	DET
ejpam-4200	9	5	operators	operator	NOUN
ejpam-4200	9	6	has	have	AUX
ejpam-4200	9	7	been	be	AUX
ejpam-4200	9	8	extensively	extensively	ADV
ejpam-4200	9	9	addressed	address	VERB
ejpam-4200	9	10	in	in	ADP
ejpam-4200	9	11	several	several	ADJ
ejpam-4200	9	12	works	work	NOUN
ejpam-4200	9	13	.	.	PUNCT
ejpam-4200	10	1	for	for	ADP
ejpam-4200	10	2	boundedness	boundedness	NOUN
ejpam-4200	10	3	on	on	ADP
ejpam-4200	10	4	lebesgue	lebesgue	ADJ
ejpam-4200	10	5	spaces	space	NOUN
ejpam-4200	10	6	,	,	PUNCT
ejpam-4200	10	7	besov	besov	NOUN
ejpam-4200	10	8	spaces	space	NOUN
ejpam-4200	10	9	,	,	PUNCT
ejpam-4200	10	10	triebel	triebel	NOUN
ejpam-4200	10	11	-	-	PUNCT
ejpam-4200	10	12	lizorkin	lizorkin	NOUN
ejpam-4200	10	13	spaces	space	NOUN
ejpam-4200	10	14	and	and	CCONJ
ejpam-4200	10	15	sobolev	sobolev	NOUN
ejpam-4200	10	16	spaces	space	NOUN
ejpam-4200	10	17	,	,	PUNCT
ejpam-4200	10	18	we	we	PRON
ejpam-4200	10	19	refer	refer	VERB
ejpam-4200	10	20	to	to	ADP
ejpam-4200	10	21	[	[	X
ejpam-4200	10	22	2	2	NUM
ejpam-4200	10	23	]	]	PUNCT
ejpam-4200	10	24	,	,	PUNCT
ejpam-4200	10	25	[	[	X
ejpam-4200	10	26	6	6	NUM
ejpam-4200	10	27	]	]	PUNCT
ejpam-4200	10	28	,	,	PUNCT
ejpam-4200	10	29	[	[	X
ejpam-4200	10	30	12	12	NUM
ejpam-4200	10	31	]	]	PUNCT
ejpam-4200	10	32	and	and	CCONJ
ejpam-4200	10	33	[	[	X
ejpam-4200	10	34	13	13	NUM
ejpam-4200	10	35	]	]	PUNCT
ejpam-4200	10	36	.	.	PUNCT
ejpam-4200	11	1	the	the	DET
ejpam-4200	11	2	boundedness	boundedness	NOUN
ejpam-4200	11	3	of	of	ADP
ejpam-4200	11	4	pseudo	pseudo	NOUN
ejpam-4200	11	5	-	-	ADJ
ejpam-4200	11	6	differential	differential	ADJ
ejpam-4200	11	7	operators	operator	NOUN
ejpam-4200	11	8	in	in	ADP
ejpam-4200	11	9	triebel	triebel	NOUN
ejpam-4200	11	10	-	-	PUNCT
ejpam-4200	11	11	lizorkin	lizorkin	NOUN
ejpam-4200	11	12	-	-	PUNCT
ejpam-4200	11	13	morrey	morrey	NOUN
ejpam-4200	11	14	spacses	spacse	NOUN
ejpam-4200	11	15	with	with	ADP
ejpam-4200	11	16	constant	constant	ADJ
ejpam-4200	11	17	exponents	exponent	NOUN
ejpam-4200	11	18	denoted	denote	VERB
ejpam-4200	11	19	es	es	ADP
ejpam-4200	11	20	p	p	X
ejpam-4200	11	21	,	,	PUNCT
ejpam-4200	11	22	u	u	NOUN
ejpam-4200	11	23	,	,	PUNCT
ejpam-4200	11	24	q	q	PUNCT
ejpam-4200	11	25	was	be	AUX
ejpam-4200	11	26	studied	study	VERB
ejpam-4200	11	27	by	by	ADP
ejpam-4200	11	28	yoshihiro	yoshihiro	PROPN
ejpam-4200	11	29	sawano	sawano	PROPN
ejpam-4200	11	30	in	in	ADP
ejpam-4200	11	31	[	[	X
ejpam-4200	11	32	15	15	NUM
ejpam-4200	11	33	]	]	PUNCT
ejpam-4200	11	34	.	.	PUNCT
ejpam-4200	12	1	our	our	PRON
ejpam-4200	12	2	focus	focus	NOUN
ejpam-4200	12	3	in	in	ADP
ejpam-4200	12	4	this	this	DET
ejpam-4200	12	5	paper	paper	NOUN
ejpam-4200	12	6	concerns	concern	VERB
ejpam-4200	12	7	the	the	DET
ejpam-4200	12	8	boundedness	boundedness	NOUN
ejpam-4200	12	9	of	of	ADP
ejpam-4200	12	10	pseudo	pseudo	NOUN
ejpam-4200	12	11	-	-	ADJ
ejpam-4200	12	12	differential	differential	ADJ
ejpam-4200	12	13	operators	operator	NOUN
ejpam-4200	12	14	on	on	ADP
ejpam-4200	12	15	triebel	triebel	NOUN
ejpam-4200	12	16	-	-	PUNCT
ejpam-4200	12	17	lizorkin	lizorkin	NOUN
ejpam-4200	12	18	-	-	PUNCT
ejpam-4200	12	19	morrey	morrey	NOUN
ejpam-4200	12	20	spaces	space	NOUN
ejpam-4200	12	21	with	with	ADP
ejpam-4200	12	22	variable	variable	ADJ
ejpam-4200	12	23	exponents	exponent	NOUN
ejpam-4200	12	24	denoted	denote	VERB
ejpam-4200	12	25	es	es	NUM
ejpam-4200	12	26	(	(	PUNCT
ejpam-4200	12	27	·	·	PUNCT
ejpam-4200	12	28	)	)	PUNCT
ejpam-4200	12	29	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	12	30	(	(	PUNCT
ejpam-4200	12	31	·	·	PUNCT
ejpam-4200	12	32	)	)	PUNCT
ejpam-4200	12	33	(	(	PUNCT
ejpam-4200	12	34	see	see	VERB
ejpam-4200	12	35	[	[	X
ejpam-4200	12	36	4	4	NUM
ejpam-4200	12	37	]	]	PUNCT
ejpam-4200	12	38	)	)	PUNCT
ejpam-4200	12	39	with	with	ADP
ejpam-4200	12	40	symbols	symbol	NOUN
ejpam-4200	12	41	in	in	ADP
ejpam-4200	12	42	the	the	DET
ejpam-4200	12	43	class	class	NOUN
ejpam-4200	12	44	cℓ	cℓ	ADP
ejpam-4200	12	45	∗s	∗s	PROPN
ejpam-4200	12	46	m	m	NOUN
ejpam-4200	12	47	1,δ	1,δ	NUM
ejpam-4200	12	48	.	.	PUNCT
ejpam-4200	13	1	the	the	DET
ejpam-4200	13	2	results	result	NOUN
ejpam-4200	13	3	of	of	ADP
ejpam-4200	13	4	this	this	DET
ejpam-4200	13	5	paper	paper	NOUN
ejpam-4200	13	6	are	be	AUX
ejpam-4200	13	7	certainly	certainly	ADV
ejpam-4200	13	8	relevant	relevant	ADJ
ejpam-4200	13	9	because	because	SCONJ
ejpam-4200	13	10	they	they	PRON
ejpam-4200	13	11	generalize	generalize	VERB
ejpam-4200	13	12	those	those	PRON
ejpam-4200	13	13	of	of	ADP
ejpam-4200	13	14	[	[	X
ejpam-4200	13	15	15	15	NUM
ejpam-4200	13	16	]	]	PUNCT
ejpam-4200	13	17	.	.	PUNCT
ejpam-4200	14	1	our	our	PRON
ejpam-4200	14	2	approach	approach	NOUN
ejpam-4200	14	3	is	be	AUX
ejpam-4200	14	4	as	as	SCONJ
ejpam-4200	14	5	follows	follow	VERB
ejpam-4200	14	6	.	.	PUNCT
ejpam-4200	15	1	to	to	PART
ejpam-4200	15	2	treat	treat	VERB
ejpam-4200	15	3	the	the	DET
ejpam-4200	15	4	boundedness	boundedness	NOUN
ejpam-4200	15	5	of	of	ADP
ejpam-4200	15	6	these	these	DET
ejpam-4200	15	7	operators	operator	NOUN
ejpam-4200	15	8	with	with	ADP
ejpam-4200	15	9	non	non	ADJ
ejpam-4200	15	10	-	-	ADJ
ejpam-4200	15	11	regular	regular	ADJ
ejpam-4200	15	12	symbols	symbol	NOUN
ejpam-4200	15	13	belonging	belong	VERB
ejpam-4200	15	14	to	to	ADP
ejpam-4200	15	15	cℓ	cℓ	ADP
ejpam-4200	15	16	∗s	∗s	PROPN
ejpam-4200	15	17	m	m	VERB
ejpam-4200	15	18	1,δ	1,δ	NUM
ejpam-4200	15	19	we	we	PRON
ejpam-4200	15	20	use	use	VERB
ejpam-4200	15	21	elementary	elementary	ADJ
ejpam-4200	15	22	symbols	symbol	NOUN
ejpam-4200	15	23	as	as	SCONJ
ejpam-4200	15	24	it	it	PRON
ejpam-4200	15	25	was	be	AUX
ejpam-4200	15	26	done	do	VERB
ejpam-4200	15	27	in	in	ADP
ejpam-4200	15	28	[	[	X
ejpam-4200	15	29	2	2	NUM
ejpam-4200	15	30	]	]	PUNCT
ejpam-4200	15	31	,	,	PUNCT
ejpam-4200	15	32	[	[	X
ejpam-4200	15	33	12	12	NUM
ejpam-4200	15	34	]	]	PUNCT
ejpam-4200	15	35	,	,	PUNCT
ejpam-4200	15	36	[	[	X
ejpam-4200	15	37	14	14	NUM
ejpam-4200	15	38	]	]	PUNCT
ejpam-4200	15	39	∗corresponding	∗corresponde	VERB
ejpam-4200	15	40	author	author	NOUN
ejpam-4200	15	41	.	.	PUNCT
ejpam-4200	16	1	doi	doi	NOUN
ejpam-4200	16	2	:	:	PUNCT
ejpam-4200	16	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4200	https://doi.org/10.29020/nybg.ejpam.v15i1.4200	ADP
ejpam-4200	16	4	email	email	NOUN
ejpam-4200	16	5	addresses	address	NOUN
ejpam-4200	16	6	:	:	PUNCT
ejpam-4200	16	7	mohamed.congo@yahoo.fr	mohamed.congo@yahoo.fr	PROPN
ejpam-4200	16	8	(	(	PUNCT
ejpam-4200	16	9	m.	m.	NOUN
ejpam-4200	16	10	congo	congo	PROPN
ejpam-4200	16	11	)	)	PUNCT
ejpam-4200	16	12	,	,	PUNCT
ejpam-4200	16	13	omfrancoise@yahoo.fr	omfrancoise@yahoo.fr	PROPN
ejpam-4200	16	14	(	(	PUNCT
ejpam-4200	16	15	m	m	PROPN
ejpam-4200	16	16	f.	f.	PROPN
ejpam-4200	16	17	ouedraogo	ouedraogo	PROPN
ejpam-4200	16	18	)	)	PUNCT
ejpam-4200	16	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4200	17	1	47	47	NUM
ejpam-4200	17	2	©	©	PROPN
ejpam-4200	17	3	2022	2022	NUM
ejpam-4200	17	4	ejpam	ejpam	VERB
ejpam-4200	17	5	all	all	DET
ejpam-4200	17	6	rights	right	NOUN
ejpam-4200	17	7	reserved	reserve	VERB
ejpam-4200	17	8	.	.	PUNCT
ejpam-4200	18	1	m.	m.	NOUN
ejpam-4200	18	2	congo	congo	PROPN
ejpam-4200	18	3	,	,	PUNCT
ejpam-4200	18	4	m.	m.	PROPN
ejpam-4200	18	5	f.	f.	PROPN
ejpam-4200	18	6	ouedraogo	ouedraogo	PROPN
ejpam-4200	18	7	/	/	SYM
ejpam-4200	18	8	eur	eur	PROPN
ejpam-4200	18	9	.	.	PUNCT
ejpam-4200	19	1	j.	j.	PROPN
ejpam-4200	19	2	pure	pure	PROPN
ejpam-4200	19	3	appl	appl	PROPN
ejpam-4200	19	4	.	.	PROPN
ejpam-4200	19	5	math	math	PROPN
ejpam-4200	19	6	,	,	PUNCT
ejpam-4200	19	7	15	15	NUM
ejpam-4200	19	8	(	(	PUNCT
ejpam-4200	19	9	1	1	NUM
ejpam-4200	19	10	)	)	PUNCT
ejpam-4200	19	11	(	(	PUNCT
ejpam-4200	19	12	2022	2022	NUM
ejpam-4200	19	13	)	)	PUNCT
ejpam-4200	19	14	,	,	PUNCT
ejpam-4200	19	15	47	47	NUM
ejpam-4200	19	16	-	-	SYM
ejpam-4200	19	17	63	63	NUM
ejpam-4200	19	18	48	48	NUM
ejpam-4200	19	19	and	and	CCONJ
ejpam-4200	19	20	[	[	X
ejpam-4200	19	21	15	15	NUM
ejpam-4200	19	22	]	]	PUNCT
ejpam-4200	19	23	.	.	PUNCT
ejpam-4200	20	1	indeed	indeed	ADV
ejpam-4200	20	2	,	,	PUNCT
ejpam-4200	20	3	the	the	DET
ejpam-4200	20	4	symbol	symbol	NOUN
ejpam-4200	20	5	reduction	reduction	NOUN
ejpam-4200	20	6	method	method	NOUN
ejpam-4200	20	7	,	,	PUNCT
ejpam-4200	20	8	due	due	ADP
ejpam-4200	20	9	to	to	ADP
ejpam-4200	20	10	coifman	coifman	NOUN
ejpam-4200	20	11	and	and	CCONJ
ejpam-4200	20	12	meyer[6	meyer[6	PROPN
ejpam-4200	20	13	]	]	PUNCT
ejpam-4200	20	14	,	,	PUNCT
ejpam-4200	20	15	makes	make	VERB
ejpam-4200	20	16	it	it	PRON
ejpam-4200	20	17	possible	possible	ADJ
ejpam-4200	20	18	to	to	PART
ejpam-4200	20	19	be	be	AUX
ejpam-4200	20	20	limited	limit	VERB
ejpam-4200	20	21	to	to	ADP
ejpam-4200	20	22	symbols	symbols	PROPN
ejpam-4200	20	23	a(x	a(x	PROPN
ejpam-4200	20	24	,	,	PUNCT
ejpam-4200	20	25	ξ	ξ	NOUN
ejpam-4200	20	26	)	)	PUNCT
ejpam-4200	20	27	∈	∈	NOUN
ejpam-4200	20	28	cℓ	cℓ	ADP
ejpam-4200	20	29	∗s	∗s	PROPN
ejpam-4200	20	30	m	m	PROPN
ejpam-4200	20	31	1,δ	1,δ	NUM
ejpam-4200	20	32	of	of	ADP
ejpam-4200	20	33	the	the	DET
ejpam-4200	20	34	form	form	NOUN
ejpam-4200	20	35	a(x	a(x	NOUN
ejpam-4200	20	36	,	,	PUNCT
ejpam-4200	20	37	ξ	ξ	NOUN
ejpam-4200	20	38	)	)	PUNCT
ejpam-4200	20	39	=	=	SYM
ejpam-4200	21	1	∑	∑	PUNCT
ejpam-4200	21	2	j≥0	j≥0	PROPN
ejpam-4200	21	3	σj(x)ψj(ξ)(see	σj(x)ψj(ξ)(see	PROPN
ejpam-4200	22	1	[	[	X
ejpam-4200	22	2	14	14	NUM
ejpam-4200	22	3	]	]	PUNCT
ejpam-4200	22	4	and	and	CCONJ
ejpam-4200	22	5	[	[	X
ejpam-4200	22	6	2	2	NUM
ejpam-4200	22	7	]	]	NUM
ejpam-4200	22	8	)	)	PUNCT
ejpam-4200	22	9	.	.	PUNCT
ejpam-4200	23	1	then	then	ADV
ejpam-4200	23	2	,	,	PUNCT
ejpam-4200	23	3	we	we	PRON
ejpam-4200	23	4	rewrite	rewrite	VERB
ejpam-4200	23	5	the	the	DET
ejpam-4200	23	6	symbol	symbol	NOUN
ejpam-4200	23	7	as	as	ADP
ejpam-4200	23	8	a	a	DET
ejpam-4200	23	9	sum	sum	NOUN
ejpam-4200	23	10	of	of	ADP
ejpam-4200	23	11	three	three	NUM
ejpam-4200	23	12	parts	part	NOUN
ejpam-4200	23	13	,	,	PUNCT
ejpam-4200	23	14	a	a	DET
ejpam-4200	23	15	”	"	PUNCT
ejpam-4200	23	16	low	low	ADJ
ejpam-4200	23	17	-	-	PUNCT
ejpam-4200	23	18	high	high	ADJ
ejpam-4200	23	19	”	"	PUNCT
ejpam-4200	23	20	,	,	PUNCT
ejpam-4200	23	21	a	a	DET
ejpam-4200	23	22	”	"	PUNCT
ejpam-4200	23	23	high	high	ADJ
ejpam-4200	23	24	-	-	PUNCT
ejpam-4200	23	25	high	high	ADJ
ejpam-4200	23	26	”	"	PUNCT
ejpam-4200	23	27	,	,	PUNCT
ejpam-4200	23	28	and	and	CCONJ
ejpam-4200	23	29	a	a	DET
ejpam-4200	23	30	”	"	PUNCT
ejpam-4200	23	31	high	high	ADJ
ejpam-4200	23	32	-	-	PUNCT
ejpam-4200	23	33	low	low	ADJ
ejpam-4200	23	34	”	"	PUNCT
ejpam-4200	23	35	part	part	NOUN
ejpam-4200	23	36	.	.	PUNCT
ejpam-4200	24	1	thus	thus	ADV
ejpam-4200	24	2	,	,	PUNCT
ejpam-4200	24	3	the	the	DET
ejpam-4200	24	4	operator	operator	NOUN
ejpam-4200	24	5	a(x	a(x	NOUN
ejpam-4200	24	6	,	,	PUNCT
ejpam-4200	24	7	d	d	NOUN
ejpam-4200	24	8	)	)	PUNCT
ejpam-4200	24	9	with	with	ADP
ejpam-4200	24	10	symbol	symbol	NOUN
ejpam-4200	24	11	a	a	PRON
ejpam-4200	24	12	can	can	AUX
ejpam-4200	24	13	be	be	AUX
ejpam-4200	24	14	resolved	resolve	VERB
ejpam-4200	24	15	into	into	ADP
ejpam-4200	24	16	three	three	NUM
ejpam-4200	24	17	operators	operator	NOUN
ejpam-4200	24	18	a1(x	a1(x	PRON
ejpam-4200	24	19	,	,	PUNCT
ejpam-4200	24	20	d	d	NOUN
ejpam-4200	24	21	)	)	PUNCT
ejpam-4200	24	22	,	,	PUNCT
ejpam-4200	24	23	a2(x	a2(x	PROPN
ejpam-4200	24	24	,	,	PUNCT
ejpam-4200	24	25	d	d	NOUN
ejpam-4200	24	26	)	)	PUNCT
ejpam-4200	24	27	and	and	CCONJ
ejpam-4200	24	28	a3(x	a3(x	PROPN
ejpam-4200	24	29	,	,	PUNCT
ejpam-4200	24	30	d	d	NOUN
ejpam-4200	24	31	)	)	PUNCT
ejpam-4200	24	32	with	with	ADP
ejpam-4200	24	33	symbols	symbol	NOUN
ejpam-4200	24	34	a1	a1	PROPN
ejpam-4200	24	35	,	,	PUNCT
ejpam-4200	24	36	a2	a2	PROPN
ejpam-4200	24	37	and	and	CCONJ
ejpam-4200	24	38	a3	a3	NOUN
ejpam-4200	24	39	.	.	PUNCT
ejpam-4200	25	1	now	now	ADV
ejpam-4200	25	2	it	it	PRON
ejpam-4200	25	3	remains	remain	VERB
ejpam-4200	25	4	to	to	PART
ejpam-4200	25	5	study	study	VERB
ejpam-4200	25	6	the	the	DET
ejpam-4200	25	7	boundedness	boundedness	NOUN
ejpam-4200	25	8	of	of	ADP
ejpam-4200	25	9	each	each	DET
ejpam-4200	25	10	elementary	elementary	ADJ
ejpam-4200	25	11	operators	operator	NOUN
ejpam-4200	25	12	.	.	PUNCT
ejpam-4200	26	1	we	we	PRON
ejpam-4200	26	2	structure	structure	VERB
ejpam-4200	26	3	this	this	DET
ejpam-4200	26	4	paper	paper	NOUN
ejpam-4200	26	5	in	in	ADP
ejpam-4200	26	6	4	4	NUM
ejpam-4200	26	7	sections	section	NOUN
ejpam-4200	26	8	as	as	SCONJ
ejpam-4200	26	9	follows	follow	VERB
ejpam-4200	26	10	.	.	PUNCT
ejpam-4200	27	1	in	in	ADP
ejpam-4200	27	2	section	section	NOUN
ejpam-4200	27	3	2	2	NUM
ejpam-4200	27	4	we	we	PRON
ejpam-4200	27	5	give	give	VERB
ejpam-4200	27	6	the	the	DET
ejpam-4200	27	7	preliminaries	preliminary	NOUN
ejpam-4200	27	8	,	,	PUNCT
ejpam-4200	27	9	where	where	SCONJ
ejpam-4200	27	10	we	we	PRON
ejpam-4200	27	11	recall	recall	VERB
ejpam-4200	27	12	the	the	DET
ejpam-4200	27	13	definitions	definition	NOUN
ejpam-4200	27	14	of	of	ADP
ejpam-4200	27	15	morrey	morrey	PROPN
ejpam-4200	27	16	spaces	space	NOUN
ejpam-4200	27	17	and	and	CCONJ
ejpam-4200	27	18	besov	besov	NOUN
ejpam-4200	27	19	-	-	PUNCT
ejpam-4200	27	20	morrey	morrey	NOUN
ejpam-4200	27	21	spaces	space	NOUN
ejpam-4200	27	22	with	with	ADP
ejpam-4200	27	23	variable	variable	ADJ
ejpam-4200	27	24	exponents	exponent	NOUN
ejpam-4200	27	25	.	.	PUNCT
ejpam-4200	28	1	in	in	ADP
ejpam-4200	28	2	section	section	NOUN
ejpam-4200	28	3	3	3	NUM
ejpam-4200	28	4	,	,	PUNCT
ejpam-4200	28	5	we	we	PRON
ejpam-4200	28	6	recall	recall	VERB
ejpam-4200	28	7	necessary	necessary	ADJ
ejpam-4200	28	8	tools	tool	NOUN
ejpam-4200	28	9	for	for	ADP
ejpam-4200	28	10	the	the	DET
ejpam-4200	28	11	proofs	proof	NOUN
ejpam-4200	28	12	of	of	ADP
ejpam-4200	28	13	the	the	DET
ejpam-4200	28	14	lemmas	lemma	NOUN
ejpam-4200	28	15	and	and	CCONJ
ejpam-4200	28	16	the	the	DET
ejpam-4200	28	17	main	main	ADJ
ejpam-4200	28	18	result	result	NOUN
ejpam-4200	28	19	that	that	SCONJ
ejpam-4200	28	20	we	we	PRON
ejpam-4200	28	21	give	give	VERB
ejpam-4200	28	22	in	in	ADP
ejpam-4200	28	23	section	section	NOUN
ejpam-4200	28	24	4	4	NUM
ejpam-4200	28	25	.	.	NOUN
ejpam-4200	28	26	2	2	NUM
ejpam-4200	28	27	.	.	X
ejpam-4200	28	28	preliminaries	preliminary	NOUN
ejpam-4200	28	29	we	we	PRON
ejpam-4200	28	30	denote	denote	VERB
ejpam-4200	28	31	by	by	ADP
ejpam-4200	28	32	rn	rn	PROPN
ejpam-4200	28	33	the	the	DET
ejpam-4200	28	34	n	n	ADV
ejpam-4200	28	35	-	-	PUNCT
ejpam-4200	28	36	dimensional	dimensional	ADJ
ejpam-4200	28	37	real	real	ADJ
ejpam-4200	28	38	euclidean	euclidean	ADJ
ejpam-4200	28	39	space	space	NOUN
ejpam-4200	28	40	,	,	PUNCT
ejpam-4200	28	41	n	n	CCONJ
ejpam-4200	28	42	the	the	DET
ejpam-4200	28	43	collection	collection	NOUN
ejpam-4200	28	44	of	of	ADP
ejpam-4200	28	45	all	all	DET
ejpam-4200	28	46	natural	natural	ADJ
ejpam-4200	28	47	numbers	number	NOUN
ejpam-4200	28	48	and	and	CCONJ
ejpam-4200	28	49	n0	n0	NOUN
ejpam-4200	28	50	=	=	SYM
ejpam-4200	28	51	n	n	PRON
ejpam-4200	28	52	∪	∪	X
ejpam-4200	28	53	{	{	PUNCT
ejpam-4200	28	54	0	0	NUM
ejpam-4200	28	55	}	}	PUNCT
ejpam-4200	28	56	.	.	PUNCT
ejpam-4200	29	1	z	z	NOUN
ejpam-4200	29	2	stands	stand	VERB
ejpam-4200	29	3	for	for	ADP
ejpam-4200	29	4	the	the	DET
ejpam-4200	29	5	set	set	NOUN
ejpam-4200	29	6	of	of	ADP
ejpam-4200	29	7	all	all	DET
ejpam-4200	29	8	integer	integer	NOUN
ejpam-4200	29	9	numbers	number	NOUN
ejpam-4200	29	10	.	.	PUNCT
ejpam-4200	30	1	we	we	PRON
ejpam-4200	30	2	write	write	VERB
ejpam-4200	30	3	b(x	b(x	NOUN
ejpam-4200	30	4	,	,	PUNCT
ejpam-4200	30	5	r	r	NOUN
ejpam-4200	30	6	)	)	PUNCT
ejpam-4200	30	7	for	for	ADP
ejpam-4200	30	8	the	the	DET
ejpam-4200	30	9	open	open	ADJ
ejpam-4200	30	10	ball	ball	NOUN
ejpam-4200	30	11	in	in	ADP
ejpam-4200	30	12	rn	rn	PROPN
ejpam-4200	30	13	centered	center	VERB
ejpam-4200	30	14	at	at	ADP
ejpam-4200	30	15	x	x	PROPN
ejpam-4200	30	16	∈	∈	PROPN
ejpam-4200	30	17	rn	rn	PROPN
ejpam-4200	30	18	with	with	ADP
ejpam-4200	30	19	radius	radius	NOUN
ejpam-4200	30	20	r	r	NOUN
ejpam-4200	30	21	>	>	X
ejpam-4200	30	22	0	0	NUM
ejpam-4200	30	23	.	.	PUNCT
ejpam-4200	31	1	we	we	PRON
ejpam-4200	31	2	use	use	VERB
ejpam-4200	31	3	c	c	PROPN
ejpam-4200	31	4	as	as	ADP
ejpam-4200	31	5	a	a	DET
ejpam-4200	31	6	generic	generic	ADJ
ejpam-4200	31	7	positive	positive	ADJ
ejpam-4200	31	8	constant	constant	ADJ
ejpam-4200	31	9	,	,	PUNCT
ejpam-4200	31	10	i.e.	i.e.	X
ejpam-4200	31	11	a	a	DET
ejpam-4200	31	12	constant	constant	ADJ
ejpam-4200	31	13	whose	whose	DET
ejpam-4200	31	14	value	value	NOUN
ejpam-4200	31	15	may	may	AUX
ejpam-4200	31	16	change	change	VERB
ejpam-4200	31	17	with	with	ADP
ejpam-4200	31	18	each	each	DET
ejpam-4200	31	19	appearance	appearance	NOUN
ejpam-4200	31	20	.	.	PUNCT
ejpam-4200	32	1	the	the	DET
ejpam-4200	32	2	expression	expression	NOUN
ejpam-4200	32	3	f	f	PROPN
ejpam-4200	32	4	≲	≲	PROPN
ejpam-4200	32	5	g	g	PROPN
ejpam-4200	32	6	means	mean	VERB
ejpam-4200	32	7	that	that	SCONJ
ejpam-4200	32	8	f	f	PROPN
ejpam-4200	32	9	≤	≤	X
ejpam-4200	32	10	cg	cg	NOUN
ejpam-4200	32	11	for	for	ADP
ejpam-4200	32	12	some	some	DET
ejpam-4200	32	13	independent	independent	ADJ
ejpam-4200	32	14	constant	constant	ADJ
ejpam-4200	32	15	c	c	NOUN
ejpam-4200	32	16	,	,	PUNCT
ejpam-4200	32	17	and	and	CCONJ
ejpam-4200	32	18	f	f	X
ejpam-4200	32	19	≈	≈	PROPN
ejpam-4200	32	20	g	g	PROPN
ejpam-4200	32	21	means	mean	VERB
ejpam-4200	32	22	f	f	PROPN
ejpam-4200	32	23	≲	≲	PROPN
ejpam-4200	32	24	g	g	PROPN
ejpam-4200	32	25	≲	≲	PROPN
ejpam-4200	32	26	f	f	PROPN
ejpam-4200	32	27	.	.	PUNCT
ejpam-4200	33	1	throughout	throughout	ADP
ejpam-4200	33	2	the	the	DET
ejpam-4200	33	3	paper	paper	NOUN
ejpam-4200	33	4	we	we	PRON
ejpam-4200	33	5	denote	denote	VERB
ejpam-4200	33	6	by	by	ADP
ejpam-4200	33	7	m(rn	m(rn	PROPN
ejpam-4200	33	8	)	)	PUNCT
ejpam-4200	33	9	the	the	DET
ejpam-4200	33	10	family	family	NOUN
ejpam-4200	33	11	of	of	ADP
ejpam-4200	33	12	all	all	DET
ejpam-4200	33	13	complex	complex	ADJ
ejpam-4200	33	14	or	or	CCONJ
ejpam-4200	33	15	extended	extended	ADJ
ejpam-4200	33	16	real	real	ADV
ejpam-4200	33	17	-	-	PUNCT
ejpam-4200	33	18	valued	value	VERB
ejpam-4200	33	19	measurable	measurable	ADJ
ejpam-4200	33	20	functions	function	NOUN
ejpam-4200	33	21	on	on	ADP
ejpam-4200	33	22	rn	rn	PROPN
ejpam-4200	33	23	.	.	PUNCT
ejpam-4200	34	1	by	by	ADP
ejpam-4200	34	2	suppf	suppf	NOUN
ejpam-4200	34	3	we	we	PRON
ejpam-4200	34	4	denote	denote	VERB
ejpam-4200	34	5	the	the	DET
ejpam-4200	34	6	support	support	NOUN
ejpam-4200	34	7	of	of	ADP
ejpam-4200	34	8	the	the	DET
ejpam-4200	34	9	function	function	NOUN
ejpam-4200	34	10	f	f	PROPN
ejpam-4200	34	11	,	,	PUNCT
ejpam-4200	34	12	i.e.	i.e.	X
ejpam-4200	34	13	,	,	PUNCT
ejpam-4200	34	14	the	the	DET
ejpam-4200	34	15	closure	closure	NOUN
ejpam-4200	34	16	of	of	ADP
ejpam-4200	34	17	its	its	PRON
ejpam-4200	34	18	non	non	ADJ
ejpam-4200	34	19	-	-	ADJ
ejpam-4200	34	20	zero	zero	NUM
ejpam-4200	34	21	set	set	NOUN
ejpam-4200	34	22	.	.	PUNCT
ejpam-4200	35	1	if	if	SCONJ
ejpam-4200	35	2	e	e	PROPN
ejpam-4200	35	3	⊂	⊂	PROPN
ejpam-4200	35	4	rn	rn	PROPN
ejpam-4200	35	5	is	be	AUX
ejpam-4200	35	6	a	a	DET
ejpam-4200	35	7	measurable	measurable	ADJ
ejpam-4200	35	8	set	set	NOUN
ejpam-4200	35	9	,	,	PUNCT
ejpam-4200	35	10	then	then	ADV
ejpam-4200	35	11	χe	χe	PROPN
ejpam-4200	35	12	denotes	denote	VERB
ejpam-4200	35	13	its	its	PRON
ejpam-4200	35	14	characteristic	characteristic	ADJ
ejpam-4200	35	15	function	function	NOUN
ejpam-4200	35	16	.	.	PUNCT
ejpam-4200	36	1	we	we	PRON
ejpam-4200	36	2	denote	denote	VERB
ejpam-4200	36	3	by	by	ADP
ejpam-4200	36	4	s(rn	s(rn	PROPN
ejpam-4200	36	5	)	)	PUNCT
ejpam-4200	36	6	the	the	DET
ejpam-4200	36	7	set	set	NOUN
ejpam-4200	36	8	of	of	ADP
ejpam-4200	36	9	all	all	DET
ejpam-4200	36	10	schwartz	schwartz	PROPN
ejpam-4200	36	11	functions	function	NOUN
ejpam-4200	36	12	on	on	ADP
ejpam-4200	36	13	rn	rn	PROPN
ejpam-4200	36	14	.	.	PUNCT
ejpam-4200	37	1	we	we	PRON
ejpam-4200	37	2	denote	denote	VERB
ejpam-4200	37	3	by	by	ADP
ejpam-4200	37	4	s	s	PRON
ejpam-4200	37	5	′	′	NUM
ejpam-4200	37	6	=	=	SYM
ejpam-4200	37	7	s	s	PART
ejpam-4200	37	8	′(rn	′(rn	PROPN
ejpam-4200	37	9	)	)	PUNCT
ejpam-4200	37	10	the	the	DET
ejpam-4200	37	11	dual	dual	ADJ
ejpam-4200	37	12	space	space	NOUN
ejpam-4200	37	13	of	of	ADP
ejpam-4200	37	14	all	all	DET
ejpam-4200	37	15	tempered	temper	VERB
ejpam-4200	37	16	distributions	distribution	NOUN
ejpam-4200	37	17	on	on	ADP
ejpam-4200	37	18	rn	rn	PROPN
ejpam-4200	37	19	.	.	PUNCT
ejpam-4200	38	1	the	the	DET
ejpam-4200	38	2	fourier	fourier	ADJ
ejpam-4200	38	3	transform	transform	NOUN
ejpam-4200	38	4	of	of	ADP
ejpam-4200	38	5	a	a	DET
ejpam-4200	38	6	tempered	temper	VERB
ejpam-4200	38	7	distribution	distribution	NOUN
ejpam-4200	38	8	f	f	NOUN
ejpam-4200	38	9	is	be	AUX
ejpam-4200	38	10	denoted	denote	VERB
ejpam-4200	38	11	by	by	ADP
ejpam-4200	38	12	ff	ff	NOUN
ejpam-4200	38	13	or	or	CCONJ
ejpam-4200	38	14	f̂	f̂	NUM
ejpam-4200	38	15	while	while	SCONJ
ejpam-4200	38	16	its	its	PRON
ejpam-4200	38	17	inverse	inverse	NOUN
ejpam-4200	38	18	transform	transform	NOUN
ejpam-4200	38	19	is	be	AUX
ejpam-4200	38	20	denoted	denote	VERB
ejpam-4200	38	21	by	by	ADP
ejpam-4200	38	22	f−1f	f−1f	PROPN
ejpam-4200	38	23	or	or	CCONJ
ejpam-4200	38	24	f̌	f̌	PROPN
ejpam-4200	38	25	.	.	PUNCT
ejpam-4200	39	1	2.1	2.1	NUM
ejpam-4200	39	2	.	.	PUNCT
ejpam-4200	40	1	variable	variable	ADJ
ejpam-4200	40	2	exponents	exponent	NOUN
ejpam-4200	40	3	for	for	ADP
ejpam-4200	40	4	more	more	ADJ
ejpam-4200	40	5	information	information	NOUN
ejpam-4200	40	6	on	on	ADP
ejpam-4200	40	7	the	the	DET
ejpam-4200	40	8	results	result	NOUN
ejpam-4200	40	9	of	of	ADP
ejpam-4200	40	10	this	this	DET
ejpam-4200	40	11	paragraph	paragraph	NOUN
ejpam-4200	40	12	,	,	PUNCT
ejpam-4200	40	13	see	see	VERB
ejpam-4200	40	14	[	[	X
ejpam-4200	40	15	11	11	NUM
ejpam-4200	40	16	]	]	PUNCT
ejpam-4200	40	17	and	and	CCONJ
ejpam-4200	41	1	[	[	X
ejpam-4200	41	2	7	7	NUM
ejpam-4200	41	3	]	]	PUNCT
ejpam-4200	41	4	.	.	PUNCT
ejpam-4200	42	1	•	•	NUM
ejpam-4200	42	2	by	by	ADP
ejpam-4200	42	3	p(rn	p(rn	PROPN
ejpam-4200	42	4	)	)	PUNCT
ejpam-4200	42	5	we	we	PRON
ejpam-4200	42	6	denote	denote	VERB
ejpam-4200	42	7	the	the	DET
ejpam-4200	42	8	set	set	NOUN
ejpam-4200	42	9	of	of	ADP
ejpam-4200	42	10	all	all	DET
ejpam-4200	42	11	measurable	measurable	ADJ
ejpam-4200	42	12	functions	function	NOUN
ejpam-4200	42	13	p	p	X
ejpam-4200	42	14	:	:	PUNCT
ejpam-4200	42	15	rn	rn	PROPN
ejpam-4200	42	16	→	→	X
ejpam-4200	42	17	(	(	PUNCT
ejpam-4200	42	18	0,+∞	0,+∞	NUM
ejpam-4200	42	19	]	]	X
ejpam-4200	42	20	(	(	PUNCT
ejpam-4200	42	21	called	call	VERB
ejpam-4200	42	22	variable	variable	ADJ
ejpam-4200	42	23	exponents	exponent	NOUN
ejpam-4200	42	24	)	)	PUNCT
ejpam-4200	42	25	which	which	PRON
ejpam-4200	42	26	are	be	AUX
ejpam-4200	42	27	essentially	essentially	ADV
ejpam-4200	42	28	bounded	bound	VERB
ejpam-4200	42	29	away	away	ADV
ejpam-4200	42	30	from	from	ADP
ejpam-4200	42	31	zero	zero	NUM
ejpam-4200	42	32	.	.	PUNCT
ejpam-4200	43	1	we	we	PRON
ejpam-4200	43	2	denote	denote	VERB
ejpam-4200	43	3	p+rn	p+rn	PROPN
ejpam-4200	43	4	:	:	PUNCT
ejpam-4200	43	5	=	=	PUNCT
ejpam-4200	43	6	ess	ess	PROPN
ejpam-4200	43	7	suprnp(x	suprnp(x	PROPN
ejpam-4200	43	8	)	)	PUNCT
ejpam-4200	43	9	and	and	CCONJ
ejpam-4200	43	10	p−rn	p−rn	NOUN
ejpam-4200	43	11	:	:	PUNCT
ejpam-4200	43	12	=	=	PUNCT
ejpam-4200	43	13	ess	ess	PROPN
ejpam-4200	43	14	infrnp(x	infrnp(x	PROPN
ejpam-4200	43	15	)	)	PUNCT
ejpam-4200	43	16	;	;	PUNCT
ejpam-4200	43	17	we	we	PRON
ejpam-4200	43	18	abbreviate	abbreviate	VERB
ejpam-4200	43	19	p+	p+	VERB
ejpam-4200	43	20	=	=	SYM
ejpam-4200	43	21	p+rn	p+rn	NOUN
ejpam-4200	43	22	and	and	CCONJ
ejpam-4200	43	23	p−	p−	NOUN
ejpam-4200	43	24	=	=	NOUN
ejpam-4200	43	25	p−rn	p−rn	NOUN
ejpam-4200	43	26	.	.	PUNCT
ejpam-4200	44	1	•	•	NUM
ejpam-4200	44	2	the	the	DET
ejpam-4200	44	3	function	function	NOUN
ejpam-4200	44	4	ϕp	ϕp	INTJ
ejpam-4200	44	5	is	be	AUX
ejpam-4200	44	6	defined	define	VERB
ejpam-4200	44	7	as	as	SCONJ
ejpam-4200	44	8	follows	follow	VERB
ejpam-4200	44	9	:	:	PUNCT
ejpam-4200	44	10	ϕp(x)(t	ϕp(x)(t	NUM
ejpam-4200	44	11	)	)	PUNCT
ejpam-4200	44	12	=	=	PUNCT
ejpam-4200	45	1			PROPN
ejpam-4200	45	2	tp(x	tp(x	NOUN
ejpam-4200	45	3	)	)	PUNCT
ejpam-4200	45	4	if	if	SCONJ
ejpam-4200	45	5	p(x	p(x	NOUN
ejpam-4200	45	6	)	)	PUNCT
ejpam-4200	45	7	∈	∈	PROPN
ejpam-4200	45	8	(	(	PUNCT
ejpam-4200	45	9	0,+∞	0,+∞	NUM
ejpam-4200	45	10	)	)	PUNCT
ejpam-4200	45	11	,	,	PUNCT
ejpam-4200	45	12	0	0	NUM
ejpam-4200	45	13	if	if	SCONJ
ejpam-4200	45	14	p(x	p(x	NOUN
ejpam-4200	45	15	)	)	PUNCT
ejpam-4200	45	16	=	=	PUNCT
ejpam-4200	46	1	+	+	PUNCT
ejpam-4200	46	2	∞	∞	NUM
ejpam-4200	46	3	and	and	CCONJ
ejpam-4200	46	4	t	t	NOUN
ejpam-4200	46	5	∈	∈	PROPN
ejpam-4200	47	1	[	[	X
ejpam-4200	47	2	0	0	NUM
ejpam-4200	47	3	,	,	PUNCT
ejpam-4200	47	4	1	1	NUM
ejpam-4200	47	5	]	]	PUNCT
ejpam-4200	47	6	,	,	PUNCT
ejpam-4200	47	7	+	+	NOUN
ejpam-4200	47	8	∞	∞	NOUN
ejpam-4200	47	9	if	if	SCONJ
ejpam-4200	47	10	p(x	p(x	VERB
ejpam-4200	47	11	)	)	PUNCT
ejpam-4200	47	12	=	=	PUNCT
ejpam-4200	48	1	+	+	PUNCT
ejpam-4200	48	2	∞	∞	NUM
ejpam-4200	48	3	and	and	CCONJ
ejpam-4200	48	4	t	t	PROPN
ejpam-4200	48	5	∈	∈	PROPN
ejpam-4200	48	6	(	(	PUNCT
ejpam-4200	48	7	1,+∞	1,+∞	NUM
ejpam-4200	48	8	]	]	PUNCT
ejpam-4200	48	9	.	.	PUNCT
ejpam-4200	49	1	the	the	DET
ejpam-4200	49	2	variable	variable	ADJ
ejpam-4200	49	3	exponent	exponent	NOUN
ejpam-4200	49	4	modular	modular	NOUN
ejpam-4200	49	5	associated	associate	VERB
ejpam-4200	49	6	to	to	ADP
ejpam-4200	49	7	p	p	X
ejpam-4200	49	8	(	(	PUNCT
ejpam-4200	49	9	·	·	PUNCT
ejpam-4200	49	10	)	)	PUNCT
ejpam-4200	49	11	is	be	AUX
ejpam-4200	49	12	defined	define	VERB
ejpam-4200	49	13	by	by	ADP
ejpam-4200	49	14	ϱp(·)(f	ϱp(·)(f	PROPN
ejpam-4200	49	15	)	)	PUNCT
ejpam-4200	50	1	:	:	PUNCT
ejpam-4200	50	2	=	=	SYM
ejpam-4200	50	3	∫	∫	PROPN
ejpam-4200	50	4	rn	rn	PROPN
ejpam-4200	50	5	ϕp(x)(|f(x)|)dx	ϕp(x)(|f(x)|)dx	PROPN
ejpam-4200	50	6	.	.	PUNCT
ejpam-4200	51	1	m.	m.	NOUN
ejpam-4200	51	2	congo	congo	PROPN
ejpam-4200	51	3	,	,	PUNCT
ejpam-4200	51	4	m.	m.	PROPN
ejpam-4200	51	5	f.	f.	PROPN
ejpam-4200	51	6	ouedraogo	ouedraogo	PROPN
ejpam-4200	51	7	/	/	SYM
ejpam-4200	51	8	eur	eur	PROPN
ejpam-4200	51	9	.	.	PUNCT
ejpam-4200	52	1	j.	j.	PROPN
ejpam-4200	52	2	pure	pure	PROPN
ejpam-4200	52	3	appl	appl	PROPN
ejpam-4200	52	4	.	.	PROPN
ejpam-4200	52	5	math	math	PROPN
ejpam-4200	52	6	,	,	PUNCT
ejpam-4200	52	7	15	15	NUM
ejpam-4200	52	8	(	(	PUNCT
ejpam-4200	52	9	1	1	NUM
ejpam-4200	52	10	)	)	PUNCT
ejpam-4200	52	11	(	(	PUNCT
ejpam-4200	52	12	2022	2022	NUM
ejpam-4200	52	13	)	)	PUNCT
ejpam-4200	52	14	,	,	PUNCT
ejpam-4200	52	15	47	47	NUM
ejpam-4200	52	16	-	-	SYM
ejpam-4200	52	17	63	63	NUM
ejpam-4200	52	18	49	49	NUM
ejpam-4200	52	19	the	the	DET
ejpam-4200	52	20	variable	variable	ADJ
ejpam-4200	52	21	exponent	exponent	NOUN
ejpam-4200	52	22	lebesgue	lebesgue	PROPN
ejpam-4200	52	23	space	space	PROPN
ejpam-4200	52	24	lp	lp	PROPN
ejpam-4200	52	25	(	(	PUNCT
ejpam-4200	52	26	·	·	PUNCT
ejpam-4200	52	27	)	)	PUNCT
ejpam-4200	52	28	:	:	PUNCT
ejpam-4200	52	29	=	=	SYM
ejpam-4200	52	30	lp(·)(rn	lp(·)(rn	X
ejpam-4200	52	31	)	)	PUNCT
ejpam-4200	52	32	is	be	AUX
ejpam-4200	52	33	the	the	DET
ejpam-4200	52	34	family	family	NOUN
ejpam-4200	52	35	of	of	ADP
ejpam-4200	52	36	(	(	PUNCT
ejpam-4200	52	37	equivalence	equivalence	NOUN
ejpam-4200	52	38	classes	class	NOUN
ejpam-4200	52	39	of	of	ADP
ejpam-4200	52	40	)	)	PUNCT
ejpam-4200	52	41	functions	function	NOUN
ejpam-4200	52	42	f	f	PROPN
ejpam-4200	52	43	∈	∈	PROPN
ejpam-4200	52	44	m(rn	m(rn	PROPN
ejpam-4200	52	45	)	)	PUNCT
ejpam-4200	52	46	such	such	ADJ
ejpam-4200	52	47	that	that	SCONJ
ejpam-4200	52	48	ϱp(·)(f	ϱp(·)(f	PROPN
ejpam-4200	52	49	/	/	SYM
ejpam-4200	52	50	λ	λ	PROPN
ejpam-4200	52	51	)	)	PUNCT
ejpam-4200	52	52	is	be	AUX
ejpam-4200	52	53	finite	finite	ADJ
ejpam-4200	52	54	for	for	ADP
ejpam-4200	52	55	some	some	DET
ejpam-4200	52	56	λ	λ	PROPN
ejpam-4200	52	57	>	>	X
ejpam-4200	52	58	0	0	NUM
ejpam-4200	52	59	.	.	PUNCT
ejpam-4200	53	1	lp	lp	ADJ
ejpam-4200	53	2	(	(	PUNCT
ejpam-4200	53	3	·	·	PUNCT
ejpam-4200	53	4	)	)	PUNCT
ejpam-4200	53	5	is	be	AUX
ejpam-4200	53	6	a	a	DET
ejpam-4200	53	7	quasi	quasi	ADJ
ejpam-4200	53	8	-	-	ADJ
ejpam-4200	53	9	banach	banach	ADJ
ejpam-4200	53	10	space	space	NOUN
ejpam-4200	53	11	equipped	equip	VERB
ejpam-4200	53	12	with	with	ADP
ejpam-4200	53	13	the	the	DET
ejpam-4200	53	14	quasinorm	quasinorm	NOUN
ejpam-4200	53	15	∥f∥p	∥f∥p	NOUN
ejpam-4200	53	16	(	(	PUNCT
ejpam-4200	53	17	·	·	PUNCT
ejpam-4200	53	18	)	)	PUNCT
ejpam-4200	53	19	:	:	PUNCT
ejpam-4200	54	1	=	=	SYM
ejpam-4200	54	2	inf	inf	PROPN
ejpam-4200	54	3	{	{	PUNCT
ejpam-4200	54	4	µ	µ	X
ejpam-4200	54	5	>	>	X
ejpam-4200	54	6	0	0	NUM
ejpam-4200	54	7	:	:	PUNCT
ejpam-4200	54	8	ϱp	ϱp	ADJ
ejpam-4200	54	9	(	(	PUNCT
ejpam-4200	54	10	·	·	PUNCT
ejpam-4200	54	11	)	)	PUNCT
ejpam-4200	54	12	(	(	PUNCT
ejpam-4200	54	13	1	1	NUM
ejpam-4200	54	14	µ	µ	PROPN
ejpam-4200	54	15	f	f	NOUN
ejpam-4200	54	16	)	)	PUNCT
ejpam-4200	54	17	≤	≤	NUM
ejpam-4200	54	18	1	1	NUM
ejpam-4200	54	19	}	}	PUNCT
ejpam-4200	54	20	.	.	PUNCT
ejpam-4200	55	1	•	•	INTJ
ejpam-4200	55	2	we	we	PRON
ejpam-4200	55	3	say	say	VERB
ejpam-4200	55	4	that	that	SCONJ
ejpam-4200	55	5	a	a	DET
ejpam-4200	55	6	continuous	continuous	ADJ
ejpam-4200	55	7	function	function	NOUN
ejpam-4200	55	8	g	g	NOUN
ejpam-4200	55	9	:	:	PUNCT
ejpam-4200	55	10	rn	rn	PROPN
ejpam-4200	55	11	→	→	SYM
ejpam-4200	55	12	r	r	NOUN
ejpam-4200	55	13	is	be	AUX
ejpam-4200	55	14	locally	locally	ADV
ejpam-4200	55	15	log	log	NOUN
ejpam-4200	55	16	-	-	PUNCT
ejpam-4200	55	17	hölder	hölder	NOUN
ejpam-4200	55	18	continuous	continuous	ADJ
ejpam-4200	55	19	,	,	PUNCT
ejpam-4200	55	20	abbreviated	abbreviate	VERB
ejpam-4200	55	21	g	g	PROPN
ejpam-4200	55	22	∈	∈	PROPN
ejpam-4200	55	23	c	c	PROPN
ejpam-4200	55	24	log	log	PROPN
ejpam-4200	55	25	loc	loc	X
ejpam-4200	55	26	(	(	PUNCT
ejpam-4200	55	27	r	r	NOUN
ejpam-4200	55	28	n	n	CCONJ
ejpam-4200	55	29	)	)	PUNCT
ejpam-4200	55	30	,	,	PUNCT
ejpam-4200	55	31	if	if	SCONJ
ejpam-4200	55	32	there	there	PRON
ejpam-4200	55	33	exists	exist	VERB
ejpam-4200	55	34	clog(g	clog(g	NOUN
ejpam-4200	55	35	)	)	PUNCT
ejpam-4200	55	36	≥	≥	NOUN
ejpam-4200	55	37	0	0	NUM
ejpam-4200	55	38	such	such	ADJ
ejpam-4200	55	39	that	that	DET
ejpam-4200	55	40	|g(x)−	|g(x)−	NOUN
ejpam-4200	55	41	g(y)|	g(y)|	PROPN
ejpam-4200	55	42	≤	≤	NUM
ejpam-4200	55	43	clog(g	clog(g	NOUN
ejpam-4200	55	44	)	)	PUNCT
ejpam-4200	56	1	log(e	log(e	PROPN
ejpam-4200	57	1	+	+	NUM
ejpam-4200	57	2	1/|x−	1/|x−	PROPN
ejpam-4200	57	3	y|	y|	NOUN
ejpam-4200	57	4	)	)	PUNCT
ejpam-4200	57	5	for	for	ADP
ejpam-4200	57	6	all	all	DET
ejpam-4200	57	7	x	x	NOUN
ejpam-4200	57	8	,	,	PUNCT
ejpam-4200	57	9	y	y	PROPN
ejpam-4200	57	10	∈	∈	PROPN
ejpam-4200	57	11	rn	rn	PROPN
ejpam-4200	57	12	.	.	PROPN
ejpam-4200	58	1	(	(	PUNCT
ejpam-4200	58	2	1	1	X
ejpam-4200	58	3	)	)	PUNCT
ejpam-4200	58	4	the	the	DET
ejpam-4200	58	5	function	function	NOUN
ejpam-4200	58	6	g	g	NOUN
ejpam-4200	58	7	:	:	PUNCT
ejpam-4200	58	8	rn	rn	PROPN
ejpam-4200	58	9	→	→	SYM
ejpam-4200	58	10	r	r	NOUN
ejpam-4200	58	11	is	be	AUX
ejpam-4200	58	12	said	say	VERB
ejpam-4200	58	13	to	to	PART
ejpam-4200	58	14	be	be	AUX
ejpam-4200	58	15	globally	globally	ADV
ejpam-4200	58	16	log	log	NOUN
ejpam-4200	58	17	-	-	PUNCT
ejpam-4200	58	18	hölder	hölder	NOUN
ejpam-4200	58	19	continuous	continuous	ADJ
ejpam-4200	58	20	,	,	PUNCT
ejpam-4200	58	21	abbreviated	abbreviate	VERB
ejpam-4200	58	22	g	g	PROPN
ejpam-4200	58	23	∈	∈	PROPN
ejpam-4200	58	24	c	c	X
ejpam-4200	58	25	log(rn	log(rn	PROPN
ejpam-4200	58	26	)	)	PUNCT
ejpam-4200	58	27	,	,	PUNCT
ejpam-4200	58	28	if	if	SCONJ
ejpam-4200	58	29	it	it	PRON
ejpam-4200	58	30	is	be	AUX
ejpam-4200	58	31	locally	locally	ADV
ejpam-4200	58	32	log	log	NOUN
ejpam-4200	58	33	-	-	PUNCT
ejpam-4200	58	34	hölder	hölder	NOUN
ejpam-4200	58	35	continuous	continuous	ADJ
ejpam-4200	58	36	and	and	CCONJ
ejpam-4200	58	37	there	there	PRON
ejpam-4200	58	38	exists	exist	VERB
ejpam-4200	58	39	g∞	g∞	PROPN
ejpam-4200	58	40	∈	∈	PROPN
ejpam-4200	58	41	r	r	NOUN
ejpam-4200	58	42	and	and	CCONJ
ejpam-4200	58	43	c∞(g	c∞(g	PROPN
ejpam-4200	58	44	)	)	PUNCT
ejpam-4200	58	45	≥	≥	NOUN
ejpam-4200	58	46	0	0	NUM
ejpam-4200	58	47	such	such	ADJ
ejpam-4200	58	48	that	that	PRON
ejpam-4200	58	49	|g(x)−	|g(x)−	NOUN
ejpam-4200	58	50	g∞|	g∞|	VERB
ejpam-4200	58	51	≤	≤	NUM
ejpam-4200	58	52	c∞(g	c∞(g	PROPN
ejpam-4200	58	53	)	)	PUNCT
ejpam-4200	59	1	log(e	log(e	PROPN
ejpam-4200	60	1	+	+	CCONJ
ejpam-4200	60	2	|x|	|x|	PROPN
ejpam-4200	60	3	)	)	PUNCT
ejpam-4200	60	4	for	for	ADP
ejpam-4200	60	5	all	all	DET
ejpam-4200	60	6	x	x	PROPN
ejpam-4200	60	7	∈	∈	PROPN
ejpam-4200	60	8	rn	rn	PROPN
ejpam-4200	60	9	.	.	PUNCT
ejpam-4200	61	1	we	we	PRON
ejpam-4200	61	2	write	write	VERB
ejpam-4200	61	3	g	g	PROPN
ejpam-4200	61	4	∈	∈	PROPN
ejpam-4200	61	5	p	p	NOUN
ejpam-4200	61	6	log(rn	log(rn	PROPN
ejpam-4200	61	7	)	)	PUNCT
ejpam-4200	61	8	if	if	SCONJ
ejpam-4200	61	9	0	0	NUM
ejpam-4200	61	10	<	<	X
ejpam-4200	61	11	g−	g−	ADJ
ejpam-4200	61	12	≤	≤	ADJ
ejpam-4200	61	13	g(x	g(x	NOUN
ejpam-4200	61	14	)	)	PUNCT
ejpam-4200	61	15	≤	≤	NUM
ejpam-4200	61	16	g+	g+	X
ejpam-4200	61	17	≤	≤	ADJ
ejpam-4200	62	1	+	+	ADJ
ejpam-4200	62	2	∞	∞	NUM
ejpam-4200	62	3	with	with	ADP
ejpam-4200	62	4	1	1	NUM
ejpam-4200	62	5	g	g	NOUN
ejpam-4200	62	6	∈	∈	PROPN
ejpam-4200	62	7	c	c	X
ejpam-4200	62	8	log(rn	log(rn	PROPN
ejpam-4200	62	9	)	)	PUNCT
ejpam-4200	62	10	.	.	PUNCT
ejpam-4200	63	1	we	we	PRON
ejpam-4200	63	2	define	define	VERB
ejpam-4200	63	3	1	1	NUM
ejpam-4200	63	4	g∞	g∞	NOUN
ejpam-4200	63	5	:	:	PUNCT
ejpam-4200	63	6	=	=	SYM
ejpam-4200	63	7	lim	lim	PROPN
ejpam-4200	63	8	|x|→+∞	|x|→+∞	NUM
ejpam-4200	63	9	1	1	NUM
ejpam-4200	63	10	g(x	g(x	NOUN
ejpam-4200	63	11	)	)	PUNCT
ejpam-4200	63	12	and	and	CCONJ
ejpam-4200	63	13	we	we	PRON
ejpam-4200	63	14	use	use	VERB
ejpam-4200	63	15	the	the	DET
ejpam-4200	63	16	convention	convention	NOUN
ejpam-4200	63	17	1	1	NUM
ejpam-4200	63	18	∞	∞	NUM
ejpam-4200	63	19	=	=	SYM
ejpam-4200	63	20	0	0	NUM
ejpam-4200	63	21	.	.	X
ejpam-4200	63	22	2.2	2.2	NUM
ejpam-4200	63	23	.	.	PUNCT
ejpam-4200	63	24	variable	variable	ADJ
ejpam-4200	63	25	exponent	exponent	NOUN
ejpam-4200	63	26	triebel	triebel	NOUN
ejpam-4200	63	27	-	-	PUNCT
ejpam-4200	63	28	lizorkin	lizorkin	NOUN
ejpam-4200	63	29	-	-	PUNCT
ejpam-4200	63	30	morrey	morrey	NOUN
ejpam-4200	63	31	spaces	space	NOUN
ejpam-4200	63	32	we	we	PRON
ejpam-4200	63	33	refer	refer	VERB
ejpam-4200	63	34	to	to	ADP
ejpam-4200	63	35	the	the	DET
ejpam-4200	63	36	papers	paper	NOUN
ejpam-4200	63	37	[	[	X
ejpam-4200	63	38	4	4	NUM
ejpam-4200	63	39	]	]	PUNCT
ejpam-4200	63	40	,	,	PUNCT
ejpam-4200	63	41	[	[	X
ejpam-4200	63	42	18	18	NUM
ejpam-4200	63	43	]	]	PUNCT
ejpam-4200	63	44	,	,	PUNCT
ejpam-4200	63	45	[	[	X
ejpam-4200	63	46	3	3	NUM
ejpam-4200	63	47	]	]	PUNCT
ejpam-4200	63	48	,	,	PUNCT
ejpam-4200	63	49	[	[	X
ejpam-4200	63	50	5	5	NUM
ejpam-4200	63	51	]	]	PUNCT
ejpam-4200	63	52	,	,	PUNCT
ejpam-4200	63	53	[	[	X
ejpam-4200	63	54	17	17	NUM
ejpam-4200	63	55	]	]	PUNCT
ejpam-4200	63	56	and	and	CCONJ
ejpam-4200	63	57	[	[	X
ejpam-4200	63	58	9	9	NUM
ejpam-4200	63	59	]	]	PUNCT
ejpam-4200	63	60	,	,	PUNCT
ejpam-4200	63	61	for	for	ADP
ejpam-4200	63	62	further	further	ADJ
ejpam-4200	63	63	results	result	NOUN
ejpam-4200	63	64	on	on	ADP
ejpam-4200	63	65	triebellizorkin	triebellizorkin	NOUN
ejpam-4200	63	66	-	-	PUNCT
ejpam-4200	63	67	morrey	morrey	NOUN
ejpam-4200	63	68	spaces	space	NOUN
ejpam-4200	63	69	and	and	CCONJ
ejpam-4200	63	70	variable	variable	ADJ
ejpam-4200	63	71	exponent	exponent	NOUN
ejpam-4200	63	72	triebel	triebel	NOUN
ejpam-4200	63	73	-	-	PUNCT
ejpam-4200	63	74	lizorkin	lizorkin	NOUN
ejpam-4200	63	75	-	-	PUNCT
ejpam-4200	63	76	morrey	morrey	NOUN
ejpam-4200	63	77	spaces	space	NOUN
ejpam-4200	63	78	.	.	PUNCT
ejpam-4200	64	1	•	•	NUM
ejpam-4200	64	2	morrey	morrey	PROPN
ejpam-4200	64	3	spaces	space	VERB
ejpam-4200	64	4	definition	definition	NOUN
ejpam-4200	64	5	1	1	NUM
ejpam-4200	64	6	.	.	PUNCT
ejpam-4200	65	1	for	for	ADP
ejpam-4200	65	2	p	p	NOUN
ejpam-4200	65	3	,	,	PUNCT
ejpam-4200	65	4	u	u	PROPN
ejpam-4200	65	5	∈	∈	PROPN
ejpam-4200	65	6	p(rn	p(rn	PROPN
ejpam-4200	65	7	)	)	PUNCT
ejpam-4200	65	8	with	with	ADP
ejpam-4200	65	9	0	0	NUM
ejpam-4200	65	10	<	<	X
ejpam-4200	65	11	p−	p−	NOUN
ejpam-4200	65	12	≤	≤	NUM
ejpam-4200	65	13	p(x	p(x	PROPN
ejpam-4200	65	14	)	)	PUNCT
ejpam-4200	65	15	≤	≤	NUM
ejpam-4200	65	16	u(x	u(x	NOUN
ejpam-4200	65	17	)	)	PUNCT
ejpam-4200	65	18	≤	≤	NOUN
ejpam-4200	66	1	+	+	PUNCT
ejpam-4200	66	2	∞	∞	PROPN
ejpam-4200	66	3	,	,	PUNCT
ejpam-4200	66	4	the	the	DET
ejpam-4200	66	5	variable	variable	ADJ
ejpam-4200	66	6	exponent	exponent	NOUN
ejpam-4200	66	7	morrey	morrey	PROPN
ejpam-4200	66	8	space	space	PROPN
ejpam-4200	66	9	mp(·),u	mp(·),u	PROPN
ejpam-4200	66	10	(	(	PUNCT
ejpam-4200	66	11	·	·	PUNCT
ejpam-4200	66	12	)	)	PUNCT
ejpam-4200	66	13	:	:	PUNCT
ejpam-4200	66	14	=	=	SYM
ejpam-4200	66	15	mp(·),u(·)(rn	mp(·),u(·)(rn	PROPN
ejpam-4200	66	16	)	)	PUNCT
ejpam-4200	66	17	consists	consist	VERB
ejpam-4200	66	18	of	of	ADP
ejpam-4200	66	19	all	all	DET
ejpam-4200	66	20	functions	function	NOUN
ejpam-4200	66	21	f	f	PROPN
ejpam-4200	66	22	∈	∈	PROPN
ejpam-4200	66	23	m(rn	m(rn	PROPN
ejpam-4200	66	24	)	)	PUNCT
ejpam-4200	66	25	with	with	ADP
ejpam-4200	66	26	finite	finite	ADJ
ejpam-4200	66	27	quasinorm	quasinorm	NOUN
ejpam-4200	66	28	∥f∥mp(·),u	∥f∥mp(·),u	PROPN
ejpam-4200	66	29	(	(	PUNCT
ejpam-4200	66	30	·	·	PUNCT
ejpam-4200	66	31	)	)	PUNCT
ejpam-4200	66	32	:	:	PUNCT
ejpam-4200	67	1	=	=	SYM
ejpam-4200	67	2	sup	sup	NOUN
ejpam-4200	67	3	x∈rn	x∈rn	PROPN
ejpam-4200	67	4	,	,	PUNCT
ejpam-4200	67	5	r>0	r>0	PROPN
ejpam-4200	67	6	r	r	NOUN
ejpam-4200	67	7	n	n	CCONJ
ejpam-4200	67	8	u(x	u(x	NOUN
ejpam-4200	67	9	)	)	PUNCT
ejpam-4200	67	10	−	−	PROPN
ejpam-4200	67	11	n	n	PRON
ejpam-4200	67	12	p(x	p(x	NOUN
ejpam-4200	67	13	)	)	PUNCT
ejpam-4200	67	14	∥∥∥fχb(x.r	∥∥∥fχb(x.r	NOUN
ejpam-4200	67	15	)	)	PUNCT
ejpam-4200	68	1	∥∥∥	∥∥∥	PROPN
ejpam-4200	68	2	lp	lp	PROPN
ejpam-4200	68	3	(	(	PUNCT
ejpam-4200	68	4	·	·	PUNCT
ejpam-4200	68	5	)	)	PUNCT
ejpam-4200	68	6	.	.	PUNCT
ejpam-4200	69	1	(	(	PUNCT
ejpam-4200	69	2	2	2	X
ejpam-4200	69	3	)	)	PUNCT
ejpam-4200	69	4	by	by	ADP
ejpam-4200	69	5	the	the	DET
ejpam-4200	69	6	definition	definition	NOUN
ejpam-4200	69	7	of	of	ADP
ejpam-4200	69	8	the	the	DET
ejpam-4200	69	9	lp	lp	PROPN
ejpam-4200	69	10	(	(	PUNCT
ejpam-4200	69	11	·	·	PUNCT
ejpam-4200	69	12	)	)	PUNCT
ejpam-4200	69	13	quasinorm	quasinorm	NOUN
ejpam-4200	69	14	,	,	PUNCT
ejpam-4200	69	15	(	(	PUNCT
ejpam-4200	69	16	2	2	X
ejpam-4200	69	17	)	)	PUNCT
ejpam-4200	69	18	can	can	AUX
ejpam-4200	69	19	also	also	ADV
ejpam-4200	69	20	be	be	AUX
ejpam-4200	69	21	written	write	VERB
ejpam-4200	69	22	as	as	ADP
ejpam-4200	69	23	∥f∥mp(·),u	∥f∥mp(·),u	PROPN
ejpam-4200	69	24	(	(	PUNCT
ejpam-4200	69	25	·	·	PUNCT
ejpam-4200	69	26	)	)	PUNCT
ejpam-4200	69	27	:	:	PUNCT
ejpam-4200	70	1	=	=	SYM
ejpam-4200	70	2	sup	sup	NOUN
ejpam-4200	70	3	x∈rn	x∈rn	PROPN
ejpam-4200	70	4	,	,	PUNCT
ejpam-4200	70	5	r>0	r>0	PROPN
ejpam-4200	70	6	inf	inf	PROPN
ejpam-4200	70	7	{	{	PUNCT
ejpam-4200	70	8	λ	λ	X
ejpam-4200	70	9	>	>	X
ejpam-4200	70	10	0	0	NUM
ejpam-4200	70	11	:	:	PUNCT
ejpam-4200	70	12	ϱ	ϱ	ADP
ejpam-4200	70	13	(	(	PUNCT
ejpam-4200	70	14	r	r	NOUN
ejpam-4200	70	15	n	n	X
ejpam-4200	70	16	u(x	u(x	NOUN
ejpam-4200	70	17	)	)	PUNCT
ejpam-4200	70	18	−	−	PROPN
ejpam-4200	70	19	n	n	SYM
ejpam-4200	70	20	p(x	p(x	PROPN
ejpam-4200	70	21	)	)	PUNCT
ejpam-4200	70	22	f	f	PROPN
ejpam-4200	70	23	λ	λ	X
ejpam-4200	70	24	χb(x.r	χb(x.r	ADV
ejpam-4200	70	25	)	)	PUNCT
ejpam-4200	70	26	)	)	PUNCT
ejpam-4200	71	1	≤	≤	ADV
ejpam-4200	71	2	1	1	NUM
ejpam-4200	71	3	}	}	PUNCT
ejpam-4200	71	4	.	.	PUNCT
ejpam-4200	72	1	definition	definition	NOUN
ejpam-4200	72	2	2	2	NUM
ejpam-4200	72	3	.	.	PUNCT
ejpam-4200	73	1	let	let	VERB
ejpam-4200	73	2	p	p	PRON
ejpam-4200	73	3	,	,	PUNCT
ejpam-4200	73	4	q	q	ADJ
ejpam-4200	73	5	,	,	PUNCT
ejpam-4200	73	6	u	u	PROPN
ejpam-4200	73	7	∈	∈	PROPN
ejpam-4200	73	8	p(rn	p(rn	PROPN
ejpam-4200	73	9	)	)	PUNCT
ejpam-4200	73	10	with	with	ADP
ejpam-4200	73	11	p(x	p(x	NOUN
ejpam-4200	73	12	)	)	PUNCT
ejpam-4200	73	13	≤	≤	NUM
ejpam-4200	73	14	u(x	u(x	NOUN
ejpam-4200	73	15	)	)	PUNCT
ejpam-4200	73	16	.	.	PUNCT
ejpam-4200	74	1	the	the	DET
ejpam-4200	74	2	mixed	mixed	ADJ
ejpam-4200	74	3	space	space	NOUN
ejpam-4200	74	4	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	74	5	(	(	PUNCT
ejpam-4200	74	6	·	·	PUNCT
ejpam-4200	74	7	)	)	PUNCT
ejpam-4200	74	8	)	)	PUNCT
ejpam-4200	74	9	consists	consist	VERB
ejpam-4200	74	10	of	of	ADP
ejpam-4200	74	11	all	all	DET
ejpam-4200	74	12	sequences	sequence	NOUN
ejpam-4200	74	13	(	(	PUNCT
ejpam-4200	74	14	fν)ν	fν)ν	PROPN
ejpam-4200	74	15	⊂	⊂	ADJ
ejpam-4200	74	16	m(rn	m(rn	PROPN
ejpam-4200	74	17	)	)	PUNCT
ejpam-4200	74	18	such	such	ADJ
ejpam-4200	74	19	that	that	SCONJ
ejpam-4200	74	20	,	,	PUNCT
ejpam-4200	74	21	∥(fν)ν∥mp(·),u(·)(ℓq	∥(fν)ν∥mp(·),u(·)(ℓq	NOUN
ejpam-4200	74	22	(	(	PUNCT
ejpam-4200	74	23	·	·	PUNCT
ejpam-4200	74	24	)	)	PUNCT
ejpam-4200	74	25	)	)	PUNCT
ejpam-4200	74	26	:	:	PUNCT
ejpam-4200	75	1	=	=	SYM
ejpam-4200	75	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	76	1	(	(	PUNCT
ejpam-4200	76	2	+	+	ADP
ejpam-4200	76	3	∞∑	∞∑	NUM
ejpam-4200	76	4	ν=0	ν=0	PRON
ejpam-4200	76	5	|fν(·)|q	|fν(·)|q	PROPN
ejpam-4200	76	6	(	(	PUNCT
ejpam-4200	76	7	·	·	PUNCT
ejpam-4200	76	8	)	)	PUNCT
ejpam-4200	76	9	)	)	PUNCT
ejpam-4200	76	10	1	1	X
ejpam-4200	76	11	/	/	SYM
ejpam-4200	76	12	q	q	NOUN
ejpam-4200	76	13	(	(	PUNCT
ejpam-4200	76	14	·	·	PUNCT
ejpam-4200	76	15	)	)	PUNCT
ejpam-4200	76	16	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	76	17	mp(·),u	mp(·),u	PROPN
ejpam-4200	76	18	(	(	PUNCT
ejpam-4200	76	19	·	·	PUNCT
ejpam-4200	76	20	)	)	PUNCT
ejpam-4200	76	21	<	<	X
ejpam-4200	77	1	+	+	PRON
ejpam-4200	77	2	∞.	∞.	PROPN
ejpam-4200	77	3	(	(	PUNCT
ejpam-4200	77	4	3	3	NUM
ejpam-4200	77	5	)	)	PUNCT
ejpam-4200	77	6	m.	m.	NOUN
ejpam-4200	77	7	congo	congo	PROPN
ejpam-4200	77	8	,	,	PUNCT
ejpam-4200	77	9	m.	m.	PROPN
ejpam-4200	77	10	f.	f.	PROPN
ejpam-4200	77	11	ouedraogo	ouedraogo	PROPN
ejpam-4200	77	12	/	/	SYM
ejpam-4200	77	13	eur	eur	PROPN
ejpam-4200	77	14	.	.	PUNCT
ejpam-4200	78	1	j.	j.	PROPN
ejpam-4200	78	2	pure	pure	PROPN
ejpam-4200	78	3	appl	appl	PROPN
ejpam-4200	78	4	.	.	PROPN
ejpam-4200	78	5	math	math	PROPN
ejpam-4200	78	6	,	,	PUNCT
ejpam-4200	78	7	15	15	NUM
ejpam-4200	78	8	(	(	PUNCT
ejpam-4200	78	9	1	1	NUM
ejpam-4200	78	10	)	)	PUNCT
ejpam-4200	78	11	(	(	PUNCT
ejpam-4200	78	12	2022	2022	NUM
ejpam-4200	78	13	)	)	PUNCT
ejpam-4200	78	14	,	,	PUNCT
ejpam-4200	78	15	47	47	NUM
ejpam-4200	78	16	-	-	SYM
ejpam-4200	78	17	63	63	NUM
ejpam-4200	78	18	50	50	NUM
ejpam-4200	78	19	remark	remark	NOUN
ejpam-4200	78	20	1	1	NUM
ejpam-4200	78	21	.	.	PUNCT
ejpam-4200	79	1	[	[	X
ejpam-4200	79	2	4	4	X
ejpam-4200	79	3	]	]	PUNCT
ejpam-4200	79	4	note	note	NOUN
ejpam-4200	79	5	that	that	SCONJ
ejpam-4200	79	6	∥·∥mp(·),u(·)(ℓq	∥·∥mp(·),u(·)(ℓq	ADJ
ejpam-4200	79	7	(	(	PUNCT
ejpam-4200	79	8	·	·	PUNCT
ejpam-4200	79	9	)	)	PUNCT
ejpam-4200	79	10	)	)	PUNCT
ejpam-4200	79	11	defined	define	VERB
ejpam-4200	79	12	a	a	DET
ejpam-4200	79	13	quasinorm	quasinorm	NOUN
ejpam-4200	79	14	on	on	ADP
ejpam-4200	79	15	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	79	16	(	(	PUNCT
ejpam-4200	79	17	·	·	PUNCT
ejpam-4200	79	18	)	)	PUNCT
ejpam-4200	79	19	)	)	PUNCT
ejpam-4200	79	20	.	.	PUNCT
ejpam-4200	80	1	it	it	PRON
ejpam-4200	80	2	is	be	AUX
ejpam-4200	80	3	a	a	DET
ejpam-4200	80	4	norm	norm	NOUN
ejpam-4200	80	5	when	when	SCONJ
ejpam-4200	80	6	min(p−	min(p−	PROPN
ejpam-4200	80	7	,	,	PUNCT
ejpam-4200	80	8	q−	q−	PROPN
ejpam-4200	80	9	)	)	PUNCT
ejpam-4200	80	10	≥	≥	NOUN
ejpam-4200	80	11	1	1	NUM
ejpam-4200	80	12	.	.	PUNCT
ejpam-4200	80	13	proposition	proposition	NOUN
ejpam-4200	80	14	1	1	NUM
ejpam-4200	80	15	.	.	PUNCT
ejpam-4200	81	1	let	let	VERB
ejpam-4200	81	2	f	f	PROPN
ejpam-4200	81	3	and	and	CCONJ
ejpam-4200	81	4	g	g	PROPN
ejpam-4200	81	5	be	be	AUX
ejpam-4200	81	6	two	two	NUM
ejpam-4200	81	7	measurable	measurable	ADJ
ejpam-4200	81	8	functions	function	NOUN
ejpam-4200	81	9	with	with	ADP
ejpam-4200	81	10	0	0	NUM
ejpam-4200	81	11	≤	≤	NUM
ejpam-4200	81	12	f(x	f(x	PROPN
ejpam-4200	81	13	)	)	PUNCT
ejpam-4200	81	14	≤	≤	NOUN
ejpam-4200	82	1	g(x	g(x	NOUN
ejpam-4200	82	2	)	)	PUNCT
ejpam-4200	82	3	for	for	ADP
ejpam-4200	82	4	a.e	a.e	PROPN
ejpam-4200	82	5	.	.	PUNCT
ejpam-4200	82	6	x	x	PROPN
ejpam-4200	82	7	∈	∈	PROPN
ejpam-4200	82	8	rn	rn	PROPN
ejpam-4200	82	9	.	.	PUNCT
ejpam-4200	83	1	then	then	ADV
ejpam-4200	83	2	it	it	PRON
ejpam-4200	83	3	holds	hold	VERB
ejpam-4200	83	4	∥f∥mp(·),u(·)(ℓq	∥f∥mp(·),u(·)(ℓq	NOUN
ejpam-4200	83	5	(	(	PUNCT
ejpam-4200	83	6	·	·	PUNCT
ejpam-4200	83	7	)	)	PUNCT
ejpam-4200	83	8	)	)	PUNCT
ejpam-4200	84	1	≤	≤	NUM
ejpam-4200	84	2	∥g∥mp(·),u(·)(ℓq	∥g∥mp(·),u(·)(ℓq	ADJ
ejpam-4200	84	3	(	(	PUNCT
ejpam-4200	84	4	·	·	PUNCT
ejpam-4200	84	5	)	)	PUNCT
ejpam-4200	84	6	)	)	PUNCT
ejpam-4200	84	7	.	.	PUNCT
ejpam-4200	85	1	proposition	proposition	NOUN
ejpam-4200	85	2	2	2	NUM
ejpam-4200	85	3	.	.	PUNCT
ejpam-4200	86	1	let	let	VERB
ejpam-4200	86	2	p	p	PRON
ejpam-4200	86	3	,	,	PUNCT
ejpam-4200	86	4	q	q	ADJ
ejpam-4200	86	5	,	,	PUNCT
ejpam-4200	86	6	u	u	PROPN
ejpam-4200	86	7	∈	∈	PROPN
ejpam-4200	86	8	p(rn	p(rn	PROPN
ejpam-4200	86	9	)	)	PUNCT
ejpam-4200	86	10	with	with	ADP
ejpam-4200	86	11	p(x	p(x	NOUN
ejpam-4200	86	12	)	)	PUNCT
ejpam-4200	86	13	≤	≤	NUM
ejpam-4200	86	14	u(x	u(x	NOUN
ejpam-4200	86	15	)	)	PUNCT
ejpam-4200	86	16	and	and	CCONJ
ejpam-4200	86	17	0	0	NUM
ejpam-4200	86	18	<	<	X
ejpam-4200	86	19	t	t	X
ejpam-4200	86	20	<	<	X
ejpam-4200	87	1	+	+	NOUN
ejpam-4200	87	2	∞.	∞.	PROPN
ejpam-4200	87	3	let	let	VERB
ejpam-4200	87	4	(	(	PUNCT
ejpam-4200	87	5	fν)ν	fν)ν	PROPN
ejpam-4200	87	6	⊂	⊂	ADJ
ejpam-4200	87	7	m(rn	m(rn	PROPN
ejpam-4200	87	8	)	)	PUNCT
ejpam-4200	88	1	∥∥(|fν	∥∥(|fν	X
ejpam-4200	88	2	|t)ν∥∥	|t)ν∥∥	X
ejpam-4200	88	3	m	m	VERB
ejpam-4200	88	4	p	p	X
ejpam-4200	88	5	(	(	PUNCT
ejpam-4200	88	6	·	·	PUNCT
ejpam-4200	88	7	)	)	PUNCT
ejpam-4200	88	8	t	t	PROPN
ejpam-4200	88	9	,	,	PUNCT
ejpam-4200	88	10	u	u	NOUN
ejpam-4200	88	11	(	(	PUNCT
ejpam-4200	88	12	·	·	PUNCT
ejpam-4200	88	13	)	)	PUNCT
ejpam-4200	88	14	t	t	PROPN
ejpam-4200	88	15	(	(	PUNCT
ejpam-4200	88	16	ℓ	ℓ	INTJ
ejpam-4200	88	17	q	q	PROPN
ejpam-4200	88	18	(	(	PUNCT
ejpam-4200	88	19	·	·	PUNCT
ejpam-4200	88	20	)	)	PUNCT
ejpam-4200	88	21	t	t	NOUN
ejpam-4200	88	22	)	)	PUNCT
ejpam-4200	89	1	=	=	SYM
ejpam-4200	89	2	∥(fν)ν∥tmp(·),u(·)(ℓq	∥(fν)ν∥tmp(·),u(·)(ℓq	X
ejpam-4200	89	3	(	(	PUNCT
ejpam-4200	89	4	·	·	PUNCT
ejpam-4200	89	5	)	)	PUNCT
ejpam-4200	89	6	)	)	PUNCT
ejpam-4200	89	7	with	with	ADP
ejpam-4200	89	8	the	the	DET
ejpam-4200	89	9	usual	usual	ADJ
ejpam-4200	89	10	modification	modification	NOUN
ejpam-4200	89	11	every	every	DET
ejpam-4200	89	12	time	time	NOUN
ejpam-4200	89	13	q(x	q(x	NOUN
ejpam-4200	89	14	)	)	PUNCT
ejpam-4200	89	15	=	=	PUNCT
ejpam-4200	90	1	+	+	NUM
ejpam-4200	90	2	∞.	∞.	PROPN
ejpam-4200	90	3	•triebel	•triebel	NOUN
ejpam-4200	90	4	-	-	PUNCT
ejpam-4200	90	5	lizorkin	lizorkin	PROPN
ejpam-4200	90	6	-	-	PUNCT
ejpam-4200	90	7	morrey	morrey	NOUN
ejpam-4200	90	8	spaces	space	NOUN
ejpam-4200	90	9	.	.	PUNCT
ejpam-4200	91	1	we	we	PRON
ejpam-4200	91	2	first	first	ADV
ejpam-4200	91	3	recall	recall	VERB
ejpam-4200	91	4	a	a	DET
ejpam-4200	91	5	littlewood	littlewood	NOUN
ejpam-4200	91	6	-	-	PUNCT
ejpam-4200	91	7	paley	paley	ADJ
ejpam-4200	91	8	partition	partition	NOUN
ejpam-4200	91	9	of	of	ADP
ejpam-4200	91	10	unity	unity	NOUN
ejpam-4200	91	11	{	{	PUNCT
ejpam-4200	91	12	ψν	ψν	NOUN
ejpam-4200	91	13	}	}	PUNCT
ejpam-4200	91	14	,	,	PUNCT
ejpam-4200	91	15	ν	ν	X
ejpam-4200	91	16	≥	≥	NOUN
ejpam-4200	91	17	0	0	NUM
ejpam-4200	91	18	.	.	PUNCT
ejpam-4200	92	1	the	the	DET
ejpam-4200	92	2	functions	function	NOUN
ejpam-4200	92	3	ψν	ψν	PRON
ejpam-4200	92	4	are	be	AUX
ejpam-4200	92	5	defined	define	VERB
ejpam-4200	92	6	as	as	SCONJ
ejpam-4200	92	7	follows	follow	VERB
ejpam-4200	92	8	.	.	PUNCT
ejpam-4200	93	1	let	let	VERB
ejpam-4200	93	2	ψ0	ψ0	PROPN
ejpam-4200	93	3	∈	∈	PROPN
ejpam-4200	93	4	c∞	c∞	PROPN
ejpam-4200	93	5	0	0	NUM
ejpam-4200	94	1	(	(	PUNCT
ejpam-4200	94	2	rn	rn	NOUN
ejpam-4200	94	3	)	)	PUNCT
ejpam-4200	95	1	such	such	ADJ
ejpam-4200	95	2	that	that	SCONJ
ejpam-4200	95	3	ψ0	ψ0	ADJ
ejpam-4200	95	4	≡	≡	PROPN
ejpam-4200	95	5	1	1	NUM
ejpam-4200	95	6	on	on	ADP
ejpam-4200	95	7	b(0	b(0	NOUN
ejpam-4200	95	8	;	;	PUNCT
ejpam-4200	95	9	1	1	NUM
ejpam-4200	95	10	)	)	PUNCT
ejpam-4200	95	11	and	and	CCONJ
ejpam-4200	95	12	suppψ0	suppψ0	X
ejpam-4200	95	13	⊂	⊂	ADJ
ejpam-4200	95	14	b(0	b(0	NOUN
ejpam-4200	95	15	;	;	PUNCT
ejpam-4200	95	16	2	2	NUM
ejpam-4200	95	17	)	)	PUNCT
ejpam-4200	95	18	.	.	PUNCT
ejpam-4200	96	1	set	set	VERB
ejpam-4200	96	2	ψν(ξ	ψν(ξ	PUNCT
ejpam-4200	96	3	)	)	PUNCT
ejpam-4200	96	4	=	=	PRON
ejpam-4200	97	1	ψ0(2	ψ0(2	PROPN
ejpam-4200	97	2	−νξ)−	−νξ)−	PRON
ejpam-4200	97	3	ψ0(2	ψ0(2	PROPN
ejpam-4200	97	4	−ν+1ξ	−ν+1ξ	NOUN
ejpam-4200	97	5	)	)	PUNCT
ejpam-4200	97	6	for	for	ADP
ejpam-4200	97	7	all	all	DET
ejpam-4200	97	8	ν	ν	X
ejpam-4200	97	9	∈	∈	PROPN
ejpam-4200	97	10	n.	n.	NOUN
ejpam-4200	97	11	then	then	ADV
ejpam-4200	97	12	ψν	ψν	PROPN
ejpam-4200	97	13	is	be	AUX
ejpam-4200	97	14	supported	support	VERB
ejpam-4200	97	15	on	on	ADP
ejpam-4200	97	16	the	the	DET
ejpam-4200	97	17	dyadic	dyadic	ADJ
ejpam-4200	97	18	shell	shell	NOUN
ejpam-4200	97	19	dν	dν	ADV
ejpam-4200	97	20	=	=	PUNCT
ejpam-4200	97	21	{	{	PUNCT
ejpam-4200	97	22	ξ	ξ	PROPN
ejpam-4200	97	23	∈	∈	PROPN
ejpam-4200	97	24	rn	rn	PROPN
ejpam-4200	97	25	:	:	PUNCT
ejpam-4200	97	26	2ν−1	2ν−1	PROPN
ejpam-4200	97	27	≤	≤	NUM
ejpam-4200	97	28	|ξ|	|ξ|	VERB
ejpam-4200	97	29	≤	≤	NOUN
ejpam-4200	97	30	2ν+1	2ν+1	NUM
ejpam-4200	97	31	}	}	PUNCT
ejpam-4200	97	32	.	.	PUNCT
ejpam-4200	98	1	if	if	SCONJ
ejpam-4200	98	2	f	f	PROPN
ejpam-4200	98	3	∈	∈	PROPN
ejpam-4200	98	4	s	s	VERB
ejpam-4200	98	5	′	′	NOUN
ejpam-4200	98	6	,	,	PUNCT
ejpam-4200	98	7	then	then	ADV
ejpam-4200	98	8	f	f	PROPN
ejpam-4200	98	9	=	=	SYM
ejpam-4200	98	10	∑	∑	PROPN
ejpam-4200	98	11	ν≥0	ν≥0	NOUN
ejpam-4200	98	12	ψνf	ψνf	NOUN
ejpam-4200	98	13	.	.	PUNCT
ejpam-4200	99	1	the	the	DET
ejpam-4200	99	2	fourier	fourier	NOUN
ejpam-4200	99	3	multiplier	multipli	ADJ
ejpam-4200	99	4	ψj(d	ψj(d	PUNCT
ejpam-4200	99	5	)	)	PUNCT
ejpam-4200	99	6	with	with	ADP
ejpam-4200	99	7	symbol	symbol	NOUN
ejpam-4200	99	8	ψj	ψj	ADV
ejpam-4200	99	9	is	be	AUX
ejpam-4200	99	10	defined	define	VERB
ejpam-4200	99	11	as	as	ADP
ejpam-4200	99	12	ψν(d)f(x	ψν(d)f(x	NOUN
ejpam-4200	99	13	)	)	PUNCT
ejpam-4200	99	14	=	=	SYM
ejpam-4200	99	15	f−1(ψν	f−1(ψν	VERB
ejpam-4200	99	16	·	·	PUNCT
ejpam-4200	99	17	f̂)(x	f̂)(x	PROPN
ejpam-4200	99	18	)	)	PUNCT
ejpam-4200	99	19	=	=	SYM
ejpam-4200	100	1	∫	∫	PROPN
ejpam-4200	100	2	rn	rn	PROPN
ejpam-4200	100	3	ψν(ξ)f̂(ξ)e	ψν(ξ)f̂(ξ)e	PROPN
ejpam-4200	100	4	ix·ξdξ	ix·ξdξ	PROPN
ejpam-4200	100	5	.	.	PUNCT
ejpam-4200	101	1	definition	definition	NOUN
ejpam-4200	101	2	3	3	X
ejpam-4200	101	3	.	.	PUNCT
ejpam-4200	102	1	let	let	AUX
ejpam-4200	102	2	{	{	PUNCT
ejpam-4200	102	3	ψν	ψν	PART
ejpam-4200	102	4	}	}	PUNCT
ejpam-4200	102	5	be	be	AUX
ejpam-4200	102	6	the	the	DET
ejpam-4200	102	7	usual	usual	ADJ
ejpam-4200	102	8	littlewood	littlewood	NOUN
ejpam-4200	102	9	-	-	PUNCT
ejpam-4200	102	10	paley	paley	NOUN
ejpam-4200	102	11	partition	partition	NOUN
ejpam-4200	102	12	of	of	ADP
ejpam-4200	102	13	unity	unity	NOUN
ejpam-4200	102	14	.	.	PUNCT
ejpam-4200	103	1	let	let	VERB
ejpam-4200	103	2	s	s	PRON
ejpam-4200	103	3	:	:	PUNCT
ejpam-4200	103	4	rn	rn	PROPN
ejpam-4200	103	5	→	→	SYM
ejpam-4200	103	6	r	r	PROPN
ejpam-4200	103	7	,	,	PUNCT
ejpam-4200	103	8	p	p	X
ejpam-4200	103	9	,	,	PUNCT
ejpam-4200	103	10	q	q	PROPN
ejpam-4200	103	11	∈	∈	PROPN
ejpam-4200	103	12	p	p	NOUN
ejpam-4200	103	13	log(rn	log(rn	PROPN
ejpam-4200	103	14	)	)	PUNCT
ejpam-4200	103	15	and	and	CCONJ
ejpam-4200	103	16	u	u	PROPN
ejpam-4200	103	17	∈	∈	PROPN
ejpam-4200	103	18	p(rn	p(rn	PROPN
ejpam-4200	103	19	)	)	PUNCT
ejpam-4200	103	20	such	such	ADJ
ejpam-4200	103	21	that	that	SCONJ
ejpam-4200	103	22	0	0	NUM
ejpam-4200	103	23	<	<	X
ejpam-4200	103	24	p−	p−	NOUN
ejpam-4200	103	25	≤	≤	NUM
ejpam-4200	103	26	p(x	p(x	PROPN
ejpam-4200	103	27	)	)	PUNCT
ejpam-4200	103	28	≤	≤	NUM
ejpam-4200	103	29	u(x	u(x	NOUN
ejpam-4200	103	30	)	)	PUNCT
ejpam-4200	103	31	≤	≤	NOUN
ejpam-4200	103	32	supu	supu	NOUN
ejpam-4200	103	33	<	<	X
ejpam-4200	103	34	+	+	NOUN
ejpam-4200	103	35	∞	∞	PROPN
ejpam-4200	103	36	and	and	CCONJ
ejpam-4200	103	37	q−	q−	PROPN
ejpam-4200	103	38	,	,	PUNCT
ejpam-4200	103	39	q+	q+	NOUN
ejpam-4200	103	40	∈	∈	PROPN
ejpam-4200	103	41	(	(	PUNCT
ejpam-4200	103	42	0,+∞	0,+∞	NUM
ejpam-4200	103	43	)	)	PUNCT
ejpam-4200	103	44	.	.	PUNCT
ejpam-4200	104	1	the	the	DET
ejpam-4200	104	2	triebel	triebel	NOUN
ejpam-4200	104	3	-	-	PUNCT
ejpam-4200	104	4	lizorkin	lizorkin	NOUN
ejpam-4200	104	5	-	-	PUNCT
ejpam-4200	104	6	morrey	morrey	PROPN
ejpam-4200	104	7	spaces	space	NOUN
ejpam-4200	104	8	es	es	VERB
ejpam-4200	104	9	(	(	PUNCT
ejpam-4200	104	10	·	·	PUNCT
ejpam-4200	104	11	)	)	PUNCT
ejpam-4200	104	12	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	104	13	(	(	PUNCT
ejpam-4200	104	14	·	·	PUNCT
ejpam-4200	104	15	)	)	PUNCT
ejpam-4200	104	16	consists	consist	VERB
ejpam-4200	104	17	of	of	ADP
ejpam-4200	104	18	all	all	DET
ejpam-4200	104	19	distributions	distribution	NOUN
ejpam-4200	104	20	f	f	PROPN
ejpam-4200	104	21	∈	∈	PROPN
ejpam-4200	104	22	s	s	PART
ejpam-4200	104	23	′(rn	′(rn	PROPN
ejpam-4200	104	24	)	)	PUNCT
ejpam-4200	104	25	such	such	ADJ
ejpam-4200	104	26	that	that	SCONJ
ejpam-4200	104	27	∥f∥es	∥f∥es	NOUN
ejpam-4200	104	28	(	(	PUNCT
ejpam-4200	104	29	·	·	PUNCT
ejpam-4200	104	30	)	)	PUNCT
ejpam-4200	104	31	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	104	32	(	(	PUNCT
ejpam-4200	104	33	·	·	PUNCT
ejpam-4200	104	34	)	)	PUNCT
ejpam-4200	104	35	:	:	PUNCT
ejpam-4200	104	36	=	=	SYM
ejpam-4200	104	37	∥ψ0(d)f∥mp(·),u	∥ψ0(d)f∥mp(·),u	PROPN
ejpam-4200	104	38	(	(	PUNCT
ejpam-4200	104	39	·	·	PUNCT
ejpam-4200	104	40	)	)	PUNCT
ejpam-4200	105	1	+	+	NUM
ejpam-4200	105	2	∥∥∥∥(2νs(·)ψν(d)fν	∥∥∥∥(2νs(·)ψν(d)fν	X
ejpam-4200	105	3	)	)	PUNCT
ejpam-4200	106	1	ν≥1	ν≥1	PROPN
ejpam-4200	106	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-4200	107	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	107	2	(	(	PUNCT
ejpam-4200	107	3	·	·	PUNCT
ejpam-4200	107	4	)	)	PUNCT
ejpam-4200	107	5	)	)	PUNCT
ejpam-4200	108	1	<	<	X
ejpam-4200	109	1	+	+	PRON
ejpam-4200	109	2	∞.	∞.	PROPN
ejpam-4200	109	3	(	(	PUNCT
ejpam-4200	109	4	4	4	NUM
ejpam-4200	109	5	)	)	PUNCT
ejpam-4200	109	6	remark	remark	NOUN
ejpam-4200	109	7	2	2	NUM
ejpam-4200	109	8	.	.	PUNCT
ejpam-4200	110	1	[	[	X
ejpam-4200	110	2	4](remark4.4	4](remark4.4	X
ejpam-4200	110	3	)	)	PUNCT
ejpam-4200	110	4	note	note	VERB
ejpam-4200	110	5	that	that	SCONJ
ejpam-4200	110	6	∥·∥es	∥·∥es	PROPN
ejpam-4200	110	7	(	(	PUNCT
ejpam-4200	110	8	·	·	PUNCT
ejpam-4200	110	9	)	)	PUNCT
ejpam-4200	110	10	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	110	11	(	(	PUNCT
ejpam-4200	110	12	·	·	PUNCT
ejpam-4200	110	13	)	)	PUNCT
ejpam-4200	110	14	defined	define	VERB
ejpam-4200	110	15	a	a	DET
ejpam-4200	110	16	quasinorm	quasinorm	NOUN
ejpam-4200	110	17	on	on	ADP
ejpam-4200	110	18	es	es	PRON
ejpam-4200	110	19	(	(	PUNCT
ejpam-4200	110	20	·	·	PUNCT
ejpam-4200	110	21	)	)	PUNCT
ejpam-4200	110	22	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	110	23	(	(	PUNCT
ejpam-4200	110	24	·	·	PUNCT
ejpam-4200	110	25	)	)	PUNCT
ejpam-4200	110	26	.	.	PUNCT
ejpam-4200	111	1	it	it	PRON
ejpam-4200	111	2	is	be	AUX
ejpam-4200	111	3	a	a	DET
ejpam-4200	111	4	norm	norm	NOUN
ejpam-4200	111	5	when	when	SCONJ
ejpam-4200	111	6	min(p−	min(p−	PROPN
ejpam-4200	111	7	,	,	PUNCT
ejpam-4200	111	8	q−	q−	PROPN
ejpam-4200	111	9	)	)	PUNCT
ejpam-4200	111	10	≥	≥	NOUN
ejpam-4200	111	11	1	1	NUM
ejpam-4200	111	12	.	.	PUNCT
ejpam-4200	111	13	m.	m.	NOUN
ejpam-4200	111	14	congo	congo	PROPN
ejpam-4200	111	15	,	,	PUNCT
ejpam-4200	111	16	m.	m.	PROPN
ejpam-4200	111	17	f.	f.	PROPN
ejpam-4200	111	18	ouedraogo	ouedraogo	PROPN
ejpam-4200	111	19	/	/	SYM
ejpam-4200	111	20	eur	eur	PROPN
ejpam-4200	111	21	.	.	PUNCT
ejpam-4200	112	1	j.	j.	PROPN
ejpam-4200	112	2	pure	pure	PROPN
ejpam-4200	112	3	appl	appl	PROPN
ejpam-4200	112	4	.	.	PROPN
ejpam-4200	112	5	math	math	PROPN
ejpam-4200	112	6	,	,	PUNCT
ejpam-4200	112	7	15	15	NUM
ejpam-4200	112	8	(	(	PUNCT
ejpam-4200	112	9	1	1	NUM
ejpam-4200	112	10	)	)	PUNCT
ejpam-4200	112	11	(	(	PUNCT
ejpam-4200	112	12	2022	2022	NUM
ejpam-4200	112	13	)	)	PUNCT
ejpam-4200	112	14	,	,	PUNCT
ejpam-4200	112	15	47	47	NUM
ejpam-4200	112	16	-	-	SYM
ejpam-4200	112	17	63	63	NUM
ejpam-4200	112	18	51	51	NUM
ejpam-4200	112	19	3	3	NUM
ejpam-4200	112	20	.	.	PUNCT
ejpam-4200	112	21	basic	basic	ADJ
ejpam-4200	112	22	tools	tool	NOUN
ejpam-4200	112	23	in	in	ADP
ejpam-4200	112	24	this	this	DET
ejpam-4200	112	25	section	section	NOUN
ejpam-4200	112	26	we	we	PRON
ejpam-4200	112	27	present	present	VERB
ejpam-4200	112	28	some	some	DET
ejpam-4200	112	29	useful	useful	ADJ
ejpam-4200	112	30	results	result	NOUN
ejpam-4200	112	31	for	for	ADP
ejpam-4200	112	32	the	the	DET
ejpam-4200	112	33	last	last	ADJ
ejpam-4200	112	34	section	section	NOUN
ejpam-4200	112	35	.	.	PUNCT
ejpam-4200	113	1	at	at	ADP
ejpam-4200	113	2	first	first	ADV
ejpam-4200	113	3	,	,	PUNCT
ejpam-4200	113	4	we	we	PRON
ejpam-4200	113	5	recall	recall	VERB
ejpam-4200	113	6	the	the	DET
ejpam-4200	113	7	η	η	NOUN
ejpam-4200	113	8	-	-	PUNCT
ejpam-4200	113	9	functions	function	NOUN
ejpam-4200	113	10	defined	define	VERB
ejpam-4200	113	11	by	by	ADP
ejpam-4200	113	12	ην	ην	NOUN
ejpam-4200	113	13	,	,	PUNCT
ejpam-4200	113	14	m(x	m(x	X
ejpam-4200	113	15	)	)	PUNCT
ejpam-4200	114	1	=	=	SYM
ejpam-4200	114	2	2nν	2nν	NOUN
ejpam-4200	114	3	(	(	PUNCT
ejpam-4200	114	4	1	1	NUM
ejpam-4200	114	5	+	+	NUM
ejpam-4200	114	6	2ν	2ν	NOUN
ejpam-4200	114	7	|x|)−m	|x|)−m	NOUN
ejpam-4200	114	8	,	,	PUNCT
ejpam-4200	114	9	ν	ν	PROPN
ejpam-4200	114	10	∈	∈	PROPN
ejpam-4200	114	11	n0	n0	PROPN
ejpam-4200	114	12	,	,	PUNCT
ejpam-4200	114	13	m	m	VERB
ejpam-4200	114	14	>	>	X
ejpam-4200	114	15	0	0	X
ejpam-4200	114	16	.	.	PUNCT
ejpam-4200	114	17	note	note	VERB
ejpam-4200	114	18	that	that	SCONJ
ejpam-4200	114	19	ην	ην	NOUN
ejpam-4200	114	20	,	,	PUNCT
ejpam-4200	114	21	m	m	PROPN
ejpam-4200	114	22	∈	∈	PROPN
ejpam-4200	114	23	l1	l1	PROPN
ejpam-4200	114	24	for	for	ADP
ejpam-4200	114	25	m	m	PROPN
ejpam-4200	114	26	>	>	X
ejpam-4200	114	27	n	n	PROPN
ejpam-4200	114	28	and	and	CCONJ
ejpam-4200	114	29	the	the	DET
ejpam-4200	114	30	corresponding	corresponding	ADJ
ejpam-4200	114	31	l1	l1	PROPN
ejpam-4200	114	32	-	-	PUNCT
ejpam-4200	114	33	norm	norm	NOUN
ejpam-4200	114	34	does	do	AUX
ejpam-4200	114	35	not	not	PART
ejpam-4200	114	36	depend	depend	VERB
ejpam-4200	114	37	on	on	ADP
ejpam-4200	114	38	ν	ν	X
ejpam-4200	114	39	.	.	PUNCT
ejpam-4200	115	1	the	the	DET
ejpam-4200	115	2	following	follow	VERB
ejpam-4200	115	3	lemma	lemma	PROPN
ejpam-4200	115	4	is	be	AUX
ejpam-4200	115	5	from	from	ADP
ejpam-4200	115	6	[	[	X
ejpam-4200	115	7	8](lemma19	8](lemma19	NUM
ejpam-4200	115	8	)	)	PUNCT
ejpam-4200	115	9	and	and	CCONJ
ejpam-4200	115	10	[	[	X
ejpam-4200	115	11	10](lemma6.1	10](lemma6.1	NUM
ejpam-4200	115	12	)	)	PUNCT
ejpam-4200	115	13	lemma	lemma	PROPN
ejpam-4200	115	14	1	1	NUM
ejpam-4200	115	15	.	.	PUNCT
ejpam-4200	116	1	let	let	VERB
ejpam-4200	116	2	α	α	PRON
ejpam-4200	116	3	∈	∈	PROPN
ejpam-4200	116	4	c	c	PROPN
ejpam-4200	116	5	log	log	PROPN
ejpam-4200	116	6	loc	loc	X
ejpam-4200	116	7	(	(	PUNCT
ejpam-4200	116	8	r	r	NOUN
ejpam-4200	116	9	n	n	CCONJ
ejpam-4200	116	10	)	)	PUNCT
ejpam-4200	116	11	and	and	CCONJ
ejpam-4200	116	12	let	let	VERB
ejpam-4200	116	13	m	m	PRON
ejpam-4200	116	14	≥	≥	NOUN
ejpam-4200	116	15	0	0	NUM
ejpam-4200	116	16	,	,	PUNCT
ejpam-4200	116	17	r	r	NOUN
ejpam-4200	116	18	≥	≥	NOUN
ejpam-4200	116	19	clog(α	clog(α	NUM
ejpam-4200	116	20	)	)	PUNCT
ejpam-4200	116	21	,	,	PUNCT
ejpam-4200	116	22	where	where	SCONJ
ejpam-4200	116	23	clog	clog	NOUN
ejpam-4200	116	24	is	be	AUX
ejpam-4200	116	25	the	the	DET
ejpam-4200	116	26	constant	constant	ADJ
ejpam-4200	116	27	from	from	ADP
ejpam-4200	116	28	(	(	PUNCT
ejpam-4200	116	29	1	1	NUM
ejpam-4200	116	30	)	)	PUNCT
ejpam-4200	116	31	for	for	ADP
ejpam-4200	116	32	α	α	X
ejpam-4200	116	33	.	.	PUNCT
ejpam-4200	117	1	then	then	ADV
ejpam-4200	117	2	2να(x)ην	2να(x)ην	NUM
ejpam-4200	117	3	,	,	PUNCT
ejpam-4200	117	4	m+r(x−	m+r(x−	PROPN
ejpam-4200	117	5	y	y	NOUN
ejpam-4200	117	6	)	)	PUNCT
ejpam-4200	117	7	≤	≤	ADJ
ejpam-4200	117	8	c2να(y)ην	c2να(y)ην	PROPN
ejpam-4200	117	9	,	,	PUNCT
ejpam-4200	117	10	m(x−	m(x−	PROPN
ejpam-4200	117	11	y	y	NOUN
ejpam-4200	117	12	)	)	PUNCT
ejpam-4200	117	13	with	with	ADP
ejpam-4200	117	14	c	c	PROPN
ejpam-4200	117	15	>	>	SYM
ejpam-4200	117	16	0	0	PROPN
ejpam-4200	117	17	independent	independent	NOUN
ejpam-4200	117	18	of	of	ADP
ejpam-4200	117	19	x	x	PROPN
ejpam-4200	117	20	,	,	PUNCT
ejpam-4200	117	21	y	y	PROPN
ejpam-4200	117	22	∈	∈	PROPN
ejpam-4200	117	23	rn	rn	PROPN
ejpam-4200	117	24	and	and	CCONJ
ejpam-4200	117	25	ν	ν	PROPN
ejpam-4200	117	26	∈	∈	PROPN
ejpam-4200	117	27	n0	n0	PROPN
ejpam-4200	117	28	.	.	PUNCT
ejpam-4200	118	1	the	the	DET
ejpam-4200	118	2	following	follow	VERB
ejpam-4200	118	3	lemma	lemma	PROPN
ejpam-4200	118	4	is	be	AUX
ejpam-4200	118	5	from	from	ADP
ejpam-4200	118	6	[	[	X
ejpam-4200	118	7	10](lemma	10](lemma	NUM
ejpam-4200	118	8	a.6	a.6	NUM
ejpam-4200	118	9	)	)	PUNCT
ejpam-4200	118	10	.	.	PUNCT
ejpam-4200	119	1	lemma	lemma	PROPN
ejpam-4200	119	2	2	2	X
ejpam-4200	119	3	.	.	PUNCT
ejpam-4200	120	1	let	let	VERB
ejpam-4200	120	2	t	t	PROPN
ejpam-4200	120	3	>	>	X
ejpam-4200	120	4	0	0	PROPN
ejpam-4200	120	5	,	,	PUNCT
ejpam-4200	120	6	ν	ν	PROPN
ejpam-4200	120	7	∈	∈	PROPN
ejpam-4200	120	8	n0	n0	PROPN
ejpam-4200	120	9	and	and	CCONJ
ejpam-4200	120	10	m	m	PROPN
ejpam-4200	120	11	>	>	X
ejpam-4200	120	12	n.	n.	NOUN
ejpam-4200	120	13	then	then	ADV
ejpam-4200	120	14	there	there	PRON
ejpam-4200	120	15	exists	exist	VERB
ejpam-4200	120	16	c	c	NOUN
ejpam-4200	120	17	=	=	SYM
ejpam-4200	120	18	c(t	c(t	PROPN
ejpam-4200	120	19	,	,	PUNCT
ejpam-4200	120	20	m	m	NOUN
ejpam-4200	120	21	,	,	PUNCT
ejpam-4200	120	22	n	n	CCONJ
ejpam-4200	120	23	)	)	PUNCT
ejpam-4200	120	24	such	such	ADJ
ejpam-4200	120	25	that	that	PRON
ejpam-4200	120	26	for	for	ADP
ejpam-4200	120	27	all	all	PRON
ejpam-4200	120	28	g	g	PROPN
ejpam-4200	120	29	∈	∈	PROPN
ejpam-4200	120	30	s	s	PART
ejpam-4200	120	31	′(rn	′(rn	PROPN
ejpam-4200	120	32	)	)	PUNCT
ejpam-4200	120	33	with	with	ADP
ejpam-4200	120	34	suppfg	suppfg	PROPN
ejpam-4200	120	35	⊂	⊂	PROPN
ejpam-4200	120	36	{	{	PUNCT
ejpam-4200	120	37	ξ	ξ	PROPN
ejpam-4200	120	38	∈	∈	PROPN
ejpam-4200	120	39	rn	rn	PROPN
ejpam-4200	120	40	:	:	PUNCT
ejpam-4200	120	41	|ξ|	|ξ|	VERB
ejpam-4200	120	42	≤	≤	NOUN
ejpam-4200	120	43	2ν+1	2ν+1	NUM
ejpam-4200	120	44	}	}	PUNCT
ejpam-4200	120	45	,	,	PUNCT
ejpam-4200	120	46	we	we	PRON
ejpam-4200	120	47	have	have	VERB
ejpam-4200	120	48	|g(x)|	|g(x)|	NOUN
ejpam-4200	120	49	≤	≤	ADJ
ejpam-4200	120	50	c	c	NOUN
ejpam-4200	120	51	(	(	PUNCT
ejpam-4200	120	52	ην	ην	NOUN
ejpam-4200	120	53	,	,	PUNCT
ejpam-4200	120	54	m	m	VERB
ejpam-4200	120	55	∗	∗	NOUN
ejpam-4200	120	56	|g|t(x	|g|t(x	PROPN
ejpam-4200	120	57	)	)	PUNCT
ejpam-4200	120	58	)	)	PUNCT
ejpam-4200	120	59	1	1	NUM
ejpam-4200	120	60	/	/	SYM
ejpam-4200	120	61	t	t	NOUN
ejpam-4200	120	62	,	,	PUNCT
ejpam-4200	120	63	x	x	PROPN
ejpam-4200	120	64	∈	∈	PROPN
ejpam-4200	120	65	rn	rn	PROPN
ejpam-4200	120	66	.	.	PUNCT
ejpam-4200	121	1	the	the	DET
ejpam-4200	121	2	following	follow	VERB
ejpam-4200	121	3	lemma	lemma	PROPN
ejpam-4200	121	4	is	be	AUX
ejpam-4200	121	5	from[4](theorem3.3	from[4](theorem3.3	NOUN
ejpam-4200	121	6	)	)	PUNCT
ejpam-4200	121	7	.	.	PUNCT
ejpam-4200	122	1	lemma	lemma	PROPN
ejpam-4200	122	2	3	3	X
ejpam-4200	122	3	.	.	PUNCT
ejpam-4200	123	1	let	let	AUX
ejpam-4200	123	2	p	p	PRON
ejpam-4200	123	3	,	,	PUNCT
ejpam-4200	123	4	q	q	PROPN
ejpam-4200	123	5	∈	∈	PROPN
ejpam-4200	123	6	p	p	NOUN
ejpam-4200	123	7	log(rn	log(rn	PROPN
ejpam-4200	123	8	)	)	PUNCT
ejpam-4200	123	9	and	and	CCONJ
ejpam-4200	123	10	u	u	PROPN
ejpam-4200	123	11	∈	∈	PROPN
ejpam-4200	123	12	p(rn	p(rn	PROPN
ejpam-4200	123	13	)	)	PUNCT
ejpam-4200	123	14	such	such	ADJ
ejpam-4200	123	15	that	that	SCONJ
ejpam-4200	123	16	1	1	NUM
ejpam-4200	123	17	<	<	NOUN
ejpam-4200	123	18	p−	p−	NOUN
ejpam-4200	123	19	≤	≤	NUM
ejpam-4200	123	20	p(x	p(x	PROPN
ejpam-4200	123	21	)	)	PUNCT
ejpam-4200	123	22	≤	≤	NUM
ejpam-4200	123	23	u(x	u(x	NOUN
ejpam-4200	123	24	)	)	PUNCT
ejpam-4200	123	25	≤	≤	NOUN
ejpam-4200	123	26	supu	supu	NOUN
ejpam-4200	123	27	<	<	X
ejpam-4200	124	1	+	+	NOUN
ejpam-4200	124	2	∞	∞	PROPN
ejpam-4200	124	3	and	and	CCONJ
ejpam-4200	124	4	q−	q−	PROPN
ejpam-4200	124	5	,	,	PUNCT
ejpam-4200	124	6	q+	q+	NOUN
ejpam-4200	124	7	∈	∈	PROPN
ejpam-4200	124	8	(	(	PUNCT
ejpam-4200	124	9	1,+∞	1,+∞	NUM
ejpam-4200	124	10	)	)	PUNCT
ejpam-4200	124	11	.	.	PUNCT
ejpam-4200	125	1	if	if	SCONJ
ejpam-4200	125	2	m	m	VERB
ejpam-4200	125	3	>	>	X
ejpam-4200	125	4	n+	n+	X
ejpam-4200	125	5	nmax	nmax	PROPN
ejpam-4200	125	6	{	{	PUNCT
ejpam-4200	125	7	0	0	NUM
ejpam-4200	125	8	,	,	PUNCT
ejpam-4200	125	9	sup	sup	NOUN
ejpam-4200	125	10	x∈rn	x∈rn	PROPN
ejpam-4200	125	11	(	(	PUNCT
ejpam-4200	125	12	1	1	NUM
ejpam-4200	125	13	p(x	p(x	NOUN
ejpam-4200	125	14	)	)	PUNCT
ejpam-4200	125	15	−	−	PROPN
ejpam-4200	125	16	1	1	NUM
ejpam-4200	125	17	u(x	u(x	NOUN
ejpam-4200	125	18	)	)	PUNCT
ejpam-4200	125	19	)	)	PUNCT
ejpam-4200	126	1	−	−	PROPN
ejpam-4200	126	2	1	1	NUM
ejpam-4200	126	3	p∞	p∞	PROPN
ejpam-4200	126	4	}	}	PUNCT
ejpam-4200	126	5	,	,	PUNCT
ejpam-4200	126	6	then	then	ADV
ejpam-4200	126	7	there	there	PRON
ejpam-4200	126	8	exists	exist	VERB
ejpam-4200	126	9	c	c	NOUN
ejpam-4200	126	10	>	>	X
ejpam-4200	126	11	0	0	NUM
ejpam-4200	127	1	such	such	ADJ
ejpam-4200	127	2	that	that	PRON
ejpam-4200	127	3	for	for	ADP
ejpam-4200	127	4	all	all	DET
ejpam-4200	127	5	sequences	sequence	NOUN
ejpam-4200	127	6	(	(	PUNCT
ejpam-4200	127	7	fν)ν	fν)ν	PROPN
ejpam-4200	127	8	⊂mp(·),u(·)(ℓq(·)).∥∥(ην	⊂mp(·),u(·)(ℓq(·)).∥∥(ην	ADJ
ejpam-4200	127	9	,	,	PUNCT
ejpam-4200	127	10	m	m	PROPN
ejpam-4200	127	11	∗	∗	NOUN
ejpam-4200	127	12	fν)ν	fν)ν	PROPN
ejpam-4200	127	13	∥∥	∥∥	PUNCT
ejpam-4200	127	14	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	127	15	(	(	PUNCT
ejpam-4200	127	16	·	·	PUNCT
ejpam-4200	127	17	)	)	PUNCT
ejpam-4200	127	18	)	)	PUNCT
ejpam-4200	128	1	≤	≤	NUM
ejpam-4200	128	2	c	c	NOUN
ejpam-4200	128	3	∥(fν)ν∥mp(·),u(·)(ℓq	∥(fν)ν∥mp(·),u(·)(ℓq	X
ejpam-4200	128	4	(	(	PUNCT
ejpam-4200	128	5	·	·	PUNCT
ejpam-4200	128	6	)	)	PUNCT
ejpam-4200	128	7	)	)	PUNCT
ejpam-4200	128	8	.	.	PUNCT
ejpam-4200	129	1	the	the	DET
ejpam-4200	129	2	following	follow	VERB
ejpam-4200	129	3	lemma	lemma	PROPN
ejpam-4200	129	4	is	be	AUX
ejpam-4200	129	5	from[1](corollary	from[1](corollary	ADJ
ejpam-4200	129	6	4.8	4.8	NUM
ejpam-4200	129	7	.	.	PUNCT
ejpam-4200	129	8	)	)	PUNCT
ejpam-4200	130	1	lemma	lemma	PROPN
ejpam-4200	130	2	4	4	X
ejpam-4200	130	3	.	.	PUNCT
ejpam-4200	131	1	let	let	VERB
ejpam-4200	131	2	p	p	PRON
ejpam-4200	131	3	∈	∈	PROPN
ejpam-4200	131	4	p	p	NOUN
ejpam-4200	131	5	log(rn	log(rn	PROPN
ejpam-4200	131	6	)	)	PUNCT
ejpam-4200	131	7	and	and	CCONJ
ejpam-4200	131	8	u	u	NOUN
ejpam-4200	131	9	∈	∈	PROPN
ejpam-4200	131	10	p	p	NOUN
ejpam-4200	131	11	with	with	ADP
ejpam-4200	131	12	1	1	NUM
ejpam-4200	131	13	<	<	NOUN
ejpam-4200	131	14	p−	p−	NOUN
ejpam-4200	131	15	≤	≤	NUM
ejpam-4200	131	16	p(x	p(x	PROPN
ejpam-4200	131	17	)	)	PUNCT
ejpam-4200	131	18	≤	≤	NUM
ejpam-4200	131	19	u(x	u(x	NOUN
ejpam-4200	131	20	)	)	PUNCT
ejpam-4200	131	21	≤	≤	NOUN
ejpam-4200	131	22	supu	supu	NOUN
ejpam-4200	131	23	<	<	X
ejpam-4200	132	1	+	+	X
ejpam-4200	132	2	∞.	∞.	PROPN
ejpam-4200	132	3	if	if	SCONJ
ejpam-4200	132	4	m	m	VERB
ejpam-4200	132	5	>	>	X
ejpam-4200	132	6	n+	n+	X
ejpam-4200	132	7	nmax	nmax	PROPN
ejpam-4200	132	8	{	{	PUNCT
ejpam-4200	132	9	0	0	NUM
ejpam-4200	132	10	,	,	PUNCT
ejpam-4200	132	11	supx∈rn	supx∈rn	PUNCT
ejpam-4200	132	12	(	(	PUNCT
ejpam-4200	132	13	1	1	NUM
ejpam-4200	132	14	p(x	p(x	NOUN
ejpam-4200	132	15	)	)	PUNCT
ejpam-4200	132	16	−	−	PROPN
ejpam-4200	132	17	1	1	NUM
ejpam-4200	132	18	u(x	u(x	NOUN
ejpam-4200	132	19	)	)	PUNCT
ejpam-4200	132	20	)	)	PUNCT
ejpam-4200	133	1	−	−	PROPN
ejpam-4200	133	2	1	1	NUM
ejpam-4200	133	3	p∞	p∞	PROPN
ejpam-4200	133	4	}	}	PUNCT
ejpam-4200	133	5	.	.	PUNCT
ejpam-4200	134	1	then	then	ADV
ejpam-4200	134	2	there	there	PRON
ejpam-4200	134	3	exists	exist	VERB
ejpam-4200	134	4	c	c	NOUN
ejpam-4200	134	5	>	>	X
ejpam-4200	134	6	0	0	NUM
ejpam-4200	134	7	such	such	ADJ
ejpam-4200	134	8	that	that	DET
ejpam-4200	134	9	∥ην	∥ην	NOUN
ejpam-4200	134	10	,	,	PUNCT
ejpam-4200	134	11	m	m	NOUN
ejpam-4200	134	12	∗	∗	NOUN
ejpam-4200	134	13	f∥mp(·),u	f∥mp(·),u	PROPN
ejpam-4200	134	14	(	(	PUNCT
ejpam-4200	134	15	·	·	PUNCT
ejpam-4200	134	16	)	)	PUNCT
ejpam-4200	134	17	≤	≤	NUM
ejpam-4200	134	18	c	c	X
ejpam-4200	134	19	∥f∥mp(·),u	∥f∥mp(·),u	PROPN
ejpam-4200	134	20	(	(	PUNCT
ejpam-4200	134	21	·	·	PUNCT
ejpam-4200	134	22	)	)	PUNCT
ejpam-4200	134	23	.	.	PUNCT
ejpam-4200	135	1	the	the	DET
ejpam-4200	135	2	following	follow	VERB
ejpam-4200	135	3	lemma	lemma	PROPN
ejpam-4200	135	4	is	be	AUX
ejpam-4200	135	5	from[4](lemma	from[4](lemma	PROPN
ejpam-4200	135	6	3.7	3.7	NUM
ejpam-4200	135	7	)	)	PUNCT
ejpam-4200	135	8	.	.	PUNCT
ejpam-4200	136	1	m.	m.	NOUN
ejpam-4200	136	2	congo	congo	PROPN
ejpam-4200	136	3	,	,	PUNCT
ejpam-4200	136	4	m.	m.	PROPN
ejpam-4200	136	5	f.	f.	PROPN
ejpam-4200	136	6	ouedraogo	ouedraogo	PROPN
ejpam-4200	136	7	/	/	SYM
ejpam-4200	136	8	eur	eur	PROPN
ejpam-4200	136	9	.	.	PUNCT
ejpam-4200	137	1	j.	j.	PROPN
ejpam-4200	137	2	pure	pure	PROPN
ejpam-4200	137	3	appl	appl	PROPN
ejpam-4200	137	4	.	.	PROPN
ejpam-4200	137	5	math	math	PROPN
ejpam-4200	137	6	,	,	PUNCT
ejpam-4200	137	7	15	15	NUM
ejpam-4200	137	8	(	(	PUNCT
ejpam-4200	137	9	1	1	NUM
ejpam-4200	137	10	)	)	PUNCT
ejpam-4200	137	11	(	(	PUNCT
ejpam-4200	137	12	2022	2022	NUM
ejpam-4200	137	13	)	)	PUNCT
ejpam-4200	137	14	,	,	PUNCT
ejpam-4200	137	15	47	47	NUM
ejpam-4200	137	16	-	-	SYM
ejpam-4200	137	17	63	63	NUM
ejpam-4200	137	18	52	52	NUM
ejpam-4200	137	19	lemma	lemma	PROPN
ejpam-4200	137	20	5	5	NUM
ejpam-4200	137	21	.	.	PUNCT
ejpam-4200	138	1	let	let	VERB
ejpam-4200	138	2	p	p	PRON
ejpam-4200	138	3	,	,	PUNCT
ejpam-4200	138	4	u	u	NOUN
ejpam-4200	138	5	,	,	PUNCT
ejpam-4200	138	6	q	q	PROPN
ejpam-4200	138	7	∈	∈	PROPN
ejpam-4200	138	8	p(rn	p(rn	PROPN
ejpam-4200	138	9	)	)	PUNCT
ejpam-4200	138	10	with	with	ADP
ejpam-4200	138	11	p(x	p(x	NOUN
ejpam-4200	138	12	)	)	PUNCT
ejpam-4200	138	13	≤	≤	NUM
ejpam-4200	138	14	u(x	u(x	NOUN
ejpam-4200	138	15	)	)	PUNCT
ejpam-4200	138	16	.	.	PUNCT
ejpam-4200	139	1	let	let	VERB
ejpam-4200	139	2	δ	δ	PRON
ejpam-4200	139	3	>	>	X
ejpam-4200	139	4	0	0	X
ejpam-4200	139	5	.	.	PUNCT
ejpam-4200	140	1	for	for	ADP
ejpam-4200	140	2	any	any	DET
ejpam-4200	140	3	sequence	sequence	NOUN
ejpam-4200	140	4	(	(	PUNCT
ejpam-4200	140	5	gj)j∈n0	gj)j∈n0	X
ejpam-4200	140	6	of	of	ADP
ejpam-4200	140	7	non	non	ADJ
ejpam-4200	140	8	negative	negative	ADJ
ejpam-4200	140	9	measurable	measurable	ADJ
ejpam-4200	140	10	functions	function	NOUN
ejpam-4200	140	11	on	on	ADP
ejpam-4200	140	12	rn	rn	PROPN
ejpam-4200	140	13	,	,	PUNCT
ejpam-4200	140	14	we	we	PRON
ejpam-4200	140	15	denote	denote	VERB
ejpam-4200	140	16	gν(x	gν(x	PUNCT
ejpam-4200	140	17	)	)	PUNCT
ejpam-4200	140	18	:	:	PUNCT
ejpam-4200	141	1	=	=	PUNCT
ejpam-4200	142	1	+	+	ADP
ejpam-4200	142	2	∞∑	∞∑	NUM
ejpam-4200	142	3	j=0	j=0	ADJ
ejpam-4200	142	4	2−|ν−j|δgj(x	2−|ν−j|δgj(x	NUM
ejpam-4200	142	5	)	)	PUNCT
ejpam-4200	142	6	,	,	PUNCT
ejpam-4200	142	7	x	x	PROPN
ejpam-4200	142	8	∈	∈	PROPN
ejpam-4200	142	9	rn	rn	PROPN
ejpam-4200	142	10	,	,	PUNCT
ejpam-4200	142	11	ν	ν	PROPN
ejpam-4200	142	12	∈	∈	PROPN
ejpam-4200	142	13	n0	n0	PROPN
ejpam-4200	142	14	.	.	PUNCT
ejpam-4200	143	1	then	then	ADV
ejpam-4200	143	2	it	it	PRON
ejpam-4200	143	3	holds	hold	VERB
ejpam-4200	143	4	∥(gν)ν∥ℓq(·)(mp(·),u	∥(gν)ν∥ℓq(·)(mp(·),u	NOUN
ejpam-4200	143	5	(	(	PUNCT
ejpam-4200	143	6	·	·	PUNCT
ejpam-4200	143	7	)	)	PUNCT
ejpam-4200	143	8	)	)	PUNCT
ejpam-4200	144	1	≤	≤	PROPN
ejpam-4200	144	2	c(δ	c(δ	PROPN
ejpam-4200	144	3	,	,	PUNCT
ejpam-4200	144	4	q	q	NOUN
ejpam-4200	144	5	)	)	PUNCT
ejpam-4200	144	6	∥∥∥(gj)j∥∥∥ℓq(·)(mp(·),u	∥∥∥(gj)j∥∥∥ℓq(·)(mp(·),u	PROPN
ejpam-4200	144	7	(	(	PUNCT
ejpam-4200	144	8	·	·	PUNCT
ejpam-4200	144	9	)	)	PUNCT
ejpam-4200	144	10	)	)	PUNCT
ejpam-4200	145	1	where	where	SCONJ
ejpam-4200	145	2	c(δ	c(δ	PROPN
ejpam-4200	145	3	,	,	PUNCT
ejpam-4200	145	4	q	q	X
ejpam-4200	145	5	)	)	PUNCT
ejpam-4200	145	6	=	=	SYM
ejpam-4200	145	7	max	max	PROPN
ejpam-4200	145	8	∑	∑	NOUN
ejpam-4200	145	9	ν∈z	ν∈z	VERB
ejpam-4200	145	10	2−|ν|δ	2−|ν|δ	NUM
ejpam-4200	145	11	,	,	PUNCT
ejpam-4200	145	12	[	[	X
ejpam-4200	145	13	∑	∑	PUNCT
ejpam-4200	145	14	ν∈z	ν∈z	NOUN
ejpam-4200	145	15	2−|ν|δq−	2−|ν|δq−	NUM
ejpam-4200	145	16	]	]	SYM
ejpam-4200	145	17	1	1	NUM
ejpam-4200	145	18	/	/	SYM
ejpam-4200	145	19	q−	q−	NOUN
ejpam-4200	145	20	.	.	PUNCT
ejpam-4200	146	1	4	4	X
ejpam-4200	146	2	.	.	X
ejpam-4200	146	3	boundedness	boundedness	NOUN
ejpam-4200	146	4	of	of	ADP
ejpam-4200	146	5	pseudo	pseudo	NOUN
ejpam-4200	146	6	-	-	NOUN
ejpam-4200	146	7	differential	differential	ADJ
ejpam-4200	146	8	operators	operator	NOUN
ejpam-4200	146	9	we	we	PRON
ejpam-4200	146	10	will	will	AUX
ejpam-4200	146	11	use	use	VERB
ejpam-4200	146	12	symbols	symbol	NOUN
ejpam-4200	146	13	for	for	ADP
ejpam-4200	146	14	which	which	PRON
ejpam-4200	146	15	x	x	NOUN
ejpam-4200	146	16	-	-	NOUN
ejpam-4200	146	17	regularity	regularity	NOUN
ejpam-4200	146	18	is	be	AUX
ejpam-4200	146	19	measured	measure	VERB
ejpam-4200	146	20	in	in	ADP
ejpam-4200	146	21	hölder	hölder	NOUN
ejpam-4200	146	22	-	-	PUNCT
ejpam-4200	146	23	zygmund	zygmund	NOUN
ejpam-4200	146	24	spaces	space	NOUN
ejpam-4200	146	25	.	.	PUNCT
ejpam-4200	147	1	definition	definition	NOUN
ejpam-4200	147	2	4	4	NUM
ejpam-4200	147	3	.	.	PUNCT
ejpam-4200	148	1	[	[	X
ejpam-4200	148	2	14	14	NUM
ejpam-4200	148	3	]	]	PUNCT
ejpam-4200	148	4	the	the	DET
ejpam-4200	148	5	function	function	NOUN
ejpam-4200	148	6	a(x	a(x	NOUN
ejpam-4200	148	7	,	,	PUNCT
ejpam-4200	148	8	ξ	ξ	NOUN
ejpam-4200	148	9	)	)	PUNCT
ejpam-4200	148	10	on	on	ADP
ejpam-4200	148	11	rn×rn	rn×rn	PROPN
ejpam-4200	148	12	belongs	belong	VERB
ejpam-4200	148	13	to	to	ADP
ejpam-4200	148	14	the	the	DET
ejpam-4200	148	15	symbol	symbol	NOUN
ejpam-4200	148	16	class	class	NOUN
ejpam-4200	148	17	cℓ	cℓ	ADP
ejpam-4200	148	18	∗s	∗s	PROPN
ejpam-4200	148	19	m	m	NOUN
ejpam-4200	148	20	1,δ	1,δ	NUM
ejpam-4200	148	21	,	,	PUNCT
ejpam-4200	148	22	δ	δ	PROPN
ejpam-4200	148	23	∈	∈	PROPN
ejpam-4200	149	1	[	[	X
ejpam-4200	149	2	0	0	NUM
ejpam-4200	149	3	,	,	PUNCT
ejpam-4200	149	4	1	1	NUM
ejpam-4200	149	5	]	]	PUNCT
ejpam-4200	149	6	,	,	PUNCT
ejpam-4200	149	7	ℓ	ℓ	INTJ
ejpam-4200	149	8	>	>	X
ejpam-4200	149	9	0	0	PUNCT
ejpam-4200	150	1	if	if	SCONJ
ejpam-4200	150	2	it	it	PRON
ejpam-4200	150	3	is	be	AUX
ejpam-4200	150	4	smooth	smooth	ADJ
ejpam-4200	150	5	in	in	ADP
ejpam-4200	150	6	ξ	ξ	PROPN
ejpam-4200	150	7	and	and	CCONJ
ejpam-4200	150	8	satisfies	satisfy	VERB
ejpam-4200	150	9	the	the	DET
ejpam-4200	150	10	following	follow	VERB
ejpam-4200	150	11	estimates:	estimates:	ADJ
ejpam-4200	150	12	∥∥∥∂αξ	∥∥∥∂αξ	PRON
ejpam-4200	150	13	a	a	DET
ejpam-4200	150	14	(	(	PUNCT
ejpam-4200	150	15	·	·	PUNCT
ejpam-4200	150	16	,	,	PUNCT
ejpam-4200	150	17	ξ)∥∥∥	ξ)∥∥∥	PROPN
ejpam-4200	150	18	cℓ	cℓ	ADP
ejpam-4200	150	19	∗s	∗s	PROPN
ejpam-4200	150	20	m	m	PROPN
ejpam-4200	150	21	1,δ	1,δ	NUM
ejpam-4200	150	22	≤	≤	NUM
ejpam-4200	150	23	cα	cα	ADP
ejpam-4200	150	24	⟨ξ⟩m−|α|+ℓδ	⟨ξ⟩m−|α|+ℓδ	PROPN
ejpam-4200	150	25	and∣∣∣∂αξ	and∣∣∣∂αξ	PROPN
ejpam-4200	150	26	a(x	a(x	PROPN
ejpam-4200	150	27	,	,	PUNCT
ejpam-4200	150	28	ξ)∣∣∣	ξ)∣∣∣	PROPN
ejpam-4200	150	29	≤	≤	ADJ
ejpam-4200	150	30	c′α	c′α	NOUN
ejpam-4200	151	1	⟨ξ⟩	⟨ξ⟩	ADJ
ejpam-4200	151	2	m−|α|	m−|α|	NOUN
ejpam-4200	151	3	(	(	PUNCT
ejpam-4200	151	4	5	5	NUM
ejpam-4200	151	5	)	)	PUNCT
ejpam-4200	151	6	in	in	ADP
ejpam-4200	151	7	(	(	PUNCT
ejpam-4200	151	8	5	5	NUM
ejpam-4200	151	9	)	)	PUNCT
ejpam-4200	151	10	,	,	PUNCT
ejpam-4200	151	11	⟨ξ⟩	⟨ξ⟩	PROPN
ejpam-4200	151	12	stand	stand	VERB
ejpam-4200	151	13	for	for	ADP
ejpam-4200	151	14	(	(	PUNCT
ejpam-4200	151	15	1	1	NUM
ejpam-4200	151	16	+	+	CCONJ
ejpam-4200	151	17	|ξ|2	|ξ|2	ADJ
ejpam-4200	151	18	)	)	PUNCT
ejpam-4200	151	19	1/2	1/2	NUM
ejpam-4200	151	20	.	.	PUNCT
ejpam-4200	152	1	a	a	DET
ejpam-4200	152	2	pseudo	pseudo	NOUN
ejpam-4200	152	3	-	-	ADJ
ejpam-4200	152	4	differential	differential	ADJ
ejpam-4200	152	5	operator	operator	NOUN
ejpam-4200	152	6	on	on	ADP
ejpam-4200	152	7	es	es	PRON
ejpam-4200	152	8	(	(	PUNCT
ejpam-4200	152	9	·	·	PUNCT
ejpam-4200	152	10	)	)	PUNCT
ejpam-4200	152	11	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	152	12	(	(	PUNCT
ejpam-4200	152	13	·	·	PUNCT
ejpam-4200	152	14	)	)	PUNCT
ejpam-4200	152	15	with	with	ADP
ejpam-4200	152	16	symbol	symbol	NOUN
ejpam-4200	152	17	a	a	DET
ejpam-4200	152	18	∈	∈	NOUN
ejpam-4200	152	19	cℓ	cℓ	ADP
ejpam-4200	152	20	∗s	∗s	PROPN
ejpam-4200	152	21	m	m	PROPN
ejpam-4200	152	22	1,δ	1,δ	NUM
ejpam-4200	152	23	is	be	AUX
ejpam-4200	152	24	defined	define	VERB
ejpam-4200	152	25	by	by	ADP
ejpam-4200	152	26	a(x	a(x	NOUN
ejpam-4200	152	27	,	,	PUNCT
ejpam-4200	152	28	d)f(x	d)f(x	NOUN
ejpam-4200	152	29	)	)	PUNCT
ejpam-4200	152	30	=	=	SYM
ejpam-4200	152	31	1	1	NUM
ejpam-4200	152	32	(	(	PUNCT
ejpam-4200	152	33	2π)n	2π)n	NUM
ejpam-4200	152	34	∫	∫	PROPN
ejpam-4200	152	35	rn	rn	PROPN
ejpam-4200	152	36	eix·ξa(x	eix·ξa(x	PROPN
ejpam-4200	152	37	,	,	PUNCT
ejpam-4200	152	38	ξ)ff(ξ)dξ	ξ)ff(ξ)dξ	NOUN
ejpam-4200	152	39	,	,	PUNCT
ejpam-4200	152	40	f	f	PROPN
ejpam-4200	152	41	∈	∈	PROPN
ejpam-4200	152	42	es	es	PROPN
ejpam-4200	152	43	(	(	PUNCT
ejpam-4200	152	44	·	·	PUNCT
ejpam-4200	152	45	)	)	PUNCT
ejpam-4200	152	46	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	152	47	(	(	PUNCT
ejpam-4200	152	48	·	·	PUNCT
ejpam-4200	152	49	)	)	PUNCT
ejpam-4200	152	50	.	.	PUNCT
ejpam-4200	153	1	definition	definition	NOUN
ejpam-4200	153	2	5	5	NUM
ejpam-4200	153	3	.	.	PUNCT
ejpam-4200	154	1	we	we	PRON
ejpam-4200	154	2	call	call	VERB
ejpam-4200	154	3	elementary	elementary	ADJ
ejpam-4200	154	4	symbol	symbol	NOUN
ejpam-4200	154	5	in	in	ADP
ejpam-4200	154	6	the	the	DET
ejpam-4200	154	7	class	class	NOUN
ejpam-4200	154	8	cℓ	cℓ	ADP
ejpam-4200	154	9	∗s	∗s	PROPN
ejpam-4200	154	10	m	m	NOUN
ejpam-4200	154	11	1,δ	1,δ	NUM
ejpam-4200	154	12	,	,	PUNCT
ejpam-4200	154	13	δ	δ	PROPN
ejpam-4200	154	14	∈	∈	PROPN
ejpam-4200	155	1	[	[	X
ejpam-4200	155	2	0	0	NUM
ejpam-4200	155	3	,	,	PUNCT
ejpam-4200	155	4	1	1	NUM
ejpam-4200	155	5	]	]	PUNCT
ejpam-4200	155	6	,	,	PUNCT
ejpam-4200	155	7	ℓ	ℓ	INTJ
ejpam-4200	155	8	>	>	X
ejpam-4200	155	9	0	0	PUNCT
ejpam-4200	156	1	an	an	DET
ejpam-4200	156	2	expression	expression	NOUN
ejpam-4200	156	3	of	of	ADP
ejpam-4200	156	4	the	the	DET
ejpam-4200	156	5	form	form	NOUN
ejpam-4200	156	6	a(x	a(x	NOUN
ejpam-4200	156	7	,	,	PUNCT
ejpam-4200	156	8	ξ	ξ	NOUN
ejpam-4200	156	9	)	)	PUNCT
ejpam-4200	156	10	=	=	SYM
ejpam-4200	156	11	∑	∑	PUNCT
ejpam-4200	156	12	j≥0	j≥0	PROPN
ejpam-4200	156	13	aj(x)ψj(ξ	aj(x)ψj(ξ	NOUN
ejpam-4200	156	14	)	)	PUNCT
ejpam-4200	156	15	where	where	SCONJ
ejpam-4200	156	16	ψ0	ψ0	PROPN
ejpam-4200	156	17	is	be	AUX
ejpam-4200	156	18	smooth	smooth	ADJ
ejpam-4200	156	19	supported	support	VERB
ejpam-4200	156	20	on	on	ADP
ejpam-4200	156	21	the	the	DET
ejpam-4200	156	22	ball	ball	NOUN
ejpam-4200	156	23	b(0	b(0	NOUN
ejpam-4200	156	24	,	,	PUNCT
ejpam-4200	156	25	2	2	NUM
ejpam-4200	156	26	)	)	PUNCT
ejpam-4200	156	27	,	,	PUNCT
ejpam-4200	156	28	ψj(ξ	ψj(ξ	PUNCT
ejpam-4200	156	29	)	)	PUNCT
ejpam-4200	157	1	=	=	SYM
ejpam-4200	157	2	ψ(2−jξ	ψ(2−jξ	NOUN
ejpam-4200	157	3	)	)	PUNCT
ejpam-4200	157	4	and	and	CCONJ
ejpam-4200	157	5	ψ	ψ	X
ejpam-4200	157	6	∈	∈	PROPN
ejpam-4200	157	7	c∞	c∞	PROPN
ejpam-4200	157	8	0	0	NUM
ejpam-4200	157	9	is	be	AUX
ejpam-4200	157	10	supported	support	VERB
ejpam-4200	157	11	on	on	ADP
ejpam-4200	157	12	the	the	DET
ejpam-4200	157	13	dyadic	dyadic	ADJ
ejpam-4200	157	14	shell	shell	NOUN
ejpam-4200	157	15	d0	d0	NOUN
ejpam-4200	157	16	=	=	SYM
ejpam-4200	157	17	{	{	PUNCT
ejpam-4200	157	18	ξ	ξ	PROPN
ejpam-4200	157	19	∈	∈	PROPN
ejpam-4200	157	20	rn	rn	PROPN
ejpam-4200	157	21	:	:	PUNCT
ejpam-4200	157	22	1/2	1/2	NUM
ejpam-4200	157	23	≤	≤	NUM
ejpam-4200	157	24	|ξ|	|ξ|	PROPN
ejpam-4200	157	25	≤	≤	NOUN
ejpam-4200	157	26	2	2	NUM
ejpam-4200	157	27	}	}	PUNCT
ejpam-4200	157	28	,	,	PUNCT
ejpam-4200	157	29	while	while	SCONJ
ejpam-4200	157	30	aj	aj	PROPN
ejpam-4200	157	31	is	be	AUX
ejpam-4200	157	32	uniformly	uniformly	ADV
ejpam-4200	157	33	bounded	bound	VERB
ejpam-4200	157	34	sequence	sequence	NOUN
ejpam-4200	157	35	such	such	ADJ
ejpam-4200	157	36	that	that	SCONJ
ejpam-4200	157	37	∥aj∥cℓ	∥aj∥cℓ	ADP
ejpam-4200	157	38	∗s	∗s	PROPN
ejpam-4200	157	39	m	m	NOUN
ejpam-4200	157	40	1,δ	1,δ	NUM
ejpam-4200	157	41	≤	≤	NOUN
ejpam-4200	157	42	c2j(m+ℓδ	c2j(m+ℓδ	NOUN
ejpam-4200	157	43	)	)	PUNCT
ejpam-4200	157	44	.	.	PUNCT
ejpam-4200	158	1	since	since	SCONJ
ejpam-4200	158	2	a(x	a(x	NOUN
ejpam-4200	158	3	,	,	PUNCT
ejpam-4200	158	4	d	d	NOUN
ejpam-4200	158	5	)	)	PUNCT
ejpam-4200	158	6	and	and	CCONJ
ejpam-4200	158	7	ψj(d	ψj(d	ADV
ejpam-4200	158	8	)	)	PUNCT
ejpam-4200	158	9	do	do	AUX
ejpam-4200	158	10	not	not	PART
ejpam-4200	158	11	commute	commute	VERB
ejpam-4200	158	12	,	,	PUNCT
ejpam-4200	158	13	to	to	PART
ejpam-4200	158	14	study	study	VERB
ejpam-4200	158	15	boundedness	boundedness	NOUN
ejpam-4200	158	16	of	of	ADP
ejpam-4200	158	17	a(x	a(x	NOUN
ejpam-4200	158	18	,	,	PUNCT
ejpam-4200	158	19	d	d	NOUN
ejpam-4200	158	20	)	)	PUNCT
ejpam-4200	158	21	,	,	PUNCT
ejpam-4200	158	22	the	the	DET
ejpam-4200	158	23	symbol	symbol	NOUN
ejpam-4200	158	24	reduction	reduction	NOUN
ejpam-4200	158	25	method	method	NOUN
ejpam-4200	158	26	due	due	ADP
ejpam-4200	158	27	to	to	ADP
ejpam-4200	158	28	coifman	coifman	NOUN
ejpam-4200	158	29	and	and	CCONJ
ejpam-4200	158	30	meyer[6	meyer[6	VERB
ejpam-4200	158	31	]	]	PUNCT
ejpam-4200	158	32	makes	make	VERB
ejpam-4200	158	33	it	it	PRON
ejpam-4200	158	34	possible	possible	ADJ
ejpam-4200	158	35	to	to	PART
ejpam-4200	158	36	be	be	AUX
ejpam-4200	158	37	limited	limit	VERB
ejpam-4200	158	38	to	to	ADP
ejpam-4200	158	39	elementary	elementary	ADJ
ejpam-4200	158	40	symbols	symbol	NOUN
ejpam-4200	158	41	.	.	PUNCT
ejpam-4200	159	1	therefore	therefore	ADV
ejpam-4200	159	2	,	,	PUNCT
ejpam-4200	159	3	the	the	DET
ejpam-4200	159	4	operator	operator	NOUN
ejpam-4200	159	5	a(x	a(x	NOUN
ejpam-4200	159	6	,	,	PUNCT
ejpam-4200	159	7	d	d	NOUN
ejpam-4200	159	8	)	)	PUNCT
ejpam-4200	159	9	with	with	ADP
ejpam-4200	159	10	symbol	symbol	NOUN
ejpam-4200	159	11	a	a	PRON
ejpam-4200	159	12	can	can	AUX
ejpam-4200	159	13	be	be	AUX
ejpam-4200	159	14	resolved	resolve	VERB
ejpam-4200	159	15	into	into	ADP
ejpam-4200	159	16	”	"	PUNCT
ejpam-4200	159	17	elementary	elementary	ADJ
ejpam-4200	159	18	operators	operator	NOUN
ejpam-4200	159	19	”	"	PUNCT
ejpam-4200	159	20	ak(x	ak(x	NOUN
ejpam-4200	159	21	,	,	PUNCT
ejpam-4200	159	22	d	d	NOUN
ejpam-4200	159	23	)	)	PUNCT
ejpam-4200	159	24	with	with	ADP
ejpam-4200	159	25	symbols	symbols	PROPN
ejpam-4200	159	26	ak	ak	PROPN
ejpam-4200	159	27	.	.	PROPN
ejpam-4200	160	1	this	this	DET
ejpam-4200	160	2	idea	idea	NOUN
ejpam-4200	160	3	has	have	AUX
ejpam-4200	160	4	been	be	AUX
ejpam-4200	160	5	exploited	exploit	VERB
ejpam-4200	160	6	to	to	PART
ejpam-4200	160	7	establish	establish	VERB
ejpam-4200	160	8	continuity	continuity	NOUN
ejpam-4200	160	9	of	of	ADP
ejpam-4200	160	10	pseudo	pseudo	NOUN
ejpam-4200	160	11	-	-	NOUN
ejpam-4200	160	12	differential	differential	ADJ
ejpam-4200	160	13	operators	operator	NOUN
ejpam-4200	160	14	with	with	ADP
ejpam-4200	160	15	non	non	ADJ
ejpam-4200	160	16	-	-	ADJ
ejpam-4200	160	17	regular	regular	ADJ
ejpam-4200	160	18	symbols	symbol	NOUN
ejpam-4200	160	19	in	in	ADP
ejpam-4200	160	20	inhomogeneous	inhomogeneous	ADJ
ejpam-4200	160	21	sobolev	sobolev	NOUN
ejpam-4200	160	22	spaces	space	NOUN
ejpam-4200	160	23	hs	hs	PROPN
ejpam-4200	160	24	,	,	PUNCT
ejpam-4200	160	25	p	p	NOUN
ejpam-4200	160	26	and	and	CCONJ
ejpam-4200	160	27	hölder	hölder	NOUN
ejpam-4200	160	28	-	-	PUNCT
ejpam-4200	160	29	zygmund	zygmund	NOUN
ejpam-4200	160	30	spaces	space	NOUN
ejpam-4200	160	31	cℓ	cℓ	ADP
ejpam-4200	160	32	∗	∗	NOUN
ejpam-4200	160	33	(	(	PUNCT
ejpam-4200	160	34	see	see	VERB
ejpam-4200	160	35	[	[	X
ejpam-4200	160	36	12	12	NUM
ejpam-4200	160	37	]	]	PUNCT
ejpam-4200	160	38	and	and	CCONJ
ejpam-4200	160	39	[	[	X
ejpam-4200	160	40	2	2	NUM
ejpam-4200	160	41	]	]	NUM
ejpam-4200	160	42	)	)	PUNCT
ejpam-4200	160	43	.	.	PUNCT
ejpam-4200	161	1	m.	m.	NOUN
ejpam-4200	161	2	congo	congo	PROPN
ejpam-4200	161	3	,	,	PUNCT
ejpam-4200	161	4	m.	m.	PROPN
ejpam-4200	161	5	f.	f.	PROPN
ejpam-4200	161	6	ouedraogo	ouedraogo	PROPN
ejpam-4200	161	7	/	/	SYM
ejpam-4200	161	8	eur	eur	PROPN
ejpam-4200	161	9	.	.	PUNCT
ejpam-4200	162	1	j.	j.	PROPN
ejpam-4200	162	2	pure	pure	PROPN
ejpam-4200	162	3	appl	appl	PROPN
ejpam-4200	162	4	.	.	PROPN
ejpam-4200	162	5	math	math	PROPN
ejpam-4200	162	6	,	,	PUNCT
ejpam-4200	162	7	15	15	NUM
ejpam-4200	162	8	(	(	PUNCT
ejpam-4200	162	9	1	1	NUM
ejpam-4200	162	10	)	)	PUNCT
ejpam-4200	162	11	(	(	PUNCT
ejpam-4200	162	12	2022	2022	NUM
ejpam-4200	162	13	)	)	PUNCT
ejpam-4200	162	14	,	,	PUNCT
ejpam-4200	162	15	47	47	NUM
ejpam-4200	162	16	-	-	SYM
ejpam-4200	162	17	63	63	NUM
ejpam-4200	162	18	53	53	NUM
ejpam-4200	162	19	lemma	lemma	PROPN
ejpam-4200	162	20	6	6	NUM
ejpam-4200	162	21	.	.	PUNCT
ejpam-4200	163	1	[	[	X
ejpam-4200	163	2	14	14	NUM
ejpam-4200	163	3	]	]	PUNCT
ejpam-4200	163	4	let	let	VERB
ejpam-4200	163	5	f	f	PROPN
ejpam-4200	163	6	=	=	PUNCT
ejpam-4200	163	7	∑	∑	PUNCT
ejpam-4200	163	8	j≥0	j≥0	PROPN
ejpam-4200	163	9	fj	fj	PROPN
ejpam-4200	163	10	in	in	ADP
ejpam-4200	163	11	s	s	PROPN
ejpam-4200	163	12	′	′	NOUN
ejpam-4200	163	13	,	,	PUNCT
ejpam-4200	163	14	with	with	ADP
ejpam-4200	163	15	suppf̂j	suppf̂j	PROPN
ejpam-4200	163	16	⊂	⊂	PROPN
ejpam-4200	163	17	b(0	b(0	PROPN
ejpam-4200	163	18	,	,	PUNCT
ejpam-4200	163	19	a2j	a2j	PROPN
ejpam-4200	163	20	)	)	PUNCT
ejpam-4200	163	21	for	for	ADP
ejpam-4200	163	22	some	some	DET
ejpam-4200	163	23	a	a	DET
ejpam-4200	163	24	>	>	X
ejpam-4200	163	25	0	0	NUM
ejpam-4200	163	26	.	.	PUNCT
ejpam-4200	164	1	then	then	ADV
ejpam-4200	164	2	,	,	PUNCT
ejpam-4200	164	3	for	for	ADP
ejpam-4200	164	4	ℓ	ℓ	PROPN
ejpam-4200	164	5	>	>	X
ejpam-4200	164	6	0	0	PROPN
ejpam-4200	164	7	,	,	PUNCT
ejpam-4200	164	8	∥f∥cℓ	∥f∥cℓ	NOUN
ejpam-4200	164	9	∗	∗	X
ejpam-4200	164	10	≤	≤	NUM
ejpam-4200	164	11	c(a	c(a	NOUN
ejpam-4200	164	12	)	)	PUNCT
ejpam-4200	164	13	sup	sup	NOUN
ejpam-4200	164	14	j≥0	j≥0	PROPN
ejpam-4200	164	15	{	{	PUNCT
ejpam-4200	164	16	2jℓ	2jℓ	ADJ
ejpam-4200	164	17	∥fj∥l∞	∥fj∥l∞	NOUN
ejpam-4200	164	18	}	}	PUNCT
ejpam-4200	164	19	.	.	PUNCT
ejpam-4200	165	1	(	(	PUNCT
ejpam-4200	165	2	6	6	X
ejpam-4200	165	3	)	)	PUNCT
ejpam-4200	165	4	the	the	DET
ejpam-4200	165	5	following	follow	VERB
ejpam-4200	165	6	lemmas	lemmas	PROPN
ejpam-4200	165	7	plays	play	VERB
ejpam-4200	165	8	a	a	DET
ejpam-4200	165	9	fundamental	fundamental	ADJ
ejpam-4200	165	10	role	role	NOUN
ejpam-4200	165	11	in	in	ADP
ejpam-4200	165	12	the	the	DET
ejpam-4200	165	13	proof	proof	NOUN
ejpam-4200	165	14	of	of	ADP
ejpam-4200	165	15	the	the	DET
ejpam-4200	165	16	boundedness	boundedness	NOUN
ejpam-4200	165	17	of	of	ADP
ejpam-4200	165	18	pseudo	pseudo	NOUN
ejpam-4200	165	19	-	-	ADJ
ejpam-4200	165	20	differential	differential	ADJ
ejpam-4200	165	21	operators	operator	NOUN
ejpam-4200	165	22	on	on	ADP
ejpam-4200	165	23	es	es	PRON
ejpam-4200	165	24	(	(	PUNCT
ejpam-4200	165	25	·	·	PUNCT
ejpam-4200	165	26	)	)	PUNCT
ejpam-4200	165	27	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	165	28	(	(	PUNCT
ejpam-4200	165	29	·	·	PUNCT
ejpam-4200	165	30	)	)	PUNCT
ejpam-4200	165	31	.	.	PUNCT
ejpam-4200	166	1	lemma	lemma	PROPN
ejpam-4200	166	2	7	7	X
ejpam-4200	166	3	.	.	PUNCT
ejpam-4200	167	1	let	let	VERB
ejpam-4200	167	2	c1	c1	PROPN
ejpam-4200	167	3	,	,	PUNCT
ejpam-4200	167	4	c2	c2	PROPN
ejpam-4200	167	5	>	>	X
ejpam-4200	167	6	0	0	NUM
ejpam-4200	167	7	,	,	PUNCT
ejpam-4200	167	8	s	s	VERB
ejpam-4200	167	9	∈	∈	PROPN
ejpam-4200	167	10	c	c	PROPN
ejpam-4200	167	11	log	log	PROPN
ejpam-4200	167	12	loc	loc	PROPN
ejpam-4200	167	13	,	,	PUNCT
ejpam-4200	167	14	p	p	X
ejpam-4200	167	15	,	,	PUNCT
ejpam-4200	167	16	q	q	PROPN
ejpam-4200	167	17	∈	∈	PROPN
ejpam-4200	167	18	p	p	NOUN
ejpam-4200	167	19	log(rn	log(rn	PROPN
ejpam-4200	167	20	)	)	PUNCT
ejpam-4200	167	21	and	and	CCONJ
ejpam-4200	167	22	u	u	PROPN
ejpam-4200	167	23	∈	∈	PROPN
ejpam-4200	167	24	p(rn	p(rn	PROPN
ejpam-4200	167	25	)	)	PUNCT
ejpam-4200	167	26	such	such	ADJ
ejpam-4200	167	27	that	that	SCONJ
ejpam-4200	167	28	0	0	NUM
ejpam-4200	167	29	<	<	X
ejpam-4200	167	30	p−	p−	NOUN
ejpam-4200	167	31	≤	≤	NUM
ejpam-4200	167	32	p(x	p(x	PROPN
ejpam-4200	167	33	)	)	PUNCT
ejpam-4200	167	34	≤	≤	NUM
ejpam-4200	167	35	u(x	u(x	NOUN
ejpam-4200	167	36	)	)	PUNCT
ejpam-4200	167	37	≤	≤	NOUN
ejpam-4200	168	1	supu	supu	VERB
ejpam-4200	168	2	<	<	X
ejpam-4200	168	3	∞	∞	PROPN
ejpam-4200	168	4	and	and	CCONJ
ejpam-4200	168	5	q−	q−	PROPN
ejpam-4200	168	6	,	,	PUNCT
ejpam-4200	168	7	q+	q+	NOUN
ejpam-4200	168	8	∈	∈	PROPN
ejpam-4200	168	9	(	(	PUNCT
ejpam-4200	168	10	0,+∞	0,+∞	NUM
ejpam-4200	168	11	)	)	PUNCT
ejpam-4200	168	12	.	.	PUNCT
ejpam-4200	169	1	let	let	VERB
ejpam-4200	169	2	{	{	PUNCT
ejpam-4200	169	3	fk}k∈n0	fk}k∈n0	INTJ
ejpam-4200	169	4	be	be	AUX
ejpam-4200	169	5	a	a	DET
ejpam-4200	169	6	sequence	sequence	NOUN
ejpam-4200	169	7	of	of	ADP
ejpam-4200	169	8	tempered	temper	VERB
ejpam-4200	169	9	distributions	distribution	NOUN
ejpam-4200	170	1	such	such	ADJ
ejpam-4200	170	2	that	that	DET
ejpam-4200	170	3	suppff0	suppff0	PROPN
ejpam-4200	170	4	⊂	⊂	PROPN
ejpam-4200	170	5	b(0	b(0	PROPN
ejpam-4200	170	6	,	,	PUNCT
ejpam-4200	170	7	2c2	2c2	NUM
ejpam-4200	170	8	)	)	PUNCT
ejpam-4200	170	9	and	and	CCONJ
ejpam-4200	170	10	suppffk	suppffk	VERB
ejpam-4200	170	11	⊂	⊂	PRON
ejpam-4200	170	12	{	{	PUNCT
ejpam-4200	170	13	ξ	ξ	PROPN
ejpam-4200	170	14	∈	∈	PROPN
ejpam-4200	170	15	rn	rn	PROPN
ejpam-4200	170	16	:	:	PUNCT
ejpam-4200	170	17	c12	c12	PROPN
ejpam-4200	170	18	k−1	k−1	PROPN
ejpam-4200	170	19	<	<	X
ejpam-4200	170	20	|ξ|	|ξ|	PROPN
ejpam-4200	170	21	<	<	X
ejpam-4200	170	22	c22	c22	PROPN
ejpam-4200	170	23	k+1	k+1	PROPN
ejpam-4200	170	24	}	}	PUNCT
ejpam-4200	170	25	for	for	ADP
ejpam-4200	170	26	k	k	PROPN
ejpam-4200	170	27	>	>	X
ejpam-4200	170	28	0	0	PUNCT
ejpam-4200	171	1	then	then	ADV
ejpam-4200	171	2	∥∥∥∥∥	∥∥∥∥∥	PUNCT
ejpam-4200	172	1	+	+	PUNCT
ejpam-4200	172	2	∞∑	∞∑	ADJ
ejpam-4200	172	3	k=0	k=0	PROPN
ejpam-4200	172	4	fk	fk	INTJ
ejpam-4200	172	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	172	6	es	es	SYM
ejpam-4200	172	7	(	(	PUNCT
ejpam-4200	172	8	·	·	PUNCT
ejpam-4200	172	9	)	)	PUNCT
ejpam-4200	172	10	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	172	11	(	(	PUNCT
ejpam-4200	172	12	·	·	PUNCT
ejpam-4200	172	13	)	)	PUNCT
ejpam-4200	172	14	≲	≲	PROPN
ejpam-4200	172	15	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4200	172	16	)	)	PUNCT
ejpam-4200	172	17	k	k	PROPN
ejpam-4200	172	18	∥∥∥	∥∥∥	PROPN
ejpam-4200	172	19	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	172	20	(	(	PUNCT
ejpam-4200	172	21	·	·	PUNCT
ejpam-4200	172	22	)	)	PUNCT
ejpam-4200	172	23	)	)	PUNCT
ejpam-4200	172	24	.	.	PUNCT
ejpam-4200	173	1	proof	proof	NOUN
ejpam-4200	173	2	.	.	PUNCT
ejpam-4200	174	1	let	let	VERB
ejpam-4200	174	2	{	{	PUNCT
ejpam-4200	174	3	ψj	ψj	ADV
ejpam-4200	174	4	}	}	PUNCT
ejpam-4200	174	5	be	be	AUX
ejpam-4200	174	6	the	the	DET
ejpam-4200	174	7	littlewood	littlewood	NOUN
ejpam-4200	174	8	-	-	PUNCT
ejpam-4200	174	9	paley	paley	NOUN
ejpam-4200	174	10	partition	partition	NOUN
ejpam-4200	174	11	of	of	ADP
ejpam-4200	174	12	unity	unity	NOUN
ejpam-4200	174	13	defined	define	VERB
ejpam-4200	174	14	above	above	ADV
ejpam-4200	174	15	.	.	PUNCT
ejpam-4200	175	1	by	by	ADP
ejpam-4200	175	2	hypothesis	hypothesis	NOUN
ejpam-4200	175	3	,	,	PUNCT
ejpam-4200	175	4	ψj	ψj	ADV
ejpam-4200	175	5	,	,	PUNCT
ejpam-4200	175	6	j	j	PROPN
ejpam-4200	175	7	≥	≥	NUM
ejpam-4200	175	8	1	1	NUM
ejpam-4200	175	9	are	be	AUX
ejpam-4200	175	10	supported	support	VERB
ejpam-4200	175	11	on	on	ADP
ejpam-4200	175	12	the	the	DET
ejpam-4200	175	13	dyadic	dyadic	ADJ
ejpam-4200	175	14	shell	shell	NOUN
ejpam-4200	175	15	dj	dj	NOUN
ejpam-4200	175	16	,	,	PUNCT
ejpam-4200	175	17	while	while	SCONJ
ejpam-4200	175	18	ψ0	ψ0	ADV
ejpam-4200	175	19	is	be	AUX
ejpam-4200	175	20	supported	support	VERB
ejpam-4200	175	21	on	on	ADP
ejpam-4200	175	22	the	the	DET
ejpam-4200	175	23	ball	ball	NOUN
ejpam-4200	175	24	b(0	b(0	NOUN
ejpam-4200	175	25	;	;	PUNCT
ejpam-4200	175	26	2	2	NUM
ejpam-4200	175	27	)	)	PUNCT
ejpam-4200	175	28	.	.	PUNCT
ejpam-4200	176	1	hence	hence	ADV
ejpam-4200	176	2	,	,	PUNCT
ejpam-4200	176	3	there	there	PRON
ejpam-4200	176	4	is	be	VERB
ejpam-4200	176	5	n1	n1	NOUN
ejpam-4200	176	6	,	,	PUNCT
ejpam-4200	176	7	n2	n2	PROPN
ejpam-4200	176	8	∈	∈	PROPN
ejpam-4200	176	9	n0	n0	X
ejpam-4200	176	10	such	such	ADJ
ejpam-4200	176	11	that	that	PRON
ejpam-4200	176	12	ψ0(d	ψ0(d	X
ejpam-4200	176	13	)	)	PUNCT
ejpam-4200	176	14	(	(	PUNCT
ejpam-4200	177	1	+	+	ADP
ejpam-4200	177	2	∞∑	∞∑	ADJ
ejpam-4200	177	3	k=0	k=0	PROPN
ejpam-4200	177	4	fk	fk	INTJ
ejpam-4200	177	5	)	)	PUNCT
ejpam-4200	177	6	=	=	SYM
ejpam-4200	177	7	ψ0(d	ψ0(d	PROPN
ejpam-4200	177	8	)	)	PUNCT
ejpam-4200	177	9	(	(	PUNCT
ejpam-4200	177	10	n1∑	n1∑	PROPN
ejpam-4200	177	11	k=0	k=0	PROPN
ejpam-4200	177	12	fk	fk	INTJ
ejpam-4200	177	13	)	)	PUNCT
ejpam-4200	177	14	and	and	CCONJ
ejpam-4200	177	15	ψj(d	ψj(d	ADV
ejpam-4200	177	16	)	)	PUNCT
ejpam-4200	177	17	(	(	PUNCT
ejpam-4200	177	18	+	+	ADP
ejpam-4200	177	19	∞∑	∞∑	ADJ
ejpam-4200	177	20	k=0	k=0	PROPN
ejpam-4200	177	21	fk	fk	INTJ
ejpam-4200	177	22	)	)	PUNCT
ejpam-4200	177	23	=	=	SYM
ejpam-4200	177	24	ψj(d	ψj(d	X
ejpam-4200	177	25	)	)	PUNCT
ejpam-4200	177	26			PROPN
ejpam-4200	177	27	j+n2∑	j+n2∑	PROPN
ejpam-4200	177	28	k	k	NOUN
ejpam-4200	177	29	=	=	NOUN
ejpam-4200	177	30	j−n1	j−n1	NOUN
ejpam-4200	177	31	fk	fk	INTJ
ejpam-4200	177	32			PROPN
ejpam-4200	177	33	then∥∥∥∥∥	then∥∥∥∥∥	PROPN
ejpam-4200	177	34	+	+	PROPN
ejpam-4200	177	35	∞∑	∞∑	PROPN
ejpam-4200	177	36	k=0	k=0	PROPN
ejpam-4200	177	37	fk	fk	INTJ
ejpam-4200	177	38	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	177	39	es	es	SYM
ejpam-4200	177	40	(	(	PUNCT
ejpam-4200	177	41	·	·	PUNCT
ejpam-4200	177	42	)	)	PUNCT
ejpam-4200	177	43	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	177	44	(	(	PUNCT
ejpam-4200	177	45	·	·	PUNCT
ejpam-4200	177	46	)	)	PUNCT
ejpam-4200	177	47	=	=	SYM
ejpam-4200	177	48	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	177	49	n1∑	n1∑	PROPN
ejpam-4200	177	50	k=0	k=0	PROPN
ejpam-4200	177	51	ψ̌0	ψ̌0	PROPN
ejpam-4200	177	52	∗	∗	PROPN
ejpam-4200	177	53	fk	fk	INTJ
ejpam-4200	177	54	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	177	55	mp(·),u	mp(·),u	PROPN
ejpam-4200	177	56	(	(	PUNCT
ejpam-4200	177	57	·	·	PUNCT
ejpam-4200	177	58	)	)	PUNCT
ejpam-4200	177	59	+	+	NUM
ejpam-4200	177	60	∥∥∥∥∥∥	∥∥∥∥∥∥	X
ejpam-4200	177	61	2js	2js	ADJ
ejpam-4200	177	62	(	(	PUNCT
ejpam-4200	177	63	·	·	PUNCT
ejpam-4200	177	64	)	)	PUNCT
ejpam-4200	177	65	j+n2∑	j+n2∑	PROPN
ejpam-4200	178	1	k	k	NOUN
ejpam-4200	178	2	=	=	NOUN
ejpam-4200	178	3	j−n1	j−n1	NOUN
ejpam-4200	178	4	ψ̌j	ψ̌j	NOUN
ejpam-4200	178	5	∗	∗	NOUN
ejpam-4200	178	6	fk	fk	INTJ
ejpam-4200	179	1			PROPN
ejpam-4200	179	2	j≥n1	j≥n1	PROPN
ejpam-4200	179	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	180	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	180	2	(	(	PUNCT
ejpam-4200	180	3	·	·	PUNCT
ejpam-4200	180	4	)	)	PUNCT
ejpam-4200	180	5	)	)	PUNCT
ejpam-4200	180	6	(	(	PUNCT
ejpam-4200	180	7	7	7	X
ejpam-4200	180	8	)	)	PUNCT
ejpam-4200	180	9	•	•	NOUN
ejpam-4200	180	10	let	let	VERB
ejpam-4200	180	11	us	we	PRON
ejpam-4200	180	12	first	first	ADV
ejpam-4200	180	13	estimate	estimate	VERB
ejpam-4200	180	14	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	181	1	2js	2js	PROPN
ejpam-4200	181	2	(	(	PUNCT
ejpam-4200	181	3	·	·	PUNCT
ejpam-4200	181	4	)	)	PUNCT
ejpam-4200	181	5	j+n2∑	j+n2∑	PROPN
ejpam-4200	182	1	k	k	NOUN
ejpam-4200	182	2	=	=	NOUN
ejpam-4200	182	3	j−n1	j−n1	NOUN
ejpam-4200	182	4	ψ̌j	ψ̌j	NOUN
ejpam-4200	182	5	∗	∗	NOUN
ejpam-4200	182	6	fk	fk	INTJ
ejpam-4200	183	1			PROPN
ejpam-4200	183	2	j≥1	j≥1	PROPN
ejpam-4200	183	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	184	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	184	2	(	(	PUNCT
ejpam-4200	184	3	·	·	PUNCT
ejpam-4200	184	4	)	)	PUNCT
ejpam-4200	184	5	)	)	PUNCT
ejpam-4200	184	6	since	since	SCONJ
ejpam-4200	184	7	ψ̌j	ψ̌j	PROPN
ejpam-4200	184	8	∗	∗	NOUN
ejpam-4200	184	9	fk	fk	INTJ
ejpam-4200	185	1	∈	∈	PROPN
ejpam-4200	185	2	s	s	PART
ejpam-4200	185	3	′	′	NOUN
ejpam-4200	185	4	and	and	CCONJ
ejpam-4200	185	5	suppf	suppf	NOUN
ejpam-4200	185	6	(	(	PUNCT
ejpam-4200	185	7	ψ̌j	ψ̌j	PROPN
ejpam-4200	185	8	∗	∗	NOUN
ejpam-4200	185	9	fk	fk	INTJ
ejpam-4200	185	10	)	)	PUNCT
ejpam-4200	186	1	⊂	⊂	PROPN
ejpam-4200	186	2	{	{	PUNCT
ejpam-4200	186	3	ξ	ξ	X
ejpam-4200	186	4	∈	∈	PROPN
ejpam-4200	186	5	rn	rn	PROPN
ejpam-4200	186	6	:	:	PUNCT
ejpam-4200	186	7	|ξ|	|ξ|	VERB
ejpam-4200	186	8	≤	≤	ADJ
ejpam-4200	186	9	2j+1	2j+1	PROPN
ejpam-4200	186	10	}	}	PUNCT
ejpam-4200	186	11	,	,	PUNCT
ejpam-4200	186	12	then	then	ADV
ejpam-4200	186	13	,	,	PUNCT
ejpam-4200	186	14	by	by	ADP
ejpam-4200	186	15	lemma	lemma	PROPN
ejpam-4200	186	16	2	2	NUM
ejpam-4200	186	17	,	,	PUNCT
ejpam-4200	186	18	|ψ̌j	|ψ̌j	PROPN
ejpam-4200	186	19	∗	∗	NOUN
ejpam-4200	186	20	fk|	fk|	NOUN
ejpam-4200	186	21	≲	≲	PROPN
ejpam-4200	186	22	(	(	PUNCT
ejpam-4200	186	23	ηj	ηj	NOUN
ejpam-4200	186	24	,	,	PUNCT
ejpam-4200	186	25	m	m	NOUN
ejpam-4200	186	26	∗	∗	NOUN
ejpam-4200	186	27	|fk|t	|fk|t	PROPN
ejpam-4200	186	28	)	)	PUNCT
ejpam-4200	186	29	1	1	NUM
ejpam-4200	186	30	/	/	SYM
ejpam-4200	186	31	t	t	NOUN
ejpam-4200	186	32	,	,	PUNCT
ejpam-4200	186	33	k	k	PROPN
ejpam-4200	186	34	=	=	PUNCT
ejpam-4200	186	35	j	j	PROPN
ejpam-4200	186	36	−n1	−n1	NOUN
ejpam-4200	186	37	,	,	PUNCT
ejpam-4200	186	38	.	.	PUNCT
ejpam-4200	186	39	.	.	PUNCT
ejpam-4200	186	40	.	.	PUNCT
ejpam-4200	187	1	,	,	PUNCT
ejpam-4200	187	2	j	j	PROPN
ejpam-4200	187	3	+	+	PROPN
ejpam-4200	187	4	n2	n2	PROPN
ejpam-4200	187	5	.	.	PUNCT
ejpam-4200	187	6	m.	m.	NOUN
ejpam-4200	187	7	congo	congo	PROPN
ejpam-4200	187	8	,	,	PUNCT
ejpam-4200	187	9	m.	m.	PROPN
ejpam-4200	187	10	f.	f.	PROPN
ejpam-4200	187	11	ouedraogo	ouedraogo	PROPN
ejpam-4200	187	12	/	/	SYM
ejpam-4200	187	13	eur	eur	PROPN
ejpam-4200	187	14	.	.	PUNCT
ejpam-4200	188	1	j.	j.	PROPN
ejpam-4200	188	2	pure	pure	PROPN
ejpam-4200	188	3	appl	appl	PROPN
ejpam-4200	188	4	.	.	PROPN
ejpam-4200	188	5	math	math	PROPN
ejpam-4200	188	6	,	,	PUNCT
ejpam-4200	188	7	15	15	NUM
ejpam-4200	188	8	(	(	PUNCT
ejpam-4200	188	9	1	1	NUM
ejpam-4200	188	10	)	)	PUNCT
ejpam-4200	188	11	(	(	PUNCT
ejpam-4200	188	12	2022	2022	NUM
ejpam-4200	188	13	)	)	PUNCT
ejpam-4200	188	14	,	,	PUNCT
ejpam-4200	188	15	47	47	NUM
ejpam-4200	188	16	-	-	SYM
ejpam-4200	188	17	63	63	NUM
ejpam-4200	188	18	54	54	NUM
ejpam-4200	188	19	for	for	ADP
ejpam-4200	188	20	any	any	DET
ejpam-4200	188	21	m	m	NOUN
ejpam-4200	188	22	>	>	X
ejpam-4200	188	23	n+	n+	NUM
ejpam-4200	188	24	clog(s	clog(s	NOUN
ejpam-4200	188	25	)	)	PUNCT
ejpam-4200	189	1	+	+	CCONJ
ejpam-4200	189	2	nmax	nmax	ADJ
ejpam-4200	189	3	{	{	PUNCT
ejpam-4200	189	4	0	0	NUM
ejpam-4200	189	5	,	,	PUNCT
ejpam-4200	189	6	supx∈rn	supx∈rn	PUNCT
ejpam-4200	189	7	(	(	PUNCT
ejpam-4200	189	8	1	1	NUM
ejpam-4200	189	9	p(x	p(x	NOUN
ejpam-4200	189	10	)	)	PUNCT
ejpam-4200	189	11	−	−	PROPN
ejpam-4200	189	12	1	1	NUM
ejpam-4200	189	13	u(x	u(x	NOUN
ejpam-4200	189	14	)	)	PUNCT
ejpam-4200	189	15	)	)	PUNCT
ejpam-4200	190	1	−	−	PROPN
ejpam-4200	190	2	1	1	NUM
ejpam-4200	190	3	p∞	p∞	PROPN
ejpam-4200	190	4	}	}	PUNCT
ejpam-4200	190	5	and	and	CCONJ
ejpam-4200	190	6	any	any	DET
ejpam-4200	190	7	t	t	NOUN
ejpam-4200	190	8	>	>	X
ejpam-4200	190	9	0	0	X
ejpam-4200	190	10	.	.	PUNCT
ejpam-4200	191	1	thus∥∥∥∥∥∥	thus∥∥∥∥∥∥	VERB
ejpam-4200	191	2	2js	2js	PROPN
ejpam-4200	191	3	(	(	PUNCT
ejpam-4200	191	4	·	·	PUNCT
ejpam-4200	191	5	)	)	PUNCT
ejpam-4200	191	6	j+n2∑	j+n2∑	PROPN
ejpam-4200	192	1	k	k	NOUN
ejpam-4200	192	2	=	=	NOUN
ejpam-4200	192	3	j−n1	j−n1	NOUN
ejpam-4200	192	4	ψ̌j	ψ̌j	NOUN
ejpam-4200	192	5	∗	∗	NOUN
ejpam-4200	192	6	fk	fk	INTJ
ejpam-4200	193	1			PROPN
ejpam-4200	193	2	j≥n1	j≥n1	PROPN
ejpam-4200	193	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	194	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	194	2	(	(	PUNCT
ejpam-4200	194	3	·	·	PUNCT
ejpam-4200	194	4	)	)	PUNCT
ejpam-4200	194	5	)	)	PUNCT
ejpam-4200	195	1	≲	≲	PROPN
ejpam-4200	195	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	195	3			PUNCT
ejpam-4200	195	4	j+n2∑	j+n2∑	NOUN
ejpam-4200	195	5	k	k	NOUN
ejpam-4200	195	6	=	=	NOUN
ejpam-4200	195	7	j−n1	j−n1	NOUN
ejpam-4200	195	8	2js	2js	NOUN
ejpam-4200	195	9	(	(	PUNCT
ejpam-4200	195	10	·	·	PUNCT
ejpam-4200	195	11	)	)	PUNCT
ejpam-4200	195	12	(	(	PUNCT
ejpam-4200	195	13	ηj	ηj	NOUN
ejpam-4200	195	14	,	,	PUNCT
ejpam-4200	195	15	m	m	NOUN
ejpam-4200	195	16	∗	∗	NOUN
ejpam-4200	195	17	|fk|t	|fk|t	PROPN
ejpam-4200	195	18	)	)	PUNCT
ejpam-4200	195	19	1	1	NUM
ejpam-4200	195	20	/	/	SYM
ejpam-4200	195	21	t	t	NUM
ejpam-4200	195	22	j	j	PROPN
ejpam-4200	195	23	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	196	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	196	2	(	(	PUNCT
ejpam-4200	196	3	·	·	PUNCT
ejpam-4200	196	4	)	)	PUNCT
ejpam-4200	196	5	)	)	PUNCT
ejpam-4200	196	6	by	by	ADP
ejpam-4200	196	7	lemma	lemma	PROPN
ejpam-4200	196	8	1	1	NUM
ejpam-4200	196	9	,	,	PUNCT
ejpam-4200	196	10	we	we	PRON
ejpam-4200	196	11	can	can	AUX
ejpam-4200	196	12	move	move	VERB
ejpam-4200	196	13	2js	2js	NOUN
ejpam-4200	196	14	(	(	PUNCT
ejpam-4200	196	15	·	·	PUNCT
ejpam-4200	196	16	)	)	PUNCT
ejpam-4200	196	17	inside	inside	ADP
ejpam-4200	196	18	the	the	DET
ejpam-4200	196	19	convolution	convolution	NOUN
ejpam-4200	196	20	2js	2js	NOUN
ejpam-4200	196	21	(	(	PUNCT
ejpam-4200	196	22	·	·	PUNCT
ejpam-4200	196	23	)	)	PUNCT
ejpam-4200	196	24	(	(	PUNCT
ejpam-4200	196	25	ηj	ηj	NOUN
ejpam-4200	196	26	,	,	PUNCT
ejpam-4200	196	27	m	m	NOUN
ejpam-4200	196	28	∗	∗	NOUN
ejpam-4200	196	29	|fk|t	|fk|t	PROPN
ejpam-4200	196	30	)	)	PUNCT
ejpam-4200	196	31	1	1	NUM
ejpam-4200	196	32	/	/	SYM
ejpam-4200	196	33	t	t	NOUN
ejpam-4200	196	34	≲	≲	PROPN
ejpam-4200	196	35	(	(	PUNCT
ejpam-4200	196	36	ηj	ηj	NOUN
ejpam-4200	196	37	,	,	PUNCT
ejpam-4200	196	38	m−clog(s	m−clog(s	PROPN
ejpam-4200	196	39	)	)	PUNCT
ejpam-4200	196	40	∗	∗	NOUN
ejpam-4200	196	41	2	2	NUM
ejpam-4200	196	42	js(·)t|fk|t	js(·)t|fk|t	ADJ
ejpam-4200	196	43	)	)	PUNCT
ejpam-4200	196	44	1	1	NUM
ejpam-4200	196	45	/	/	SYM
ejpam-4200	196	46	t	t	NOUN
ejpam-4200	196	47	.	.	PUNCT
ejpam-4200	197	1	then	then	ADV
ejpam-4200	197	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	198	1	2js	2js	PROPN
ejpam-4200	198	2	(	(	PUNCT
ejpam-4200	198	3	·	·	PUNCT
ejpam-4200	198	4	)	)	PUNCT
ejpam-4200	198	5	j+n2∑	j+n2∑	PROPN
ejpam-4200	199	1	k	k	NOUN
ejpam-4200	199	2	=	=	NOUN
ejpam-4200	199	3	j−n1	j−n1	NOUN
ejpam-4200	199	4	ψ̌j	ψ̌j	NOUN
ejpam-4200	199	5	∗	∗	NOUN
ejpam-4200	199	6	fk	fk	INTJ
ejpam-4200	200	1			PROPN
ejpam-4200	200	2	j≥n1	j≥n1	PROPN
ejpam-4200	200	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	201	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	201	2	(	(	PUNCT
ejpam-4200	201	3	·	·	PUNCT
ejpam-4200	201	4	)	)	PUNCT
ejpam-4200	201	5	)	)	PUNCT
ejpam-4200	202	1	≲	≲	PROPN
ejpam-4200	202	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	202	3			PUNCT
ejpam-4200	202	4	j+n2∑	j+n2∑	NOUN
ejpam-4200	202	5	k	k	NOUN
ejpam-4200	202	6	=	=	NOUN
ejpam-4200	202	7	j−n1	j−n1	NOUN
ejpam-4200	202	8	(	(	PUNCT
ejpam-4200	202	9	ηj	ηj	NOUN
ejpam-4200	202	10	,	,	PUNCT
ejpam-4200	202	11	m−clog(s	m−clog(s	PROPN
ejpam-4200	202	12	)	)	PUNCT
ejpam-4200	202	13	∗	∗	NOUN
ejpam-4200	202	14	2	2	NUM
ejpam-4200	202	15	js(·)t|fk|t	js(·)t|fk|t	ADJ
ejpam-4200	202	16	)	)	PUNCT
ejpam-4200	202	17	1	1	X
ejpam-4200	202	18	/	/	SYM
ejpam-4200	202	19	t	t	NUM
ejpam-4200	202	20	j	j	PROPN
ejpam-4200	202	21	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	203	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	203	2	(	(	PUNCT
ejpam-4200	203	3	·	·	PUNCT
ejpam-4200	203	4	)	)	PUNCT
ejpam-4200	203	5	)	)	PUNCT
ejpam-4200	204	1	=	=	SYM
ejpam-4200	204	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	204	3			PUNCT
ejpam-4200	204	4	j+n2∑	j+n2∑	NOUN
ejpam-4200	204	5	k	k	NOUN
ejpam-4200	204	6	=	=	NOUN
ejpam-4200	204	7	j−n1	j−n1	NOUN
ejpam-4200	204	8	(	(	PUNCT
ejpam-4200	204	9	ηj	ηj	NOUN
ejpam-4200	204	10	,	,	PUNCT
ejpam-4200	204	11	m−clog(s	m−clog(s	PROPN
ejpam-4200	204	12	)	)	PUNCT
ejpam-4200	204	13	∗	∗	NOUN
ejpam-4200	204	14	2	2	NUM
ejpam-4200	204	15	js(·)t|fk|t	js(·)t|fk|t	ADJ
ejpam-4200	204	16	)	)	PUNCT
ejpam-4200	205	1			PROPN
ejpam-4200	205	2	j	j	PROPN
ejpam-4200	205	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	205	4	m	m	VERB
ejpam-4200	205	5	p	p	X
ejpam-4200	205	6	(	(	PUNCT
ejpam-4200	205	7	·	·	PUNCT
ejpam-4200	205	8	)	)	PUNCT
ejpam-4200	205	9	t	t	PROPN
ejpam-4200	205	10	,	,	PUNCT
ejpam-4200	205	11	u	u	NOUN
ejpam-4200	205	12	(	(	PUNCT
ejpam-4200	205	13	·	·	PUNCT
ejpam-4200	205	14	)	)	PUNCT
ejpam-4200	205	15	t	t	PROPN
ejpam-4200	205	16	(	(	PUNCT
ejpam-4200	205	17	ℓ	ℓ	INTJ
ejpam-4200	205	18	q	q	PROPN
ejpam-4200	205	19	(	(	PUNCT
ejpam-4200	205	20	·	·	PUNCT
ejpam-4200	205	21	)	)	PUNCT
ejpam-4200	205	22	t	t	NOUN
ejpam-4200	205	23	)	)	PUNCT
ejpam-4200	205	24	.	.	PUNCT
ejpam-4200	206	1	with	with	ADP
ejpam-4200	206	2	t	t	PROPN
ejpam-4200	206	3	∈	∈	PROPN
ejpam-4200	206	4	(	(	PUNCT
ejpam-4200	206	5	0,min	0,min	NUM
ejpam-4200	206	6	{	{	PUNCT
ejpam-4200	206	7	1	1	NUM
ejpam-4200	206	8	,	,	PUNCT
ejpam-4200	206	9	p−	p−	NOUN
ejpam-4200	206	10	,	,	PUNCT
ejpam-4200	206	11	q−	q−	PROPN
ejpam-4200	206	12	}	}	PUNCT
ejpam-4200	206	13	)	)	PUNCT
ejpam-4200	206	14	,	,	PUNCT
ejpam-4200	206	15	lemma	lemma	PROPN
ejpam-4200	206	16	4	4	NUM
ejpam-4200	206	17	yields∥∥∥∥∥∥	yields∥∥∥∥∥∥	PROPN
ejpam-4200	206	18	2js	2js	PROPN
ejpam-4200	206	19	(	(	PUNCT
ejpam-4200	206	20	·	·	PUNCT
ejpam-4200	206	21	)	)	PUNCT
ejpam-4200	206	22	j+n2∑	j+n2∑	PROPN
ejpam-4200	207	1	k	k	NOUN
ejpam-4200	207	2	=	=	NOUN
ejpam-4200	207	3	j−n1	j−n1	NOUN
ejpam-4200	207	4	ψ̌j	ψ̌j	NOUN
ejpam-4200	207	5	∗	∗	NOUN
ejpam-4200	207	6	fk	fk	INTJ
ejpam-4200	208	1			PROPN
ejpam-4200	208	2	j≥n1	j≥n1	PROPN
ejpam-4200	208	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	209	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	209	2	(	(	PUNCT
ejpam-4200	209	3	·	·	PUNCT
ejpam-4200	209	4	)	)	PUNCT
ejpam-4200	209	5	)	)	PUNCT
ejpam-4200	210	1	≲	≲	PROPN
ejpam-4200	210	2	n1+n2∑	n1+n2∑	ADJ
ejpam-4200	210	3	k=0	k=0	PROPN
ejpam-4200	210	4	∥∥∥∥(2js(·)t|fj+k−n1	∥∥∥∥(2js(·)t|fj+k−n1	NUM
ejpam-4200	210	5	|t	|t	NOUN
ejpam-4200	210	6	)	)	PUNCT
ejpam-4200	210	7	j	j	PROPN
ejpam-4200	210	8	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4200	210	9	m	m	VERB
ejpam-4200	210	10	p	p	X
ejpam-4200	210	11	(	(	PUNCT
ejpam-4200	210	12	·	·	PUNCT
ejpam-4200	210	13	)	)	PUNCT
ejpam-4200	210	14	t	t	PROPN
ejpam-4200	210	15	,	,	PUNCT
ejpam-4200	210	16	u	u	NOUN
ejpam-4200	210	17	(	(	PUNCT
ejpam-4200	210	18	·	·	PUNCT
ejpam-4200	210	19	)	)	PUNCT
ejpam-4200	210	20	t	t	PROPN
ejpam-4200	210	21	(	(	PUNCT
ejpam-4200	210	22	ℓ	ℓ	INTJ
ejpam-4200	210	23	q	q	PROPN
ejpam-4200	210	24	(	(	PUNCT
ejpam-4200	210	25	·	·	PUNCT
ejpam-4200	210	26	)	)	PUNCT
ejpam-4200	210	27	t	t	NOUN
ejpam-4200	210	28	)	)	PUNCT
ejpam-4200	210	29	.	.	PUNCT
ejpam-4200	211	1	then	then	ADV
ejpam-4200	211	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	212	1	2js	2js	PROPN
ejpam-4200	212	2	(	(	PUNCT
ejpam-4200	212	3	·	·	PUNCT
ejpam-4200	212	4	)	)	PUNCT
ejpam-4200	212	5	j+n2∑	j+n2∑	PROPN
ejpam-4200	213	1	k	k	NOUN
ejpam-4200	213	2	=	=	NOUN
ejpam-4200	213	3	j−n1	j−n1	NOUN
ejpam-4200	213	4	ψ̌j	ψ̌j	NOUN
ejpam-4200	213	5	∗	∗	NOUN
ejpam-4200	213	6	fk	fk	INTJ
ejpam-4200	214	1			PROPN
ejpam-4200	214	2	j≥1	j≥1	PROPN
ejpam-4200	214	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	215	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	215	2	(	(	PUNCT
ejpam-4200	215	3	·	·	PUNCT
ejpam-4200	215	4	)	)	PUNCT
ejpam-4200	215	5	)	)	PUNCT
ejpam-4200	216	1	≲	≲	PROPN
ejpam-4200	216	2	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4200	216	3	)	)	PUNCT
ejpam-4200	216	4	k	k	PROPN
ejpam-4200	216	5	∥∥∥	∥∥∥	PROPN
ejpam-4200	216	6	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	216	7	(	(	PUNCT
ejpam-4200	216	8	·	·	PUNCT
ejpam-4200	216	9	)	)	PUNCT
ejpam-4200	216	10	)	)	PUNCT
ejpam-4200	216	11	.	.	PUNCT
ejpam-4200	217	1	•	•	INTJ
ejpam-4200	217	2	now	now	ADV
ejpam-4200	217	3	we	we	PRON
ejpam-4200	217	4	estimate	estimate	VERB
ejpam-4200	217	5	the	the	DET
ejpam-4200	217	6	first	first	ADJ
ejpam-4200	217	7	term	term	NOUN
ejpam-4200	217	8	.	.	PUNCT
ejpam-4200	218	1	since	since	SCONJ
ejpam-4200	218	2	suppf	suppf	PROPN
ejpam-4200	218	3	(	(	PUNCT
ejpam-4200	218	4	ψ̌0	ψ̌0	X
ejpam-4200	218	5	∗	∗	PROPN
ejpam-4200	218	6	fk	fk	INTJ
ejpam-4200	218	7	)	)	PUNCT
ejpam-4200	218	8	⊂	⊂	PRON
ejpam-4200	218	9	{	{	PUNCT
ejpam-4200	218	10	ξ	ξ	PROPN
ejpam-4200	218	11	∈	∈	PROPN
ejpam-4200	218	12	rn	rn	PROPN
ejpam-4200	218	13	:	:	PUNCT
ejpam-4200	218	14	|ξ|	|ξ|	VERB
ejpam-4200	218	15	≤	≤	ADJ
ejpam-4200	218	16	2	2	NUM
ejpam-4200	218	17	}	}	PUNCT
ejpam-4200	218	18	,	,	PUNCT
ejpam-4200	218	19	then	then	ADV
ejpam-4200	218	20	by	by	ADP
ejpam-4200	218	21	lemma	lemma	PROPN
ejpam-4200	218	22	2	2	NUM
ejpam-4200	218	23	,	,	PUNCT
ejpam-4200	218	24	∣∣ψ̌0	∣∣ψ̌0	NOUN
ejpam-4200	218	25	∗	∗	NOUN
ejpam-4200	218	26	fk	fk	X
ejpam-4200	218	27	∣∣	∣∣	NUM
ejpam-4200	218	28	≲	≲	PROPN
ejpam-4200	218	29	|fk|	|fk|	PROPN
ejpam-4200	218	30	.	.	PUNCT
ejpam-4200	219	1	thus	thus	ADV
ejpam-4200	219	2	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-4200	219	3	n1∑	n1∑	PROPN
ejpam-4200	219	4	k=0	k=0	PROPN
ejpam-4200	219	5	ψ̌0	ψ̌0	PROPN
ejpam-4200	219	6	∗	∗	PROPN
ejpam-4200	219	7	fk	fk	INTJ
ejpam-4200	219	8	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	219	9	mp(·),u	mp(·),u	PROPN
ejpam-4200	219	10	(	(	PUNCT
ejpam-4200	219	11	·	·	PUNCT
ejpam-4200	219	12	)	)	PUNCT
ejpam-4200	220	1	≲	≲	PROPN
ejpam-4200	220	2	n1∑	n1∑	PROPN
ejpam-4200	220	3	k=0	k=0	PROPN
ejpam-4200	220	4	∥fk∥mp(·),u	∥fk∥mp(·),u	PROPN
ejpam-4200	220	5	(	(	PUNCT
ejpam-4200	220	6	·	·	PUNCT
ejpam-4200	220	7	)	)	PUNCT
ejpam-4200	220	8	=	=	SYM
ejpam-4200	221	1	n1∑	n1∑	PROPN
ejpam-4200	221	2	k=0	k=0	PROPN
ejpam-4200	221	3	∥(0	∥(0	VERB
ejpam-4200	221	4	,	,	PUNCT
ejpam-4200	221	5	.	.	PUNCT
ejpam-4200	221	6	.	.	PUNCT
ejpam-4200	221	7	.	.	PUNCT
ejpam-4200	222	1	,	,	PUNCT
ejpam-4200	222	2	fk	fk	INTJ
ejpam-4200	222	3	,	,	PUNCT
ejpam-4200	222	4	0	0	NUM
ejpam-4200	222	5	,	,	PUNCT
ejpam-4200	222	6	.	.	PUNCT
ejpam-4200	222	7	.	.	PUNCT
ejpam-4200	223	1	.)∥ℓq(·)(mp(·),u	.)∥ℓq(·)(mp(·),u	PROPN
ejpam-4200	223	2	(	(	PUNCT
ejpam-4200	223	3	·	·	PUNCT
ejpam-4200	223	4	)	)	PUNCT
ejpam-4200	223	5	)	)	PUNCT
ejpam-4200	223	6	m.	m.	NOUN
ejpam-4200	223	7	congo	congo	PROPN
ejpam-4200	223	8	,	,	PUNCT
ejpam-4200	223	9	m.	m.	PROPN
ejpam-4200	223	10	f.	f.	PROPN
ejpam-4200	223	11	ouedraogo	ouedraogo	PROPN
ejpam-4200	223	12	/	/	SYM
ejpam-4200	223	13	eur	eur	PROPN
ejpam-4200	223	14	.	.	PUNCT
ejpam-4200	224	1	j.	j.	PROPN
ejpam-4200	224	2	pure	pure	PROPN
ejpam-4200	224	3	appl	appl	PROPN
ejpam-4200	224	4	.	.	PROPN
ejpam-4200	224	5	math	math	PROPN
ejpam-4200	224	6	,	,	PUNCT
ejpam-4200	224	7	15	15	NUM
ejpam-4200	224	8	(	(	PUNCT
ejpam-4200	224	9	1	1	NUM
ejpam-4200	224	10	)	)	PUNCT
ejpam-4200	224	11	(	(	PUNCT
ejpam-4200	224	12	2022	2022	NUM
ejpam-4200	224	13	)	)	PUNCT
ejpam-4200	224	14	,	,	PUNCT
ejpam-4200	224	15	47	47	NUM
ejpam-4200	224	16	-	-	SYM
ejpam-4200	224	17	63	63	NUM
ejpam-4200	224	18	55	55	NUM
ejpam-4200	224	19	≲	≲	PROPN
ejpam-4200	224	20	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	PROPN
ejpam-4200	224	21	)	)	PUNCT
ejpam-4200	224	22	k	k	PROPN
ejpam-4200	224	23	∥∥∥	∥∥∥	PROPN
ejpam-4200	224	24	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4200	224	25	(	(	PUNCT
ejpam-4200	224	26	·	·	PUNCT
ejpam-4200	224	27	)	)	PUNCT
ejpam-4200	224	28	)	)	PUNCT
ejpam-4200	224	29	.	.	PUNCT
ejpam-4200	225	1	the	the	DET
ejpam-4200	225	2	proof	proof	NOUN
ejpam-4200	225	3	is	be	AUX
ejpam-4200	225	4	completed	complete	VERB
ejpam-4200	225	5	.	.	PUNCT
ejpam-4200	226	1	□	□	PUNCT
ejpam-4200	226	2	lemma	lemma	PROPN
ejpam-4200	226	3	8	8	NUM
ejpam-4200	226	4	.	.	PUNCT
ejpam-4200	227	1	let	let	VERB
ejpam-4200	227	2	c	c	PROPN
ejpam-4200	227	3	>	>	X
ejpam-4200	227	4	0	0	NUM
ejpam-4200	227	5	,	,	PUNCT
ejpam-4200	227	6	s	s	VERB
ejpam-4200	227	7	∈	∈	PROPN
ejpam-4200	227	8	c	c	PROPN
ejpam-4200	227	9	log	log	PROPN
ejpam-4200	227	10	loc	loc	PROPN
ejpam-4200	227	11	,	,	PUNCT
ejpam-4200	227	12	p	p	X
ejpam-4200	227	13	,	,	PUNCT
ejpam-4200	227	14	q	q	PROPN
ejpam-4200	227	15	∈	∈	PROPN
ejpam-4200	227	16	p	p	NOUN
ejpam-4200	227	17	log(rn	log(rn	PROPN
ejpam-4200	227	18	)	)	PUNCT
ejpam-4200	227	19	and	and	CCONJ
ejpam-4200	227	20	u	u	PROPN
ejpam-4200	227	21	∈	∈	PROPN
ejpam-4200	227	22	p(rn	p(rn	PROPN
ejpam-4200	227	23	)	)	PUNCT
ejpam-4200	227	24	such	such	ADJ
ejpam-4200	227	25	that	that	SCONJ
ejpam-4200	227	26	0	0	NUM
ejpam-4200	227	27	<	<	X
ejpam-4200	227	28	p−	p−	NOUN
ejpam-4200	227	29	≤	≤	NUM
ejpam-4200	227	30	p(x	p(x	PROPN
ejpam-4200	227	31	)	)	PUNCT
ejpam-4200	227	32	≤	≤	NUM
ejpam-4200	227	33	u(x	u(x	NOUN
ejpam-4200	227	34	)	)	PUNCT
ejpam-4200	227	35	≤	≤	NOUN
ejpam-4200	227	36	supu	supu	NOUN
ejpam-4200	227	37	<	<	X
ejpam-4200	227	38	+	+	PROPN
ejpam-4200	227	39	∞	∞	PROPN
ejpam-4200	227	40	,	,	PUNCT
ejpam-4200	227	41	s−	s−	PROPN
ejpam-4200	227	42	>	>	X
ejpam-4200	227	43	0	0	PUNCT
ejpam-4200	227	44	and	and	CCONJ
ejpam-4200	227	45	q−	q−	PROPN
ejpam-4200	227	46	,	,	PUNCT
ejpam-4200	227	47	q+	q+	NOUN
ejpam-4200	227	48	∈	∈	PROPN
ejpam-4200	227	49	(	(	PUNCT
ejpam-4200	227	50	0,+∞	0,+∞	NUM
ejpam-4200	227	51	)	)	PUNCT
ejpam-4200	227	52	.	.	PUNCT
ejpam-4200	228	1	let	let	VERB
ejpam-4200	228	2	{	{	PUNCT
ejpam-4200	228	3	fk}k∈n0	fk}k∈n0	INTJ
ejpam-4200	228	4	be	be	AUX
ejpam-4200	228	5	a	a	DET
ejpam-4200	228	6	sequence	sequence	NOUN
ejpam-4200	228	7	of	of	ADP
ejpam-4200	228	8	tempered	temper	VERB
ejpam-4200	228	9	distributions	distribution	NOUN
ejpam-4200	228	10	such	such	ADJ
ejpam-4200	228	11	that	that	PRON
ejpam-4200	228	12	suppffk	suppffk	VERB
ejpam-4200	228	13	⊂	⊂	PROPN
ejpam-4200	228	14	b(0	b(0	PROPN
ejpam-4200	228	15	,	,	PUNCT
ejpam-4200	228	16	c2k+1	c2k+1	NOUN
ejpam-4200	228	17	)	)	PUNCT
ejpam-4200	228	18	then	then	ADV
ejpam-4200	228	19	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-4200	229	1	+	+	PUNCT
ejpam-4200	229	2	∞∑	∞∑	ADJ
ejpam-4200	229	3	k=0	k=0	PROPN
ejpam-4200	229	4	fk	fk	INTJ
ejpam-4200	229	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	229	6	es	es	SYM
ejpam-4200	229	7	(	(	PUNCT
ejpam-4200	229	8	·	·	PUNCT
ejpam-4200	229	9	)	)	PUNCT
ejpam-4200	229	10	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	229	11	(	(	PUNCT
ejpam-4200	229	12	·	·	PUNCT
ejpam-4200	229	13	)	)	PUNCT
ejpam-4200	230	1	≲	≲	PROPN
ejpam-4200	230	2	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4200	230	3	)	)	PUNCT
ejpam-4200	230	4	k	k	PROPN
ejpam-4200	230	5	∥∥∥	∥∥∥	PROPN
ejpam-4200	230	6	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	230	7	(	(	PUNCT
ejpam-4200	230	8	·	·	PUNCT
ejpam-4200	230	9	)	)	PUNCT
ejpam-4200	230	10	)	)	PUNCT
ejpam-4200	230	11	proof	proof	NOUN
ejpam-4200	230	12	.	.	PUNCT
ejpam-4200	231	1	in	in	ADP
ejpam-4200	231	2	view	view	NOUN
ejpam-4200	231	3	of	of	ADP
ejpam-4200	231	4	the	the	DET
ejpam-4200	231	5	hypothesis	hypothesis	NOUN
ejpam-4200	231	6	on	on	ADP
ejpam-4200	231	7	suppψj	suppψj	PROPN
ejpam-4200	231	8	,	,	PUNCT
ejpam-4200	231	9	there	there	PRON
ejpam-4200	231	10	is	be	VERB
ejpam-4200	231	11	n	n	DET
ejpam-4200	231	12	∈	∈	PROPN
ejpam-4200	231	13	n0	n0	NOUN
ejpam-4200	231	14	such	such	ADJ
ejpam-4200	231	15	that∥∥∥∥∥	that∥∥∥∥∥	PROPN
ejpam-4200	231	16	+	+	PROPN
ejpam-4200	231	17	∞∑	∞∑	PROPN
ejpam-4200	231	18	k=0	k=0	PROPN
ejpam-4200	231	19	fk	fk	INTJ
ejpam-4200	231	20	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	231	21	es	es	SYM
ejpam-4200	231	22	(	(	PUNCT
ejpam-4200	231	23	·	·	PUNCT
ejpam-4200	231	24	)	)	PUNCT
ejpam-4200	231	25	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	231	26	(	(	PUNCT
ejpam-4200	231	27	·	·	PUNCT
ejpam-4200	231	28	)	)	PUNCT
ejpam-4200	231	29	=	=	SYM
ejpam-4200	231	30	∥∥∥∥∥ψ0(d	∥∥∥∥∥ψ0(d	X
ejpam-4200	231	31	)	)	PUNCT
ejpam-4200	231	32	(	(	PUNCT
ejpam-4200	232	1	+	+	ADP
ejpam-4200	232	2	∞∑	∞∑	ADJ
ejpam-4200	232	3	k=0	k=0	PROPN
ejpam-4200	232	4	fk	fk	INTJ
ejpam-4200	232	5	)	)	PUNCT
ejpam-4200	232	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	232	7	mp(·),u	mp(·),u	PROPN
ejpam-4200	232	8	(	(	PUNCT
ejpam-4200	232	9	·	·	PUNCT
ejpam-4200	232	10	)	)	PUNCT
ejpam-4200	233	1	+	+	NUM
ejpam-4200	233	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	233	3	2js(·)ψj(d	2js(·)ψj(d	ADV
ejpam-4200	233	4	)	)	PUNCT
ejpam-4200	234	1			PROPN
ejpam-4200	234	2	+	+	PROPN
ejpam-4200	234	3	∞∑	∞∑	PROPN
ejpam-4200	234	4	k	k	X
ejpam-4200	234	5	=	=	ADJ
ejpam-4200	234	6	j−n	j−n	PROPN
ejpam-4200	234	7	fk	fk	INTJ
ejpam-4200	234	8			NOUN
ejpam-4200	235	1	j≥n	j≥n	PROPN
ejpam-4200	236	1	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	237	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	237	2	(	(	PUNCT
ejpam-4200	237	3	·	·	PUNCT
ejpam-4200	237	4	)	)	PUNCT
ejpam-4200	237	5	)	)	PUNCT
ejpam-4200	237	6	.	.	PUNCT
ejpam-4200	238	1	(	(	PUNCT
ejpam-4200	238	2	8)	8)	NUM
ejpam-4200	238	3	(	(	PUNCT
ejpam-4200	238	4	i	i	NOUN
ejpam-4200	238	5	)	)	PUNCT
ejpam-4200	238	6	at	at	ADP
ejpam-4200	238	7	first	first	ADV
ejpam-4200	238	8	we	we	PRON
ejpam-4200	238	9	estimate	estimate	VERB
ejpam-4200	238	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	239	1	2js(·)ψj(d	2js(·)ψj(d	ADV
ejpam-4200	239	2	)	)	PUNCT
ejpam-4200	240	1			PROPN
ejpam-4200	240	2	+	+	PROPN
ejpam-4200	240	3	∞∑	∞∑	PROPN
ejpam-4200	240	4	k	k	X
ejpam-4200	240	5	=	=	ADJ
ejpam-4200	240	6	j−n	j−n	PROPN
ejpam-4200	240	7	fk	fk	NOUN
ejpam-4200	240	8			NOUN
ejpam-4200	241	1	j	j	PROPN
ejpam-4200	241	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	241	3	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	241	4	(	(	PUNCT
ejpam-4200	241	5	·	·	PUNCT
ejpam-4200	241	6	)	)	PUNCT
ejpam-4200	241	7	)	)	PUNCT
ejpam-4200	241	8	.	.	PUNCT
ejpam-4200	242	1	we	we	PRON
ejpam-4200	242	2	have∥∥∥∥∥∥	have∥∥∥∥∥∥	VERB
ejpam-4200	242	3	2js(·)ψj(d	2js(·)ψj(d	ADV
ejpam-4200	242	4	)	)	PUNCT
ejpam-4200	243	1			PROPN
ejpam-4200	243	2	+	+	PROPN
ejpam-4200	243	3	∞∑	∞∑	PROPN
ejpam-4200	243	4	k	k	X
ejpam-4200	243	5	=	=	ADJ
ejpam-4200	243	6	j−n	j−n	PROPN
ejpam-4200	243	7	fk	fk	INTJ
ejpam-4200	243	8			NOUN
ejpam-4200	243	9	j≥n	j≥n	PROPN
ejpam-4200	243	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	244	1	ℓq(·)(mp(·),u	ℓq(·)(mp(·),u	PROPN
ejpam-4200	244	2	(	(	PUNCT
ejpam-4200	244	3	·	·	PUNCT
ejpam-4200	244	4	)	)	PUNCT
ejpam-4200	244	5	)	)	PUNCT
ejpam-4200	245	1	=	=	SYM
ejpam-4200	245	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	245	3			PUNCT
ejpam-4200	246	1	+	+	ADJ
ejpam-4200	246	2	∞∑	∞∑	ADJ
ejpam-4200	246	3	k	k	X
ejpam-4200	246	4	=	=	PROPN
ejpam-4200	246	5	j−n	j−n	ADJ
ejpam-4200	246	6	2js	2js	NOUN
ejpam-4200	246	7	(	(	PUNCT
ejpam-4200	246	8	·	·	PUNCT
ejpam-4200	246	9	)	)	PUNCT
ejpam-4200	246	10	(	(	PUNCT
ejpam-4200	246	11	ψ̌j	ψ̌j	PROPN
ejpam-4200	246	12	∗	∗	NOUN
ejpam-4200	246	13	fk	fk	INTJ
ejpam-4200	246	14	)	)	PUNCT
ejpam-4200	247	1			ADP
ejpam-4200	247	2	j	j	PROPN
ejpam-4200	247	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	247	4	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	247	5	(	(	PUNCT
ejpam-4200	247	6	·	·	PUNCT
ejpam-4200	247	7	)	)	PUNCT
ejpam-4200	247	8	)	)	PUNCT
ejpam-4200	247	9	since	since	SCONJ
ejpam-4200	247	10	{	{	PUNCT
ejpam-4200	247	11	suppf	suppf	NOUN
ejpam-4200	247	12	(	(	PUNCT
ejpam-4200	247	13	ψ̌j	ψ̌j	PROPN
ejpam-4200	247	14	∗	∗	NOUN
ejpam-4200	247	15	fk	fk	INTJ
ejpam-4200	247	16	)	)	PUNCT
ejpam-4200	247	17	⊂	⊂	PROPN
ejpam-4200	247	18	{	{	PUNCT
ejpam-4200	247	19	ξ	ξ	X
ejpam-4200	247	20	∈	∈	PROPN
ejpam-4200	247	21	rn	rn	PROPN
ejpam-4200	247	22	:	:	PUNCT
ejpam-4200	247	23	|ξ|	|ξ|	VERB
ejpam-4200	247	24	≤	≤	ADJ
ejpam-4200	247	25	2j+1	2j+1	PROPN
ejpam-4200	247	26	}	}	PUNCT
ejpam-4200	247	27	suppf	suppf	NOUN
ejpam-4200	247	28	(	(	PUNCT
ejpam-4200	247	29	ψ̌j	ψ̌j	PROPN
ejpam-4200	247	30	∗	∗	NOUN
ejpam-4200	247	31	fk	fk	INTJ
ejpam-4200	247	32	)	)	PUNCT
ejpam-4200	248	1	⊂	⊂	PROPN
ejpam-4200	248	2	{	{	PUNCT
ejpam-4200	248	3	ξ	ξ	X
ejpam-4200	248	4	∈	∈	PROPN
ejpam-4200	248	5	rn	rn	PROPN
ejpam-4200	248	6	:	:	PUNCT
ejpam-4200	248	7	|ξ|	|ξ|	VERB
ejpam-4200	248	8	≤	≤	NOUN
ejpam-4200	248	9	2k+1	2k+1	PROPN
ejpam-4200	248	10	}	}	PUNCT
ejpam-4200	248	11	,	,	PUNCT
ejpam-4200	248	12	by	by	ADP
ejpam-4200	248	13	lemma	lemma	PROPN
ejpam-4200	248	14	2	2	NUM
ejpam-4200	248	15	,	,	PUNCT
ejpam-4200	248	16	{	{	PUNCT
ejpam-4200	248	17	2js	2js	ADJ
ejpam-4200	248	18	(	(	PUNCT
ejpam-4200	248	19	·	·	PUNCT
ejpam-4200	248	20	)	)	PUNCT
ejpam-4200	248	21	(	(	PUNCT
ejpam-4200	248	22	ψ̌j	ψ̌j	PROPN
ejpam-4200	248	23	∗	∗	NOUN
ejpam-4200	248	24	fk	fk	INTJ
ejpam-4200	248	25	)	)	PUNCT
ejpam-4200	249	1	≲	≲	PROPN
ejpam-4200	249	2	2js	2js	NOUN
ejpam-4200	249	3	(	(	PUNCT
ejpam-4200	249	4	·	·	PUNCT
ejpam-4200	249	5	)	)	PUNCT
ejpam-4200	249	6	(	(	PUNCT
ejpam-4200	249	7	ηj	ηj	NOUN
ejpam-4200	249	8	,	,	PUNCT
ejpam-4200	249	9	m	m	NOUN
ejpam-4200	249	10	∗	∗	NOUN
ejpam-4200	249	11	|fk|t	|fk|t	PROPN
ejpam-4200	249	12	)	)	PUNCT
ejpam-4200	249	13	1	1	NUM
ejpam-4200	249	14	/	/	SYM
ejpam-4200	249	15	t	t	NOUN
ejpam-4200	249	16	2js	2js	NOUN
ejpam-4200	249	17	(	(	PUNCT
ejpam-4200	249	18	·	·	PUNCT
ejpam-4200	249	19	)	)	PUNCT
ejpam-4200	249	20	(	(	PUNCT
ejpam-4200	249	21	ψ̌j	ψ̌j	PROPN
ejpam-4200	249	22	∗	∗	NOUN
ejpam-4200	249	23	fk	fk	INTJ
ejpam-4200	249	24	)	)	PUNCT
ejpam-4200	249	25	≲	≲	PROPN
ejpam-4200	249	26	2js	2js	NOUN
ejpam-4200	249	27	(	(	PUNCT
ejpam-4200	249	28	·	·	PUNCT
ejpam-4200	249	29	)	)	PUNCT
ejpam-4200	249	30	(	(	PUNCT
ejpam-4200	249	31	ηk	ηk	PROPN
ejpam-4200	249	32	,	,	PUNCT
ejpam-4200	249	33	m	m	NOUN
ejpam-4200	249	34	∗	∗	NOUN
ejpam-4200	249	35	|fk|t	|fk|t	PROPN
ejpam-4200	249	36	)	)	PUNCT
ejpam-4200	249	37	1	1	NUM
ejpam-4200	249	38	/	/	SYM
ejpam-4200	249	39	t	t	NOUN
ejpam-4200	249	40	.	.	PUNCT
ejpam-4200	250	1	for	for	ADP
ejpam-4200	250	2	m	m	PROPN
ejpam-4200	250	3	>	>	X
ejpam-4200	250	4	n+	n+	PUNCT
ejpam-4200	250	5	clog(1	clog(1	NOUN
ejpam-4200	250	6	/	/	SYM
ejpam-4200	250	7	q	q	NOUN
ejpam-4200	250	8	)	)	PUNCT
ejpam-4200	250	9	+	+	NUM
ejpam-4200	250	10	clog(s	clog(s	NOUN
ejpam-4200	250	11	)	)	PUNCT
ejpam-4200	250	12	+	+	CCONJ
ejpam-4200	250	13	nmax	nmax	ADJ
ejpam-4200	250	14	{	{	PUNCT
ejpam-4200	250	15	0	0	NUM
ejpam-4200	250	16	,	,	PUNCT
ejpam-4200	250	17	supx∈rn	supx∈rn	PUNCT
ejpam-4200	250	18	(	(	PUNCT
ejpam-4200	250	19	1	1	NUM
ejpam-4200	250	20	p(x	p(x	NOUN
ejpam-4200	250	21	)	)	PUNCT
ejpam-4200	250	22	−	−	PROPN
ejpam-4200	250	23	1	1	NUM
ejpam-4200	250	24	u(x	u(x	NOUN
ejpam-4200	250	25	)	)	PUNCT
ejpam-4200	250	26	)	)	PUNCT
ejpam-4200	250	27	−	−	PROPN
ejpam-4200	250	28	1	1	NUM
ejpam-4200	250	29	p∞	p∞	PROPN
ejpam-4200	250	30	}	}	PUNCT
ejpam-4200	250	31	and	and	CCONJ
ejpam-4200	250	32	t	t	X
ejpam-4200	250	33	>	>	X
ejpam-4200	250	34	0	0	PUNCT
ejpam-4200	250	35	.	.	PUNCT
ejpam-4200	251	1	therefore∥∥∥∥∥∥	therefore∥∥∥∥∥∥	VERB
ejpam-4200	251	2	2js(·)ψj(d	2js(·)ψj(d	ADV
ejpam-4200	251	3	)	)	PUNCT
ejpam-4200	252	1			PROPN
ejpam-4200	252	2	+	+	PROPN
ejpam-4200	252	3	∞∑	∞∑	PROPN
ejpam-4200	252	4	k	k	X
ejpam-4200	252	5	=	=	ADJ
ejpam-4200	252	6	j−n	j−n	PROPN
ejpam-4200	252	7	fk	fk	INTJ
ejpam-4200	252	8			NOUN
ejpam-4200	253	1	j≥n	j≥n	PROPN
ejpam-4200	253	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	254	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	254	2	(	(	PUNCT
ejpam-4200	254	3	·	·	PUNCT
ejpam-4200	254	4	)	)	PUNCT
ejpam-4200	254	5	)	)	PUNCT
ejpam-4200	255	1	≲	≲	PROPN
ejpam-4200	255	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	255	3			PUNCT
ejpam-4200	255	4	j∑	j∑	PROPN
ejpam-4200	255	5	k	k	X
ejpam-4200	255	6	=	=	PROPN
ejpam-4200	255	7	j−n	j−n	ADJ
ejpam-4200	255	8	2js	2js	NOUN
ejpam-4200	255	9	(	(	PUNCT
ejpam-4200	255	10	·	·	PUNCT
ejpam-4200	255	11	)	)	PUNCT
ejpam-4200	255	12	(	(	PUNCT
ejpam-4200	255	13	ηj	ηj	NOUN
ejpam-4200	255	14	,	,	PUNCT
ejpam-4200	255	15	m	m	NOUN
ejpam-4200	255	16	∗	∗	NOUN
ejpam-4200	255	17	|fk|t	|fk|t	PROPN
ejpam-4200	255	18	)	)	PUNCT
ejpam-4200	255	19	1	1	NUM
ejpam-4200	255	20	/	/	SYM
ejpam-4200	255	21	t	t	NUM
ejpam-4200	255	22	j	j	PROPN
ejpam-4200	255	23	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	256	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	256	2	(	(	PUNCT
ejpam-4200	256	3	·	·	PUNCT
ejpam-4200	256	4	)	)	PUNCT
ejpam-4200	256	5	)	)	PUNCT
ejpam-4200	256	6	m.	m.	NOUN
ejpam-4200	256	7	congo	congo	PROPN
ejpam-4200	256	8	,	,	PUNCT
ejpam-4200	256	9	m.	m.	PROPN
ejpam-4200	256	10	f.	f.	PROPN
ejpam-4200	256	11	ouedraogo	ouedraogo	PROPN
ejpam-4200	256	12	/	/	SYM
ejpam-4200	256	13	eur	eur	PROPN
ejpam-4200	256	14	.	.	PUNCT
ejpam-4200	257	1	j.	j.	PROPN
ejpam-4200	257	2	pure	pure	PROPN
ejpam-4200	257	3	appl	appl	PROPN
ejpam-4200	257	4	.	.	PROPN
ejpam-4200	257	5	math	math	PROPN
ejpam-4200	257	6	,	,	PUNCT
ejpam-4200	257	7	15	15	NUM
ejpam-4200	257	8	(	(	PUNCT
ejpam-4200	257	9	1	1	NUM
ejpam-4200	257	10	)	)	PUNCT
ejpam-4200	257	11	(	(	PUNCT
ejpam-4200	257	12	2022	2022	NUM
ejpam-4200	257	13	)	)	PUNCT
ejpam-4200	257	14	,	,	PUNCT
ejpam-4200	257	15	47	47	NUM
ejpam-4200	257	16	-	-	SYM
ejpam-4200	257	17	63	63	NUM
ejpam-4200	257	18	56	56	NUM
ejpam-4200	257	19	+	+	CCONJ
ejpam-4200	257	20	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	257	21			PUNCT
ejpam-4200	258	1	+	+	ADJ
ejpam-4200	258	2	∞∑	∞∑	ADJ
ejpam-4200	258	3	k	k	X
ejpam-4200	258	4	=	=	NOUN
ejpam-4200	258	5	j+1	j+1	ADJ
ejpam-4200	258	6	2−(k−j)s(·)2ks	2−(k−j)s(·)2ks	NUM
ejpam-4200	258	7	(	(	PUNCT
ejpam-4200	258	8	·	·	PUNCT
ejpam-4200	258	9	)	)	PUNCT
ejpam-4200	258	10	(	(	PUNCT
ejpam-4200	258	11	ηk	ηk	PROPN
ejpam-4200	258	12	,	,	PUNCT
ejpam-4200	258	13	m	m	NOUN
ejpam-4200	258	14	∗	∗	NOUN
ejpam-4200	258	15	|fk|t	|fk|t	PROPN
ejpam-4200	258	16	)	)	PUNCT
ejpam-4200	258	17	1	1	NUM
ejpam-4200	258	18	/	/	SYM
ejpam-4200	258	19	t	t	NUM
ejpam-4200	258	20	j	j	PROPN
ejpam-4200	258	21	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	259	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	259	2	(	(	PUNCT
ejpam-4200	259	3	·	·	PUNCT
ejpam-4200	259	4	)	)	PUNCT
ejpam-4200	259	5	)	)	PUNCT
ejpam-4200	259	6	let	let	VERB
ejpam-4200	259	7	us	we	PRON
ejpam-4200	259	8	estimate	estimate	VERB
ejpam-4200	259	9	each	each	DET
ejpam-4200	259	10	one	one	NUM
ejpam-4200	259	11	of	of	ADP
ejpam-4200	259	12	the	the	DET
ejpam-4200	259	13	two	two	NUM
ejpam-4200	259	14	terms	term	NOUN
ejpam-4200	259	15	on	on	ADP
ejpam-4200	259	16	the	the	DET
ejpam-4200	259	17	right	right	ADJ
ejpam-4200	259	18	-	-	PUNCT
ejpam-4200	259	19	hand	hand	NOUN
ejpam-4200	259	20	side	side	NOUN
ejpam-4200	259	21	.	.	PUNCT
ejpam-4200	260	1	using	use	VERB
ejpam-4200	260	2	lemmas	lemmas	PROPN
ejpam-4200	260	3	1	1	NUM
ejpam-4200	260	4	we	we	PRON
ejpam-4200	260	5	can	can	AUX
ejpam-4200	260	6	move	move	VERB
ejpam-4200	260	7	2νs	2νs	ADJ
ejpam-4200	260	8	(	(	PUNCT
ejpam-4200	260	9	·	·	PUNCT
ejpam-4200	260	10	)	)	PUNCT
ejpam-4200	260	11	inside	inside	ADP
ejpam-4200	260	12	the	the	DET
ejpam-4200	260	13	convolution	convolution	NOUN
ejpam-4200	260	14	2νs	2νs	NOUN
ejpam-4200	260	15	(	(	PUNCT
ejpam-4200	260	16	·	·	PUNCT
ejpam-4200	260	17	)	)	PUNCT
ejpam-4200	260	18	(	(	PUNCT
ejpam-4200	260	19	ην	ην	NOUN
ejpam-4200	260	20	,	,	PUNCT
ejpam-4200	260	21	m	m	NOUN
ejpam-4200	260	22	∗	∗	NOUN
ejpam-4200	260	23	|fk|t	|fk|t	PROPN
ejpam-4200	260	24	)	)	PUNCT
ejpam-4200	260	25	1	1	NUM
ejpam-4200	260	26	/	/	SYM
ejpam-4200	260	27	t	t	NOUN
ejpam-4200	260	28	.	.	PUNCT
ejpam-4200	261	1	and	and	CCONJ
ejpam-4200	261	2	we	we	PRON
ejpam-4200	261	3	have	have	VERB
ejpam-4200	261	4	2νs	2νs	ADJ
ejpam-4200	261	5	(	(	PUNCT
ejpam-4200	261	6	·	·	PUNCT
ejpam-4200	261	7	)	)	PUNCT
ejpam-4200	261	8	(	(	PUNCT
ejpam-4200	261	9	ην	ην	NOUN
ejpam-4200	261	10	,	,	PUNCT
ejpam-4200	261	11	m	m	NOUN
ejpam-4200	261	12	∗	∗	NOUN
ejpam-4200	261	13	|fk|t	|fk|t	PROPN
ejpam-4200	261	14	)	)	PUNCT
ejpam-4200	261	15	1	1	NUM
ejpam-4200	261	16	/	/	SYM
ejpam-4200	261	17	t	t	NOUN
ejpam-4200	262	1	≲	≲	PROPN
ejpam-4200	262	2	(	(	PUNCT
ejpam-4200	262	3	ην	ην	NOUN
ejpam-4200	262	4	,	,	PUNCT
ejpam-4200	262	5	m0	m0	NOUN
ejpam-4200	262	6	∗	∗	NOUN
ejpam-4200	262	7	2νs(·)t|fk|t	2νs(·)t|fk|t	NUM
ejpam-4200	262	8	)	)	PUNCT
ejpam-4200	262	9	1	1	NUM
ejpam-4200	262	10	/	/	SYM
ejpam-4200	262	11	t	t	NOUN
ejpam-4200	262	12	,	,	PUNCT
ejpam-4200	262	13	ν	ν	X
ejpam-4200	262	14	=	=	SYM
ejpam-4200	262	15	j	j	PROPN
ejpam-4200	262	16	or	or	CCONJ
ejpam-4200	262	17	k	k	PROPN
ejpam-4200	262	18	where	where	SCONJ
ejpam-4200	262	19	m0	m0	PROPN
ejpam-4200	262	20	=	=	PUNCT
ejpam-4200	262	21	m−	m−	PROPN
ejpam-4200	262	22	clog(s	clog(s	PROPN
ejpam-4200	262	23	)	)	PUNCT
ejpam-4200	262	24	thus	thus	ADV
ejpam-4200	262	25	•	•	NUM
ejpam-4200	262	26	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	262	27			NUM
ejpam-4200	262	28	j∑	j∑	PROPN
ejpam-4200	262	29	k	k	X
ejpam-4200	262	30	=	=	PROPN
ejpam-4200	262	31	j−n	j−n	ADJ
ejpam-4200	262	32	2js	2js	NOUN
ejpam-4200	262	33	(	(	PUNCT
ejpam-4200	262	34	·	·	PUNCT
ejpam-4200	262	35	)	)	PUNCT
ejpam-4200	262	36	(	(	PUNCT
ejpam-4200	262	37	ηj	ηj	NOUN
ejpam-4200	262	38	,	,	PUNCT
ejpam-4200	262	39	m	m	NOUN
ejpam-4200	262	40	∗	∗	NOUN
ejpam-4200	262	41	|fk|t	|fk|t	PROPN
ejpam-4200	262	42	)	)	PUNCT
ejpam-4200	262	43	1	1	NUM
ejpam-4200	262	44	/	/	SYM
ejpam-4200	262	45	t	t	NUM
ejpam-4200	262	46	j	j	PROPN
ejpam-4200	262	47	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	263	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	263	2	(	(	PUNCT
ejpam-4200	263	3	·	·	PUNCT
ejpam-4200	263	4	)	)	PUNCT
ejpam-4200	263	5	)	)	PUNCT
ejpam-4200	264	1	=	=	SYM
ejpam-4200	264	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	264	3			NUM
ejpam-4200	264	4	j∑	j∑	PROPN
ejpam-4200	264	5	k	k	X
ejpam-4200	264	6	=	=	PROPN
ejpam-4200	264	7	j−n	j−n	PROPN
ejpam-4200	264	8	ηj	ηj	NOUN
ejpam-4200	264	9	,	,	PUNCT
ejpam-4200	264	10	m0	m0	PROPN
ejpam-4200	264	11	∗	∗	NOUN
ejpam-4200	264	12	2js(·)t|fk|t	2js(·)t|fk|t	NUM
ejpam-4200	264	13			PROPN
ejpam-4200	264	14	j	j	PROPN
ejpam-4200	264	15	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	264	16	m	m	VERB
ejpam-4200	264	17	p	p	X
ejpam-4200	264	18	(	(	PUNCT
ejpam-4200	264	19	·	·	PUNCT
ejpam-4200	264	20	)	)	PUNCT
ejpam-4200	264	21	t	t	PROPN
ejpam-4200	264	22	,	,	PUNCT
ejpam-4200	264	23	u	u	NOUN
ejpam-4200	264	24	(	(	PUNCT
ejpam-4200	264	25	·	·	PUNCT
ejpam-4200	264	26	)	)	PUNCT
ejpam-4200	264	27	t	t	PROPN
ejpam-4200	264	28	(	(	PUNCT
ejpam-4200	264	29	ℓ	ℓ	INTJ
ejpam-4200	264	30	q	q	PROPN
ejpam-4200	264	31	(	(	PUNCT
ejpam-4200	264	32	·	·	PUNCT
ejpam-4200	264	33	)	)	PUNCT
ejpam-4200	264	34	t	t	NOUN
ejpam-4200	264	35	)	)	PUNCT
ejpam-4200	265	1	≲	≲	PROPN
ejpam-4200	265	2	0∑	0∑	NOUN
ejpam-4200	265	3	k=−n	k=−n	PROPN
ejpam-4200	265	4	∥∥∥∥{ηj	∥∥∥∥{ηj	NUM
ejpam-4200	265	5	,	,	PUNCT
ejpam-4200	265	6	m0	m0	NOUN
ejpam-4200	265	7	∗	∗	NOUN
ejpam-4200	265	8	2js(·)t|fk+j	2js(·)t|fk+j	NUM
ejpam-4200	265	9	|t	|t	NOUN
ejpam-4200	265	10	}	}	PUNCT
ejpam-4200	265	11	j	j	PROPN
ejpam-4200	265	12	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4200	265	13	m	m	VERB
ejpam-4200	265	14	p	p	X
ejpam-4200	265	15	(	(	PUNCT
ejpam-4200	265	16	·	·	PUNCT
ejpam-4200	265	17	)	)	PUNCT
ejpam-4200	265	18	t	t	PROPN
ejpam-4200	265	19	,	,	PUNCT
ejpam-4200	265	20	u	u	NOUN
ejpam-4200	265	21	(	(	PUNCT
ejpam-4200	265	22	·	·	PUNCT
ejpam-4200	265	23	)	)	PUNCT
ejpam-4200	265	24	t	t	PROPN
ejpam-4200	265	25	(	(	PUNCT
ejpam-4200	265	26	ℓ	ℓ	INTJ
ejpam-4200	265	27	q	q	PROPN
ejpam-4200	265	28	(	(	PUNCT
ejpam-4200	265	29	·	·	PUNCT
ejpam-4200	265	30	)	)	PUNCT
ejpam-4200	265	31	t	t	PROPN
ejpam-4200	265	32	)	)	PUNCT
ejpam-4200	265	33	.	.	PUNCT
ejpam-4200	266	1	for	for	ADP
ejpam-4200	266	2	t	t	PROPN
ejpam-4200	266	3	∈	∈	PROPN
ejpam-4200	266	4	(	(	PUNCT
ejpam-4200	266	5	0,min	0,min	NUM
ejpam-4200	266	6	{	{	PUNCT
ejpam-4200	266	7	p−	p−	NOUN
ejpam-4200	266	8	,	,	PUNCT
ejpam-4200	266	9	q−	q−	PROPN
ejpam-4200	266	10	}	}	PUNCT
ejpam-4200	266	11	)	)	PUNCT
ejpam-4200	266	12	,	,	PUNCT
ejpam-4200	266	13	lemma	lemma	PROPN
ejpam-4200	266	14	3	3	NUM
ejpam-4200	266	15	yields	yield	NOUN
ejpam-4200	266	16	0∑	0∑	PROPN
ejpam-4200	266	17	k=−n	k=−n	PROPN
ejpam-4200	266	18	∥∥∥∥{ηj	∥∥∥∥{ηj	NUM
ejpam-4200	266	19	,	,	PUNCT
ejpam-4200	266	20	m0	m0	NOUN
ejpam-4200	266	21	∗	∗	NOUN
ejpam-4200	266	22	2js(·)t|fk+j	2js(·)t|fk+j	NUM
ejpam-4200	266	23	|t	|t	NOUN
ejpam-4200	266	24	}	}	PUNCT
ejpam-4200	266	25	j	j	PROPN
ejpam-4200	266	26	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4200	266	27	m	m	VERB
ejpam-4200	266	28	p	p	X
ejpam-4200	266	29	(	(	PUNCT
ejpam-4200	266	30	·	·	PUNCT
ejpam-4200	266	31	)	)	PUNCT
ejpam-4200	266	32	t	t	PROPN
ejpam-4200	266	33	,	,	PUNCT
ejpam-4200	266	34	u	u	NOUN
ejpam-4200	266	35	(	(	PUNCT
ejpam-4200	266	36	·	·	PUNCT
ejpam-4200	266	37	)	)	PUNCT
ejpam-4200	266	38	t	t	PROPN
ejpam-4200	266	39	(	(	PUNCT
ejpam-4200	266	40	ℓ	ℓ	INTJ
ejpam-4200	266	41	q	q	PROPN
ejpam-4200	266	42	(	(	PUNCT
ejpam-4200	266	43	·	·	PUNCT
ejpam-4200	266	44	)	)	PUNCT
ejpam-4200	266	45	t	t	NOUN
ejpam-4200	266	46	)	)	PUNCT
ejpam-4200	267	1	≲	≲	PROPN
ejpam-4200	267	2	0∑	0∑	NOUN
ejpam-4200	267	3	k=−n	k=−n	PROPN
ejpam-4200	267	4	∥∥∥∥{2js(·)t|fk+j	∥∥∥∥{2js(·)t|fk+j	NUM
ejpam-4200	267	5	|t	|t	NOUN
ejpam-4200	267	6	}	}	PUNCT
ejpam-4200	267	7	j	j	PROPN
ejpam-4200	267	8	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4200	267	9	m	m	VERB
ejpam-4200	267	10	p	p	X
ejpam-4200	267	11	(	(	PUNCT
ejpam-4200	267	12	·	·	PUNCT
ejpam-4200	267	13	)	)	PUNCT
ejpam-4200	267	14	t	t	PROPN
ejpam-4200	267	15	,	,	PUNCT
ejpam-4200	267	16	u	u	NOUN
ejpam-4200	267	17	(	(	PUNCT
ejpam-4200	267	18	·	·	PUNCT
ejpam-4200	267	19	)	)	PUNCT
ejpam-4200	267	20	t	t	PROPN
ejpam-4200	267	21	(	(	PUNCT
ejpam-4200	267	22	ℓ	ℓ	INTJ
ejpam-4200	267	23	q	q	PROPN
ejpam-4200	267	24	(	(	PUNCT
ejpam-4200	267	25	·	·	PUNCT
ejpam-4200	267	26	)	)	PUNCT
ejpam-4200	267	27	t	t	NOUN
ejpam-4200	267	28	)	)	PUNCT
ejpam-4200	267	29	.	.	PUNCT
ejpam-4200	268	1	then∥∥∥∥∥∥	then∥∥∥∥∥∥	PROPN
ejpam-4200	268	2			NUM
ejpam-4200	268	3	j∑	j∑	PROPN
ejpam-4200	268	4	k	k	X
ejpam-4200	269	1	=	=	PROPN
ejpam-4200	269	2	j−n	j−n	ADJ
ejpam-4200	269	3	2js	2js	NOUN
ejpam-4200	269	4	(	(	PUNCT
ejpam-4200	269	5	·	·	PUNCT
ejpam-4200	269	6	)	)	PUNCT
ejpam-4200	269	7	(	(	PUNCT
ejpam-4200	269	8	ηj	ηj	NOUN
ejpam-4200	269	9	,	,	PUNCT
ejpam-4200	269	10	m	m	NOUN
ejpam-4200	269	11	∗	∗	NOUN
ejpam-4200	269	12	|fk|t	|fk|t	PROPN
ejpam-4200	269	13	)	)	PUNCT
ejpam-4200	269	14	1	1	NUM
ejpam-4200	269	15	/	/	SYM
ejpam-4200	269	16	t	t	NUM
ejpam-4200	269	17	j	j	PROPN
ejpam-4200	269	18	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	270	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	270	2	(	(	PUNCT
ejpam-4200	270	3	·	·	PUNCT
ejpam-4200	270	4	)	)	PUNCT
ejpam-4200	270	5	)	)	PUNCT
ejpam-4200	271	1	≲	≲	PROPN
ejpam-4200	271	2	∥∥∥∥(2js(·)fj)j	∥∥∥∥(2js(·)fj)j	NUM
ejpam-4200	271	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-4200	271	4	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	271	5	(	(	PUNCT
ejpam-4200	271	6	·	·	PUNCT
ejpam-4200	271	7	)	)	PUNCT
ejpam-4200	271	8	)	)	PUNCT
ejpam-4200	271	9	.	.	PUNCT
ejpam-4200	272	1	and	and	CCONJ
ejpam-4200	272	2	•	•	X
ejpam-4200	272	3	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	272	4			PUNCT
ejpam-4200	272	5	+	+	ADJ
ejpam-4200	272	6	∞∑	∞∑	ADJ
ejpam-4200	272	7	k	k	X
ejpam-4200	272	8	=	=	NOUN
ejpam-4200	272	9	j+1	j+1	ADJ
ejpam-4200	272	10	2−(k−j)s(·)2ks	2−(k−j)s(·)2ks	NUM
ejpam-4200	272	11	(	(	PUNCT
ejpam-4200	272	12	·	·	PUNCT
ejpam-4200	272	13	)	)	PUNCT
ejpam-4200	272	14	(	(	PUNCT
ejpam-4200	272	15	ηk	ηk	PROPN
ejpam-4200	272	16	,	,	PUNCT
ejpam-4200	272	17	m	m	NOUN
ejpam-4200	272	18	∗	∗	NOUN
ejpam-4200	272	19	|fk|t	|fk|t	PROPN
ejpam-4200	272	20	)	)	PUNCT
ejpam-4200	272	21	1	1	NUM
ejpam-4200	272	22	/	/	SYM
ejpam-4200	272	23	t	t	NUM
ejpam-4200	272	24	j	j	PROPN
ejpam-4200	272	25	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	273	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	273	2	(	(	PUNCT
ejpam-4200	273	3	·	·	PUNCT
ejpam-4200	273	4	)	)	PUNCT
ejpam-4200	273	5	)	)	PUNCT
ejpam-4200	274	1	≲	≲	PROPN
ejpam-4200	274	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	274	3			PUNCT
ejpam-4200	274	4	+	+	ADJ
ejpam-4200	274	5	∞∑	∞∑	ADJ
ejpam-4200	274	6	k	k	NOUN
ejpam-4200	274	7	=	=	ADJ
ejpam-4200	274	8	j+1	j+1	ADJ
ejpam-4200	274	9	2−|j−k|s	2−|j−k|s	NUM
ejpam-4200	274	10	(	(	PUNCT
ejpam-4200	274	11	·	·	PUNCT
ejpam-4200	274	12	)	)	PUNCT
ejpam-4200	274	13	(	(	PUNCT
ejpam-4200	274	14	ηk	ηk	PROPN
ejpam-4200	274	15	,	,	PUNCT
ejpam-4200	274	16	m0	m0	NOUN
ejpam-4200	274	17	∗	∗	NOUN
ejpam-4200	274	18	2ks(·)t|fk|t	2ks(·)t|fk|t	NUM
ejpam-4200	274	19	)	)	PUNCT
ejpam-4200	275	1			PROPN
ejpam-4200	275	2	j	j	PROPN
ejpam-4200	275	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	275	4	m	m	VERB
ejpam-4200	275	5	p	p	X
ejpam-4200	275	6	(	(	PUNCT
ejpam-4200	275	7	·	·	PUNCT
ejpam-4200	275	8	)	)	PUNCT
ejpam-4200	275	9	t	t	PROPN
ejpam-4200	275	10	,	,	PUNCT
ejpam-4200	275	11	u	u	NOUN
ejpam-4200	275	12	(	(	PUNCT
ejpam-4200	275	13	·	·	PUNCT
ejpam-4200	275	14	)	)	PUNCT
ejpam-4200	275	15	t	t	PROPN
ejpam-4200	275	16	(	(	PUNCT
ejpam-4200	275	17	ℓ	ℓ	INTJ
ejpam-4200	275	18	q	q	PROPN
ejpam-4200	275	19	(	(	PUNCT
ejpam-4200	275	20	·	·	PUNCT
ejpam-4200	275	21	)	)	PUNCT
ejpam-4200	275	22	t	t	NOUN
ejpam-4200	275	23	)	)	PUNCT
ejpam-4200	276	1	≲	≲	PROPN
ejpam-4200	276	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	277	1			PUNCT
ejpam-4200	277	2	+	+	ADJ
ejpam-4200	277	3	∞∑	∞∑	ADJ
ejpam-4200	277	4	k	k	NOUN
ejpam-4200	277	5	=	=	NOUN
ejpam-4200	277	6	j+1	j+1	ADJ
ejpam-4200	277	7	2−|j−k|s−	2−|j−k|s−	NUM
ejpam-4200	277	8	(	(	PUNCT
ejpam-4200	277	9	ηk	ηk	PROPN
ejpam-4200	277	10	,	,	PUNCT
ejpam-4200	277	11	m0	m0	NOUN
ejpam-4200	277	12	∗	∗	NOUN
ejpam-4200	277	13	2ks(·)t|fk|t	2ks(·)t|fk|t	NUM
ejpam-4200	277	14	)	)	PUNCT
ejpam-4200	278	1			PROPN
ejpam-4200	278	2	j	j	PROPN
ejpam-4200	278	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	278	4	m	m	VERB
ejpam-4200	278	5	p	p	X
ejpam-4200	278	6	(	(	PUNCT
ejpam-4200	278	7	·	·	PUNCT
ejpam-4200	278	8	)	)	PUNCT
ejpam-4200	278	9	t	t	PROPN
ejpam-4200	278	10	,	,	PUNCT
ejpam-4200	278	11	u	u	NOUN
ejpam-4200	278	12	(	(	PUNCT
ejpam-4200	278	13	·	·	PUNCT
ejpam-4200	278	14	)	)	PUNCT
ejpam-4200	278	15	t	t	PROPN
ejpam-4200	278	16	(	(	PUNCT
ejpam-4200	278	17	ℓ	ℓ	INTJ
ejpam-4200	278	18	q	q	PROPN
ejpam-4200	278	19	(	(	PUNCT
ejpam-4200	278	20	·	·	PUNCT
ejpam-4200	278	21	)	)	PUNCT
ejpam-4200	278	22	t	t	PROPN
ejpam-4200	278	23	)	)	PUNCT
ejpam-4200	278	24	m.	m.	NOUN
ejpam-4200	278	25	congo	congo	PROPN
ejpam-4200	278	26	,	,	PUNCT
ejpam-4200	278	27	m.	m.	PROPN
ejpam-4200	278	28	f.	f.	PROPN
ejpam-4200	278	29	ouedraogo	ouedraogo	PROPN
ejpam-4200	278	30	/	/	SYM
ejpam-4200	278	31	eur	eur	PROPN
ejpam-4200	278	32	.	.	PUNCT
ejpam-4200	279	1	j.	j.	PROPN
ejpam-4200	279	2	pure	pure	PROPN
ejpam-4200	279	3	appl	appl	PROPN
ejpam-4200	279	4	.	.	PROPN
ejpam-4200	279	5	math	math	PROPN
ejpam-4200	279	6	,	,	PUNCT
ejpam-4200	279	7	15	15	NUM
ejpam-4200	279	8	(	(	PUNCT
ejpam-4200	279	9	1	1	NUM
ejpam-4200	279	10	)	)	PUNCT
ejpam-4200	279	11	(	(	PUNCT
ejpam-4200	279	12	2022	2022	NUM
ejpam-4200	279	13	)	)	PUNCT
ejpam-4200	279	14	,	,	PUNCT
ejpam-4200	279	15	47	47	NUM
ejpam-4200	279	16	-	-	SYM
ejpam-4200	279	17	63	63	NUM
ejpam-4200	279	18	57	57	NUM
ejpam-4200	279	19	≲	≲	PROPN
ejpam-4200	279	20	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	280	1	{	{	PUNCT
ejpam-4200	281	1	+	+	ADP
ejpam-4200	281	2	∞∑	∞∑	ADJ
ejpam-4200	281	3	k=0	k=0	PROPN
ejpam-4200	281	4	2−|j−k|s−	2−|j−k|s−	NUM
ejpam-4200	281	5	(	(	PUNCT
ejpam-4200	281	6	ηk	ηk	PROPN
ejpam-4200	281	7	,	,	PUNCT
ejpam-4200	281	8	m0	m0	NOUN
ejpam-4200	281	9	∗	∗	NOUN
ejpam-4200	281	10	2ks(·)t|fk|t	2ks(·)t|fk|t	NUM
ejpam-4200	281	11	)	)	PUNCT
ejpam-4200	281	12	}	}	PUNCT
ejpam-4200	282	1	j	j	PROPN
ejpam-4200	282	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	282	3	m	m	VERB
ejpam-4200	282	4	p	p	X
ejpam-4200	282	5	(	(	PUNCT
ejpam-4200	282	6	·	·	PUNCT
ejpam-4200	282	7	)	)	PUNCT
ejpam-4200	282	8	t	t	PROPN
ejpam-4200	282	9	,	,	PUNCT
ejpam-4200	282	10	u	u	NOUN
ejpam-4200	282	11	(	(	PUNCT
ejpam-4200	282	12	·	·	PUNCT
ejpam-4200	282	13	)	)	PUNCT
ejpam-4200	282	14	t	t	PROPN
ejpam-4200	282	15	(	(	PUNCT
ejpam-4200	282	16	ℓ	ℓ	INTJ
ejpam-4200	282	17	q	q	PROPN
ejpam-4200	282	18	(	(	PUNCT
ejpam-4200	282	19	·	·	PUNCT
ejpam-4200	282	20	)	)	PUNCT
ejpam-4200	282	21	t	t	NOUN
ejpam-4200	282	22	)	)	PUNCT
ejpam-4200	282	23	by	by	ADP
ejpam-4200	282	24	lemma	lemma	PROPN
ejpam-4200	282	25	5	5	NUM
ejpam-4200	282	26	,	,	PUNCT
ejpam-4200	282	27	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	282	28	{	{	PUNCT
ejpam-4200	283	1	+	+	ADP
ejpam-4200	283	2	∞∑	∞∑	ADJ
ejpam-4200	283	3	k=0	k=0	PROPN
ejpam-4200	283	4	2−|j−k|s−	2−|j−k|s−	NUM
ejpam-4200	283	5	(	(	PUNCT
ejpam-4200	283	6	ηk	ηk	PROPN
ejpam-4200	283	7	,	,	PUNCT
ejpam-4200	283	8	m0	m0	NOUN
ejpam-4200	283	9	∗	∗	NOUN
ejpam-4200	283	10	2ks(·)t|fk|t	2ks(·)t|fk|t	NUM
ejpam-4200	283	11	)	)	PUNCT
ejpam-4200	283	12	}	}	PUNCT
ejpam-4200	284	1	j	j	PROPN
ejpam-4200	284	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	284	3	m	m	VERB
ejpam-4200	284	4	p	p	X
ejpam-4200	284	5	(	(	PUNCT
ejpam-4200	284	6	·	·	PUNCT
ejpam-4200	284	7	)	)	PUNCT
ejpam-4200	284	8	t	t	PROPN
ejpam-4200	284	9	,	,	PUNCT
ejpam-4200	284	10	u	u	NOUN
ejpam-4200	284	11	(	(	PUNCT
ejpam-4200	284	12	·	·	PUNCT
ejpam-4200	284	13	)	)	PUNCT
ejpam-4200	284	14	t	t	PROPN
ejpam-4200	284	15	(	(	PUNCT
ejpam-4200	284	16	ℓ	ℓ	INTJ
ejpam-4200	284	17	q	q	PROPN
ejpam-4200	284	18	(	(	PUNCT
ejpam-4200	284	19	·	·	PUNCT
ejpam-4200	284	20	)	)	PUNCT
ejpam-4200	284	21	t	t	NOUN
ejpam-4200	284	22	)	)	PUNCT
ejpam-4200	285	1	≲	≲	PROPN
ejpam-4200	285	2	∥∥∥(ηk	∥∥∥(ηk	PROPN
ejpam-4200	285	3	,	,	PUNCT
ejpam-4200	285	4	m0	m0	NOUN
ejpam-4200	285	5	∗	∗	NOUN
ejpam-4200	285	6	2ks(·)t|fk|t	2ks(·)t|fk|t	NUM
ejpam-4200	285	7	)	)	PUNCT
ejpam-4200	286	1	k	k	PROPN
ejpam-4200	286	2	∥∥∥	∥∥∥	PROPN
ejpam-4200	286	3	m	m	VERB
ejpam-4200	286	4	p	p	X
ejpam-4200	286	5	(	(	PUNCT
ejpam-4200	286	6	·	·	PUNCT
ejpam-4200	286	7	)	)	PUNCT
ejpam-4200	286	8	t	t	PROPN
ejpam-4200	286	9	,	,	PUNCT
ejpam-4200	286	10	u	u	NOUN
ejpam-4200	286	11	(	(	PUNCT
ejpam-4200	286	12	·	·	PUNCT
ejpam-4200	286	13	)	)	PUNCT
ejpam-4200	286	14	t	t	PROPN
ejpam-4200	286	15	(	(	PUNCT
ejpam-4200	286	16	ℓ	ℓ	INTJ
ejpam-4200	286	17	q	q	PROPN
ejpam-4200	286	18	(	(	PUNCT
ejpam-4200	286	19	·	·	PUNCT
ejpam-4200	286	20	)	)	PUNCT
ejpam-4200	286	21	t	t	PROPN
ejpam-4200	286	22	)	)	PUNCT
ejpam-4200	286	23	.	.	PUNCT
ejpam-4200	287	1	for	for	ADP
ejpam-4200	287	2	t	t	PROPN
ejpam-4200	287	3	∈	∈	PROPN
ejpam-4200	287	4	(	(	PUNCT
ejpam-4200	287	5	0,min	0,min	NUM
ejpam-4200	287	6	p−	p−	NOUN
ejpam-4200	287	7	,	,	PUNCT
ejpam-4200	287	8	q−	q−	PROPN
ejpam-4200	287	9	)	)	PUNCT
ejpam-4200	287	10	,	,	PUNCT
ejpam-4200	287	11	lemma	lemma	PROPN
ejpam-4200	287	12	3	3	NUM
ejpam-4200	287	13	yields∥∥∥(ηk	yields∥∥∥(ηk	PROPN
ejpam-4200	287	14	,	,	PUNCT
ejpam-4200	287	15	m0	m0	NOUN
ejpam-4200	287	16	∗	∗	NOUN
ejpam-4200	287	17	2ks(·)t|fk|t	2ks(·)t|fk|t	NUM
ejpam-4200	287	18	)	)	PUNCT
ejpam-4200	288	1	k	k	PROPN
ejpam-4200	288	2	∥∥∥	∥∥∥	PROPN
ejpam-4200	288	3	m	m	VERB
ejpam-4200	288	4	p	p	X
ejpam-4200	288	5	(	(	PUNCT
ejpam-4200	288	6	·	·	PUNCT
ejpam-4200	288	7	)	)	PUNCT
ejpam-4200	288	8	t	t	PROPN
ejpam-4200	288	9	,	,	PUNCT
ejpam-4200	288	10	u	u	NOUN
ejpam-4200	288	11	(	(	PUNCT
ejpam-4200	288	12	·	·	PUNCT
ejpam-4200	288	13	)	)	PUNCT
ejpam-4200	288	14	t	t	PROPN
ejpam-4200	288	15	(	(	PUNCT
ejpam-4200	288	16	ℓ	ℓ	INTJ
ejpam-4200	288	17	q	q	PROPN
ejpam-4200	288	18	(	(	PUNCT
ejpam-4200	288	19	·	·	PUNCT
ejpam-4200	288	20	)	)	PUNCT
ejpam-4200	288	21	t	t	NOUN
ejpam-4200	288	22	)	)	PUNCT
ejpam-4200	288	23	≲	≲	PROPN
ejpam-4200	288	24	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	PROPN
ejpam-4200	288	25	)	)	PUNCT
ejpam-4200	288	26	k	k	PROPN
ejpam-4200	288	27	∥∥∥	∥∥∥	PROPN
ejpam-4200	288	28	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	288	29	(	(	PUNCT
ejpam-4200	288	30	·	·	PUNCT
ejpam-4200	288	31	)	)	PUNCT
ejpam-4200	288	32	)	)	PUNCT
ejpam-4200	288	33	.	.	PUNCT
ejpam-4200	289	1	then∥∥∥∥∥∥	then∥∥∥∥∥∥	VERB
ejpam-4200	289	2			PUNCT
ejpam-4200	289	3	+	+	PROPN
ejpam-4200	289	4	∞∑	∞∑	ADJ
ejpam-4200	289	5	k	k	X
ejpam-4200	289	6	=	=	NOUN
ejpam-4200	289	7	j+1	j+1	ADJ
ejpam-4200	289	8	2−(k−j)s(·)2ks	2−(k−j)s(·)2ks	NUM
ejpam-4200	289	9	(	(	PUNCT
ejpam-4200	289	10	·	·	PUNCT
ejpam-4200	289	11	)	)	PUNCT
ejpam-4200	289	12	(	(	PUNCT
ejpam-4200	289	13	ηk	ηk	PROPN
ejpam-4200	289	14	,	,	PUNCT
ejpam-4200	289	15	m0	m0	NOUN
ejpam-4200	289	16	∗	∗	NOUN
ejpam-4200	289	17	|fk|t	|fk|t	PROPN
ejpam-4200	289	18	)	)	PUNCT
ejpam-4200	289	19	1	1	NUM
ejpam-4200	289	20	/	/	SYM
ejpam-4200	289	21	t	t	NUM
ejpam-4200	289	22	j	j	PROPN
ejpam-4200	289	23	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	290	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	290	2	(	(	PUNCT
ejpam-4200	290	3	·	·	PUNCT
ejpam-4200	290	4	)	)	PUNCT
ejpam-4200	290	5	)	)	PUNCT
ejpam-4200	291	1	≲	≲	PROPN
ejpam-4200	291	2	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	NUM
ejpam-4200	291	3	)	)	PUNCT
ejpam-4200	291	4	k	k	PROPN
ejpam-4200	291	5	∥∥∥	∥∥∥	PROPN
ejpam-4200	291	6	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	291	7	(	(	PUNCT
ejpam-4200	291	8	·	·	PUNCT
ejpam-4200	291	9	)	)	PUNCT
ejpam-4200	291	10	)	)	PUNCT
ejpam-4200	291	11	.	.	PUNCT
ejpam-4200	292	1	(	(	PUNCT
ejpam-4200	292	2	ii	ii	NOUN
ejpam-4200	292	3	)	)	PUNCT
ejpam-4200	292	4	now	now	ADV
ejpam-4200	292	5	we	we	PRON
ejpam-4200	292	6	estimate	estimate	VERB
ejpam-4200	292	7	∥∥∥∥∥ψ0(d	∥∥∥∥∥ψ0(d	ADV
ejpam-4200	292	8	)	)	PUNCT
ejpam-4200	293	1	(	(	PUNCT
ejpam-4200	293	2	+	+	ADP
ejpam-4200	293	3	∞∑	∞∑	ADJ
ejpam-4200	293	4	k=0	k=0	PROPN
ejpam-4200	293	5	fk	fk	INTJ
ejpam-4200	293	6	)	)	PUNCT
ejpam-4200	293	7	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	293	8	mp(·),u	mp(·),u	PROPN
ejpam-4200	293	9	(	(	PUNCT
ejpam-4200	293	10	·	·	PUNCT
ejpam-4200	293	11	)	)	PUNCT
ejpam-4200	293	12	.	.	PUNCT
ejpam-4200	294	1	since	since	SCONJ
ejpam-4200	294	2	suppf	suppf	PROPN
ejpam-4200	294	3	(	(	PUNCT
ejpam-4200	294	4	ψ̌0	ψ̌0	X
ejpam-4200	294	5	∗	∗	PROPN
ejpam-4200	294	6	fk	fk	INTJ
ejpam-4200	294	7	)	)	PUNCT
ejpam-4200	294	8	⊂	⊂	PROPN
ejpam-4200	294	9	{	{	PUNCT
ejpam-4200	294	10	ξ	ξ	X
ejpam-4200	294	11	∈	∈	PROPN
ejpam-4200	294	12	rn	rn	PROPN
ejpam-4200	294	13	:	:	PUNCT
ejpam-4200	294	14	|ξ|	|ξ|	VERB
ejpam-4200	294	15	≤	≤	NOUN
ejpam-4200	294	16	2k+1	2k+1	PROPN
ejpam-4200	294	17	}	}	PUNCT
ejpam-4200	294	18	,	,	PUNCT
ejpam-4200	294	19	then	then	ADV
ejpam-4200	294	20	∥∥∥∥∥ψ0(d	∥∥∥∥∥ψ0(d	X
ejpam-4200	294	21	)	)	PUNCT
ejpam-4200	294	22	(	(	PUNCT
ejpam-4200	294	23	+	+	ADP
ejpam-4200	294	24	∞∑	∞∑	ADJ
ejpam-4200	294	25	k=0	k=0	PROPN
ejpam-4200	294	26	fk	fk	INTJ
ejpam-4200	294	27	)	)	PUNCT
ejpam-4200	294	28	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	294	29	mp(·),u	mp(·),u	PROPN
ejpam-4200	294	30	(	(	PUNCT
ejpam-4200	294	31	·	·	PUNCT
ejpam-4200	294	32	)	)	PUNCT
ejpam-4200	294	33	=	=	SYM
ejpam-4200	295	1	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	295	2	n∑	n∑	NOUN
ejpam-4200	295	3	k=0	k=0	PROPN
ejpam-4200	295	4	ψ0	ψ0	PROPN
ejpam-4200	295	5	∗	∗	PROPN
ejpam-4200	295	6	fk	fk	INTJ
ejpam-4200	295	7	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	295	8	mp(·),u	mp(·),u	PROPN
ejpam-4200	295	9	(	(	PUNCT
ejpam-4200	295	10	·	·	PUNCT
ejpam-4200	295	11	)	)	PUNCT
ejpam-4200	296	1	≲	≲	PROPN
ejpam-4200	296	2	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-4200	296	3	∞∑	∞∑	NUM
ejpam-4200	296	4	k=0	k=0	PROPN
ejpam-4200	296	5	(	(	PUNCT
ejpam-4200	296	6	ηk	ηk	X
ejpam-4200	296	7	,	,	PUNCT
ejpam-4200	296	8	m	m	NOUN
ejpam-4200	296	9	∗	∗	NOUN
ejpam-4200	296	10	|fk|t	|fk|t	PROPN
ejpam-4200	296	11	)	)	PUNCT
ejpam-4200	296	12	1	1	NUM
ejpam-4200	296	13	/	/	SYM
ejpam-4200	296	14	t∥∥∥∥∥	t∥∥∥∥∥	PROPN
ejpam-4200	296	15	mp(·),u	mp(·),u	PROPN
ejpam-4200	296	16	(	(	PUNCT
ejpam-4200	296	17	·	·	PUNCT
ejpam-4200	296	18	)	)	PUNCT
ejpam-4200	296	19	,	,	PUNCT
ejpam-4200	296	20	for	for	ADP
ejpam-4200	296	21	m	m	PROPN
ejpam-4200	296	22	>	>	X
ejpam-4200	296	23	n+	n+	PUNCT
ejpam-4200	296	24	clog(1	clog(1	NOUN
ejpam-4200	296	25	/	/	SYM
ejpam-4200	296	26	q	q	NOUN
ejpam-4200	296	27	)	)	PUNCT
ejpam-4200	296	28	+	+	NUM
ejpam-4200	296	29	clog(s	clog(s	NOUN
ejpam-4200	296	30	)	)	PUNCT
ejpam-4200	297	1	+	+	CCONJ
ejpam-4200	297	2	nmax	nmax	ADJ
ejpam-4200	297	3	{	{	PUNCT
ejpam-4200	297	4	0	0	NUM
ejpam-4200	297	5	,	,	PUNCT
ejpam-4200	297	6	supx∈rn	supx∈rn	PUNCT
ejpam-4200	297	7	(	(	PUNCT
ejpam-4200	297	8	1	1	NUM
ejpam-4200	297	9	p(x	p(x	NOUN
ejpam-4200	297	10	)	)	PUNCT
ejpam-4200	297	11	−	−	PROPN
ejpam-4200	297	12	1	1	NUM
ejpam-4200	297	13	u(x	u(x	NOUN
ejpam-4200	297	14	)	)	PUNCT
ejpam-4200	297	15	)	)	PUNCT
ejpam-4200	298	1	−	−	PROPN
ejpam-4200	298	2	1	1	NUM
ejpam-4200	298	3	p∞	p∞	PROPN
ejpam-4200	298	4	}	}	PUNCT
ejpam-4200	298	5	by	by	ADP
ejpam-4200	298	6	lemma	lemma	PROPN
ejpam-4200	298	7	2	2	NUM
ejpam-4200	298	8	.	.	PUNCT
ejpam-4200	299	1	then	then	ADV
ejpam-4200	299	2	by	by	ADP
ejpam-4200	299	3	lemma	lemma	PROPN
ejpam-4200	299	4	1∥∥∥∥∥ψ0(d	1∥∥∥∥∥ψ0(d	NUM
ejpam-4200	299	5	)	)	PUNCT
ejpam-4200	299	6	(	(	PUNCT
ejpam-4200	299	7	+	+	ADP
ejpam-4200	299	8	∞∑	∞∑	ADJ
ejpam-4200	299	9	k=0	k=0	PROPN
ejpam-4200	299	10	fk	fk	INTJ
ejpam-4200	299	11	)	)	PUNCT
ejpam-4200	299	12	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	299	13	mp(·),u	mp(·),u	PROPN
ejpam-4200	299	14	(	(	PUNCT
ejpam-4200	299	15	·	·	PUNCT
ejpam-4200	299	16	)	)	PUNCT
ejpam-4200	300	1	≲	≲	PROPN
ejpam-4200	300	2	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-4200	300	3	∞∑	∞∑	NUM
ejpam-4200	300	4	k=0	k=0	PROPN
ejpam-4200	300	5	2−ks−	2−ks−	NUM
ejpam-4200	300	6	(	(	PUNCT
ejpam-4200	300	7	ηk	ηk	PROPN
ejpam-4200	300	8	,	,	PUNCT
ejpam-4200	300	9	m−clog(s	m−clog(s	PROPN
ejpam-4200	300	10	)	)	PUNCT
ejpam-4200	300	11	∗	∗	NOUN
ejpam-4200	300	12	2	2	NUM
ejpam-4200	300	13	ks(·)t|fk|t	ks(·)t|fk|t	NOUN
ejpam-4200	300	14	)	)	PUNCT
ejpam-4200	300	15	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	301	1	m	m	PRON
ejpam-4200	301	2	p	p	X
ejpam-4200	301	3	(	(	PUNCT
ejpam-4200	301	4	·	·	PUNCT
ejpam-4200	301	5	)	)	PUNCT
ejpam-4200	301	6	t	t	PROPN
ejpam-4200	301	7	,	,	PUNCT
ejpam-4200	301	8	u	u	NOUN
ejpam-4200	301	9	(	(	PUNCT
ejpam-4200	301	10	·	·	PUNCT
ejpam-4200	301	11	)	)	PUNCT
ejpam-4200	301	12	t	t	NOUN
ejpam-4200	301	13	=	=	SYM
ejpam-4200	301	14	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	301	15	{	{	PUNCT
ejpam-4200	302	1	+	+	ADP
ejpam-4200	302	2	∞∑	∞∑	ADJ
ejpam-4200	302	3	k=0	k=0	PROPN
ejpam-4200	302	4	2−ks−	2−ks−	NUM
ejpam-4200	302	5	(	(	PUNCT
ejpam-4200	302	6	ηk	ηk	PROPN
ejpam-4200	302	7	,	,	PUNCT
ejpam-4200	302	8	m−clog(s	m−clog(s	PROPN
ejpam-4200	302	9	)	)	PUNCT
ejpam-4200	302	10	∗	∗	NOUN
ejpam-4200	302	11	2	2	NUM
ejpam-4200	302	12	ks(·)t|fk|t	ks(·)t|fk|t	NOUN
ejpam-4200	302	13	)	)	PUNCT
ejpam-4200	302	14	}	}	PUNCT
ejpam-4200	303	1	j	j	PROPN
ejpam-4200	303	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	303	3	m	m	VERB
ejpam-4200	303	4	p	p	X
ejpam-4200	303	5	(	(	PUNCT
ejpam-4200	303	6	·	·	PUNCT
ejpam-4200	303	7	)	)	PUNCT
ejpam-4200	303	8	t	t	PROPN
ejpam-4200	303	9	,	,	PUNCT
ejpam-4200	303	10	u	u	NOUN
ejpam-4200	303	11	(	(	PUNCT
ejpam-4200	303	12	·	·	PUNCT
ejpam-4200	303	13	)	)	PUNCT
ejpam-4200	303	14	t	t	PROPN
ejpam-4200	303	15	(	(	PUNCT
ejpam-4200	303	16	ℓ	ℓ	INTJ
ejpam-4200	303	17	q	q	PROPN
ejpam-4200	303	18	(	(	PUNCT
ejpam-4200	303	19	·	·	PUNCT
ejpam-4200	303	20	)	)	PUNCT
ejpam-4200	303	21	t	t	PROPN
ejpam-4200	303	22	)	)	PUNCT
ejpam-4200	303	23	m.	m.	NOUN
ejpam-4200	303	24	congo	congo	PROPN
ejpam-4200	303	25	,	,	PUNCT
ejpam-4200	303	26	m.	m.	PROPN
ejpam-4200	303	27	f.	f.	PROPN
ejpam-4200	303	28	ouedraogo	ouedraogo	PROPN
ejpam-4200	303	29	/	/	SYM
ejpam-4200	303	30	eur	eur	PROPN
ejpam-4200	303	31	.	.	PUNCT
ejpam-4200	304	1	j.	j.	PROPN
ejpam-4200	304	2	pure	pure	PROPN
ejpam-4200	304	3	appl	appl	PROPN
ejpam-4200	304	4	.	.	PROPN
ejpam-4200	304	5	math	math	PROPN
ejpam-4200	304	6	,	,	PUNCT
ejpam-4200	304	7	15	15	NUM
ejpam-4200	304	8	(	(	PUNCT
ejpam-4200	304	9	1	1	NUM
ejpam-4200	304	10	)	)	PUNCT
ejpam-4200	304	11	(	(	PUNCT
ejpam-4200	304	12	2022	2022	NUM
ejpam-4200	304	13	)	)	PUNCT
ejpam-4200	304	14	,	,	PUNCT
ejpam-4200	304	15	47	47	NUM
ejpam-4200	304	16	-	-	SYM
ejpam-4200	304	17	63	63	NUM
ejpam-4200	304	18	58	58	NUM
ejpam-4200	304	19	thus∥∥∥∥∥ψ0(d	thus∥∥∥∥∥ψ0(d	NOUN
ejpam-4200	304	20	)	)	PUNCT
ejpam-4200	304	21	(	(	PUNCT
ejpam-4200	305	1	+	+	ADP
ejpam-4200	305	2	∞∑	∞∑	ADJ
ejpam-4200	305	3	k=0	k=0	PROPN
ejpam-4200	305	4	fk	fk	INTJ
ejpam-4200	305	5	)	)	PUNCT
ejpam-4200	305	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-4200	305	7	mp(·),u	mp(·),u	PROPN
ejpam-4200	305	8	(	(	PUNCT
ejpam-4200	305	9	·	·	PUNCT
ejpam-4200	305	10	)	)	PUNCT
ejpam-4200	305	11	≲	≲	PROPN
ejpam-4200	305	12	∥∥∥(ηk	∥∥∥(ηk	PROPN
ejpam-4200	305	13	,	,	PUNCT
ejpam-4200	305	14	m−clog(s	m−clog(s	PROPN
ejpam-4200	305	15	)	)	PUNCT
ejpam-4200	305	16	∗	∗	NOUN
ejpam-4200	305	17	2	2	NUM
ejpam-4200	305	18	ks(·)t|fk|t	ks(·)t|fk|t	NOUN
ejpam-4200	305	19	)	)	PUNCT
ejpam-4200	306	1	k	k	PROPN
ejpam-4200	306	2	∥∥∥	∥∥∥	PROPN
ejpam-4200	306	3	m	m	VERB
ejpam-4200	306	4	p	p	X
ejpam-4200	306	5	(	(	PUNCT
ejpam-4200	306	6	·	·	PUNCT
ejpam-4200	306	7	)	)	PUNCT
ejpam-4200	306	8	t	t	PROPN
ejpam-4200	306	9	,	,	PUNCT
ejpam-4200	306	10	u	u	NOUN
ejpam-4200	306	11	(	(	PUNCT
ejpam-4200	306	12	·	·	PUNCT
ejpam-4200	306	13	)	)	PUNCT
ejpam-4200	306	14	t	t	PROPN
ejpam-4200	306	15	(	(	PUNCT
ejpam-4200	306	16	ℓ	ℓ	INTJ
ejpam-4200	306	17	q	q	PROPN
ejpam-4200	306	18	(	(	PUNCT
ejpam-4200	306	19	·	·	PUNCT
ejpam-4200	306	20	)	)	PUNCT
ejpam-4200	306	21	t	t	NOUN
ejpam-4200	306	22	)	)	PUNCT
ejpam-4200	307	1	≲	≲	PROPN
ejpam-4200	307	2	∥∥∥(2ks(·)fk	∥∥∥(2ks(·)fk	PROPN
ejpam-4200	307	3	)	)	PUNCT
ejpam-4200	307	4	k	k	PROPN
ejpam-4200	307	5	∥∥∥	∥∥∥	PROPN
ejpam-4200	307	6	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	307	7	(	(	PUNCT
ejpam-4200	307	8	·	·	PUNCT
ejpam-4200	307	9	)	)	PUNCT
ejpam-4200	307	10	)	)	PUNCT
ejpam-4200	307	11	by	by	ADP
ejpam-4200	307	12	lemma	lemma	PROPN
ejpam-4200	307	13	5	5	NUM
ejpam-4200	307	14	and	and	CCONJ
ejpam-4200	307	15	lemma	lemma	PROPN
ejpam-4200	307	16	2	2	NUM
ejpam-4200	307	17	.	.	PUNCT
ejpam-4200	308	1	the	the	DET
ejpam-4200	308	2	proof	proof	NOUN
ejpam-4200	308	3	is	be	AUX
ejpam-4200	308	4	completed	complete	VERB
ejpam-4200	308	5	.	.	PUNCT
ejpam-4200	309	1	□	□	PUNCT
ejpam-4200	309	2	theorem	theorem	NOUN
ejpam-4200	309	3	1	1	X
ejpam-4200	309	4	.	.	PUNCT
ejpam-4200	310	1	let	let	VERB
ejpam-4200	310	2	a(x	a(x	NOUN
ejpam-4200	310	3	,	,	PUNCT
ejpam-4200	310	4	ξ	ξ	NOUN
ejpam-4200	310	5	)	)	PUNCT
ejpam-4200	310	6	∈	∈	NOUN
ejpam-4200	310	7	cℓ	cℓ	ADP
ejpam-4200	310	8	∗s	∗s	PROPN
ejpam-4200	310	9	m	m	PROPN
ejpam-4200	310	10	1,δ	1,δ	NUM
ejpam-4200	310	11	where	where	SCONJ
ejpam-4200	310	12	m	m	VERB
ejpam-4200	310	13	∈	∈	PROPN
ejpam-4200	310	14	r	r	NOUN
ejpam-4200	310	15	,	,	PUNCT
ejpam-4200	310	16	δ	δ	PROPN
ejpam-4200	310	17	∈	∈	PROPN
ejpam-4200	311	1	[	[	X
ejpam-4200	311	2	0	0	NUM
ejpam-4200	311	3	,	,	PUNCT
ejpam-4200	311	4	1	1	NUM
ejpam-4200	311	5	]	]	PUNCT
ejpam-4200	311	6	and	and	CCONJ
ejpam-4200	311	7	ℓ	ℓ	INTJ
ejpam-4200	311	8	>	>	X
ejpam-4200	311	9	0	0	X
ejpam-4200	311	10	.	.	PUNCT
ejpam-4200	312	1	let	let	VERB
ejpam-4200	312	2	1	1	NUM
ejpam-4200	312	3	≤	≤	NOUN
ejpam-4200	312	4	p−	p−	NOUN
ejpam-4200	312	5	≤	≤	NUM
ejpam-4200	312	6	p(x	p(x	PROPN
ejpam-4200	312	7	)	)	PUNCT
ejpam-4200	312	8	≤	≤	NUM
ejpam-4200	312	9	u(x	u(x	NOUN
ejpam-4200	312	10	)	)	PUNCT
ejpam-4200	312	11	≤	≤	NOUN
ejpam-4200	312	12	supu	supu	NOUN
ejpam-4200	312	13	<	<	X
ejpam-4200	312	14	+	+	NOUN
ejpam-4200	312	15	∞	∞	PROPN
ejpam-4200	312	16	and	and	CCONJ
ejpam-4200	312	17	q−	q−	PROPN
ejpam-4200	312	18	,	,	PUNCT
ejpam-4200	312	19	q+	q+	NOUN
ejpam-4200	312	20	∈	∈	PROPN
ejpam-4200	313	1	[	[	X
ejpam-4200	313	2	1,+∞	1,+∞	NUM
ejpam-4200	313	3	)	)	PUNCT
ejpam-4200	313	4	.	.	PUNCT
ejpam-4200	314	1	let	let	VERB
ejpam-4200	314	2	s	s	PRON
ejpam-4200	314	3	∈	∈	VERB
ejpam-4200	314	4	c	c	PROPN
ejpam-4200	314	5	log	log	PROPN
ejpam-4200	314	6	loc	loc	PROPN
ejpam-4200	314	7	such	such	ADJ
ejpam-4200	314	8	that	that	SCONJ
ejpam-4200	314	9	0	0	NUM
ejpam-4200	314	10	<	<	X
ejpam-4200	314	11	s−	s−	PROPN
ejpam-4200	314	12	≤	≤	NOUN
ejpam-4200	314	13	s+	s+	PUNCT
ejpam-4200	314	14	<	<	X
ejpam-4200	314	15	ℓ.	ℓ.	NOUN
ejpam-4200	314	16	then	then	ADV
ejpam-4200	314	17	a(x	a(x	NOUN
ejpam-4200	314	18	,	,	PUNCT
ejpam-4200	314	19	d	d	NOUN
ejpam-4200	314	20	)	)	PUNCT
ejpam-4200	314	21	:	:	PUNCT
ejpam-4200	314	22	es(·)+m	es(·)+m	NOUN
ejpam-4200	314	23	p(·),u()·,q	p(·),u()·,q	PROPN
ejpam-4200	314	24	(	(	PUNCT
ejpam-4200	314	25	·	·	PUNCT
ejpam-4200	314	26	)	)	PUNCT
ejpam-4200	314	27	−→	−→	NOUN
ejpam-4200	314	28	es	es	PROPN
ejpam-4200	314	29	(	(	PUNCT
ejpam-4200	314	30	·	·	PUNCT
ejpam-4200	314	31	)	)	PUNCT
ejpam-4200	314	32	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	314	33	(	(	PUNCT
ejpam-4200	314	34	·	·	PUNCT
ejpam-4200	314	35	)	)	PUNCT
ejpam-4200	314	36	is	be	AUX
ejpam-4200	314	37	bounded	bound	VERB
ejpam-4200	314	38	.	.	PUNCT
ejpam-4200	315	1	proof	proof	NOUN
ejpam-4200	315	2	.	.	PUNCT
ejpam-4200	316	1	we	we	PRON
ejpam-4200	316	2	recall	recall	VERB
ejpam-4200	316	3	that	that	SCONJ
ejpam-4200	316	4	the	the	DET
ejpam-4200	316	5	symbol	symbol	NOUN
ejpam-4200	316	6	reduction	reduction	NOUN
ejpam-4200	316	7	method	method	NOUN
ejpam-4200	316	8	,	,	PUNCT
ejpam-4200	316	9	due	due	ADP
ejpam-4200	316	10	to	to	ADP
ejpam-4200	316	11	coifman	coifman	NOUN
ejpam-4200	316	12	and	and	CCONJ
ejpam-4200	316	13	meyer[6	meyer[6	PROPN
ejpam-4200	316	14	]	]	PUNCT
ejpam-4200	316	15	,	,	PUNCT
ejpam-4200	316	16	makes	make	VERB
ejpam-4200	316	17	it	it	PRON
ejpam-4200	316	18	possible	possible	ADJ
ejpam-4200	316	19	to	to	PART
ejpam-4200	316	20	be	be	AUX
ejpam-4200	316	21	limited	limit	VERB
ejpam-4200	316	22	to	to	ADP
ejpam-4200	316	23	symbols	symbols	PROPN
ejpam-4200	316	24	a(x	a(x	PROPN
ejpam-4200	316	25	,	,	PUNCT
ejpam-4200	316	26	ξ	ξ	NOUN
ejpam-4200	316	27	)	)	PUNCT
ejpam-4200	316	28	∈	∈	NOUN
ejpam-4200	316	29	cℓ	cℓ	ADP
ejpam-4200	316	30	∗s	∗s	PROPN
ejpam-4200	316	31	m	m	PROPN
ejpam-4200	316	32	1,δ	1,δ	NUM
ejpam-4200	316	33	of	of	ADP
ejpam-4200	316	34	the	the	DET
ejpam-4200	316	35	form	form	NOUN
ejpam-4200	316	36	(	(	PUNCT
ejpam-4200	316	37	see	see	VERB
ejpam-4200	316	38	[	[	X
ejpam-4200	316	39	14	14	NUM
ejpam-4200	316	40	]	]	PUNCT
ejpam-4200	316	41	and	and	CCONJ
ejpam-4200	316	42	[	[	X
ejpam-4200	316	43	2	2	NUM
ejpam-4200	316	44	]	]	SYM
ejpam-4200	316	45	)	)	PUNCT
ejpam-4200	316	46	a(x	a(x	PROPN
ejpam-4200	316	47	,	,	PUNCT
ejpam-4200	316	48	ξ	ξ	NOUN
ejpam-4200	316	49	)	)	PUNCT
ejpam-4200	316	50	=	=	SYM
ejpam-4200	316	51	∑	∑	ADP
ejpam-4200	316	52	j≥0	j≥0	ADJ
ejpam-4200	316	53	σj(x)ψj(ξ	σj(x)ψj(ξ	NOUN
ejpam-4200	316	54	)	)	PUNCT
ejpam-4200	316	55	where	where	SCONJ
ejpam-4200	316	56	σj	σj	ADJ
ejpam-4200	316	57	satisfies	satisfie	NOUN
ejpam-4200	316	58	∥σj∥cℓ	∥σj∥cℓ	X
ejpam-4200	316	59	∗	∗	NOUN
ejpam-4200	316	60	≤	≤	NUM
ejpam-4200	316	61	c2j(m+ℓδ	c2j(m+ℓδ	NUM
ejpam-4200	316	62	)	)	PUNCT
ejpam-4200	316	63	(	(	PUNCT
ejpam-4200	316	64	9	9	NUM
ejpam-4200	316	65	)	)	PUNCT
ejpam-4200	316	66	and	and	CCONJ
ejpam-4200	316	67	∥σj∥l∞	∥σj∥l∞	SYM
ejpam-4200	316	68	≤	≤	NUM
ejpam-4200	316	69	c	c	NOUN
ejpam-4200	316	70	(	(	PUNCT
ejpam-4200	316	71	10	10	NUM
ejpam-4200	316	72	)	)	PUNCT
ejpam-4200	316	73	with	with	ADP
ejpam-4200	316	74	c	c	NOUN
ejpam-4200	316	75	depending	depend	VERB
ejpam-4200	316	76	on	on	ADP
ejpam-4200	316	77	δ	δ	PROPN
ejpam-4200	316	78	and	and	CCONJ
ejpam-4200	316	79	ℓ	ℓ	PROPN
ejpam-4200	316	80	but	but	CCONJ
ejpam-4200	316	81	not	not	PART
ejpam-4200	316	82	on	on	ADP
ejpam-4200	316	83	j.	j.	PROPN
ejpam-4200	316	84	and	and	CCONJ
ejpam-4200	316	85	ψj	ψj	ADV
ejpam-4200	316	86	is	be	AUX
ejpam-4200	316	87	exactly	exactly	ADV
ejpam-4200	316	88	a	a	DET
ejpam-4200	316	89	littlewood	littlewood	NOUN
ejpam-4200	316	90	-	-	PUNCT
ejpam-4200	316	91	paley	paley	NOUN
ejpam-4200	316	92	function	function	NOUN
ejpam-4200	316	93	.	.	PUNCT
ejpam-4200	317	1	we	we	PRON
ejpam-4200	317	2	have	have	VERB
ejpam-4200	317	3	σj(x	σj(x	NOUN
ejpam-4200	317	4	)	)	PUNCT
ejpam-4200	317	5	=	=	PUNCT
ejpam-4200	318	1	+	+	ADP
ejpam-4200	318	2	∞∑	∞∑	PRON
ejpam-4200	318	3	k=0	k=0	PROPN
ejpam-4200	318	4	ψj(d)σj(x	ψj(d)σj(x	PROPN
ejpam-4200	318	5	)	)	PUNCT
ejpam-4200	318	6	.	.	PUNCT
ejpam-4200	319	1	then	then	ADV
ejpam-4200	319	2	σj(x)ψj(ξ	σj(x)ψj(ξ	VERB
ejpam-4200	319	3	)	)	PUNCT
ejpam-4200	319	4	=	=	NOUN
ejpam-4200	320	1	(	(	PUNCT
ejpam-4200	320	2	+	+	ADP
ejpam-4200	320	3	∞∑	∞∑	PRON
ejpam-4200	320	4	k=0	k=0	PROPN
ejpam-4200	320	5	ψj(d)σj(x)ψj(ξ	ψj(d)σj(x)ψj(ξ	PROPN
ejpam-4200	320	6	)	)	PUNCT
ejpam-4200	320	7	)	)	PUNCT
ejpam-4200	320	8	.	.	PUNCT
ejpam-4200	321	1	therefore	therefore	ADV
ejpam-4200	321	2	a(x	a(x	NOUN
ejpam-4200	321	3	,	,	PUNCT
ejpam-4200	321	4	ξ	ξ	NOUN
ejpam-4200	321	5	)	)	PUNCT
ejpam-4200	321	6	=	=	PUNCT
ejpam-4200	322	1	+	+	ADP
ejpam-4200	322	2	∞∑	∞∑	NUM
ejpam-4200	322	3	j=0	j=0	PROPN
ejpam-4200	322	4	(	(	PUNCT
ejpam-4200	322	5	+	+	ADP
ejpam-4200	322	6	∞∑	∞∑	PRON
ejpam-4200	322	7	k=0	k=0	PROPN
ejpam-4200	322	8	ψk(d)σj(x	ψk(d)σj(x	X
ejpam-4200	322	9	)	)	PUNCT
ejpam-4200	322	10	)	)	PUNCT
ejpam-4200	322	11	ψj(ξ	ψj(ξ	NUM
ejpam-4200	322	12	)	)	PUNCT
ejpam-4200	322	13	.	.	PUNCT
ejpam-4200	323	1	set	set	VERB
ejpam-4200	323	2	akj	akj	ADJ
ejpam-4200	323	3	=	=	PUNCT
ejpam-4200	323	4	ψk(d)σj	ψk(d)σj	PUNCT
ejpam-4200	323	5	.	.	PUNCT
ejpam-4200	324	1	then	then	ADV
ejpam-4200	324	2	a(x	a(x	PROPN
ejpam-4200	324	3	,	,	PUNCT
ejpam-4200	324	4	ξ	ξ	NOUN
ejpam-4200	324	5	)	)	PUNCT
ejpam-4200	324	6	=	=	PUNCT
ejpam-4200	325	1	+	+	ADP
ejpam-4200	325	2	∞∑	∞∑	NUM
ejpam-4200	325	3	j=0	j=0	PROPN
ejpam-4200	325	4	(	(	PUNCT
ejpam-4200	325	5	+	+	ADP
ejpam-4200	325	6	∞∑	∞∑	ADJ
ejpam-4200	325	7	k=0	k=0	ADV
ejpam-4200	325	8	akj	akj	ADJ
ejpam-4200	325	9	)	)	PUNCT
ejpam-4200	325	10	ψj(ξ	ψj(ξ	PROPN
ejpam-4200	325	11	)	)	PUNCT
ejpam-4200	325	12	.	.	PUNCT
ejpam-4200	326	1	(	(	PUNCT
ejpam-4200	326	2	11	11	NUM
ejpam-4200	326	3	)	)	PUNCT
ejpam-4200	326	4	m.	m.	NOUN
ejpam-4200	326	5	congo	congo	PROPN
ejpam-4200	326	6	,	,	PUNCT
ejpam-4200	326	7	m.	m.	PROPN
ejpam-4200	326	8	f.	f.	PROPN
ejpam-4200	326	9	ouedraogo	ouedraogo	PROPN
ejpam-4200	326	10	/	/	SYM
ejpam-4200	326	11	eur	eur	PROPN
ejpam-4200	326	12	.	.	PUNCT
ejpam-4200	327	1	j.	j.	PROPN
ejpam-4200	327	2	pure	pure	PROPN
ejpam-4200	327	3	appl	appl	PROPN
ejpam-4200	327	4	.	.	PROPN
ejpam-4200	327	5	math	math	PROPN
ejpam-4200	327	6	,	,	PUNCT
ejpam-4200	327	7	15	15	NUM
ejpam-4200	327	8	(	(	PUNCT
ejpam-4200	327	9	1	1	NUM
ejpam-4200	327	10	)	)	PUNCT
ejpam-4200	327	11	(	(	PUNCT
ejpam-4200	327	12	2022	2022	NUM
ejpam-4200	327	13	)	)	PUNCT
ejpam-4200	327	14	,	,	PUNCT
ejpam-4200	327	15	47	47	NUM
ejpam-4200	327	16	-	-	SYM
ejpam-4200	327	17	63	63	NUM
ejpam-4200	327	18	59	59	NUM
ejpam-4200	327	19	(	(	PUNCT
ejpam-4200	327	20	i	i	NOUN
ejpam-4200	327	21	)	)	PUNCT
ejpam-4200	327	22	at	at	ADP
ejpam-4200	327	23	first	first	ADV
ejpam-4200	327	24	,	,	PUNCT
ejpam-4200	327	25	it	it	PRON
ejpam-4200	327	26	’s	’	VERB
ejpam-4200	327	27	necessary	necessary	ADJ
ejpam-4200	327	28	to	to	PART
ejpam-4200	327	29	estimate	estimate	VERB
ejpam-4200	327	30	∥akj∥l∞	∥akj∥l∞	PUNCT
ejpam-4200	327	31	.	.	PUNCT
ejpam-4200	328	1	we	we	PRON
ejpam-4200	328	2	recall	recall	VERB
ejpam-4200	328	3	the	the	DET
ejpam-4200	328	4	quasinorm	quasinorm	NOUN
ejpam-4200	328	5	of	of	ADP
ejpam-4200	328	6	cℓ	cℓ	ADP
ejpam-4200	328	7	∗	∗	NOUN
ejpam-4200	328	8	:	:	PUNCT
ejpam-4200	328	9	∥ψk(d)σj∥cℓ	∥ψk(d)σj∥cℓ	NOUN
ejpam-4200	328	10	∗	∗	NOUN
ejpam-4200	328	11	=	=	PUNCT
ejpam-4200	328	12	supk	supk	PRON
ejpam-4200	328	13	2	2	NUM
ejpam-4200	328	14	kℓ	kℓ	NOUN
ejpam-4200	328	15	∥ψk(d)σj∥l∞	∥ψk(d)σj∥l∞	NOUN
ejpam-4200	328	16	.	.	PUNCT
ejpam-4200	329	1	since	since	SCONJ
ejpam-4200	329	2	∥ψk(d)σj∥cℓ	∥ψk(d)σj∥cℓ	NOUN
ejpam-4200	329	3	∗	∗	NOUN
ejpam-4200	329	4	≤	≤	NUM
ejpam-4200	329	5	c	c	NOUN
ejpam-4200	329	6	∥σj∥cℓ	∥σj∥cℓ	PRON
ejpam-4200	329	7	∗	∗	NOUN
ejpam-4200	329	8	.	.	PUNCT
ejpam-4200	330	1	then	then	ADV
ejpam-4200	330	2	sup	sup	NOUN
ejpam-4200	330	3	k	k	PROPN
ejpam-4200	330	4	2kℓ	2kℓ	NOUN
ejpam-4200	330	5	∥ψk(d)σj∥l∞	∥ψk(d)σj∥l∞	ADP
ejpam-4200	330	6	≤	≤	NOUN
ejpam-4200	330	7	c	c	NOUN
ejpam-4200	331	1	∥σj∥cℓ	∥σj∥cℓ	NOUN
ejpam-4200	331	2	∗	∗	NOUN
ejpam-4200	331	3	.	.	PUNCT
ejpam-4200	332	1	using	use	VERB
ejpam-4200	332	2	(	(	PUNCT
ejpam-4200	332	3	9	9	NUM
ejpam-4200	332	4	)	)	PUNCT
ejpam-4200	332	5	,	,	PUNCT
ejpam-4200	332	6	we	we	PRON
ejpam-4200	332	7	obtain	obtain	VERB
ejpam-4200	332	8	∥akj∥l∞	∥akj∥l∞	PUNCT
ejpam-4200	332	9	≤	≤	NUM
ejpam-4200	332	10	c2j(m+ℓδ)2−kℓ.	c2j(m+ℓδ)2−kℓ.	NOUN
ejpam-4200	332	11	(	(	PUNCT
ejpam-4200	332	12	12	12	NUM
ejpam-4200	332	13	)	)	PUNCT
ejpam-4200	332	14	note	note	NOUN
ejpam-4200	332	15	that	that	SCONJ
ejpam-4200	332	16	(	(	PUNCT
ejpam-4200	332	17	1	1	NUM
ejpam-4200	332	18	−	−	PROPN
ejpam-4200	332	19	∆	∆	PROPN
ejpam-4200	332	20	)	)	PUNCT
ejpam-4200	333	1	m	m	PROPN
ejpam-4200	333	2	2	2	NUM
ejpam-4200	333	3	,	,	PUNCT
ejpam-4200	333	4	m	m	VERB
ejpam-4200	333	5	∈	∈	NOUN
ejpam-4200	333	6	r	r	NOUN
ejpam-4200	333	7	is	be	AUX
ejpam-4200	333	8	an	an	DET
ejpam-4200	333	9	isomorphism	isomorphism	NOUN
ejpam-4200	333	10	that	that	PRON
ejpam-4200	333	11	composes	compose	VERB
ejpam-4200	333	12	well	well	ADV
ejpam-4200	333	13	with	with	ADP
ejpam-4200	333	14	pseudodifferential	pseudodifferential	ADJ
ejpam-4200	333	15	operators	operator	NOUN
ejpam-4200	333	16	(	(	PUNCT
ejpam-4200	333	17	see[14	see[14	PROPN
ejpam-4200	333	18	]	]	PUNCT
ejpam-4200	333	19	and	and	CCONJ
ejpam-4200	333	20	[	[	X
ejpam-4200	333	21	15	15	NUM
ejpam-4200	333	22	]	]	NUM
ejpam-4200	333	23	)	)	PUNCT
ejpam-4200	333	24	.	.	PUNCT
ejpam-4200	334	1	therefore	therefore	ADV
ejpam-4200	334	2	,	,	PUNCT
ejpam-4200	334	3	it	it	PRON
ejpam-4200	334	4	is	be	AUX
ejpam-4200	334	5	enough	enough	ADJ
ejpam-4200	334	6	to	to	PART
ejpam-4200	334	7	examine	examine	VERB
ejpam-4200	334	8	the	the	DET
ejpam-4200	334	9	casem	casem	NOUN
ejpam-4200	334	10	=	=	PROPN
ejpam-4200	334	11	0	0	PROPN
ejpam-4200	334	12	.	.	PUNCT
ejpam-4200	335	1	if	if	SCONJ
ejpam-4200	335	2	m	m	ADV
ejpam-4200	335	3	=	=	X
ejpam-4200	335	4	0	0	PUNCT
ejpam-4200	335	5	then	then	ADV
ejpam-4200	335	6	∥akj∥l∞	∥akj∥l∞	CCONJ
ejpam-4200	335	7	≤	≤	NUM
ejpam-4200	335	8	c2jℓδ2−kℓ	c2jℓδ2−kℓ	NOUN
ejpam-4200	335	9	(	(	PUNCT
ejpam-4200	335	10	13	13	NUM
ejpam-4200	335	11	)	)	PUNCT
ejpam-4200	335	12	(	(	PUNCT
ejpam-4200	335	13	ii	ii	NOUN
ejpam-4200	335	14	)	)	PUNCT
ejpam-4200	335	15	now	now	ADV
ejpam-4200	335	16	we	we	PRON
ejpam-4200	335	17	rewrite	rewrite	VERB
ejpam-4200	335	18	the	the	DET
ejpam-4200	335	19	symbol	symbol	NOUN
ejpam-4200	335	20	as	as	ADP
ejpam-4200	335	21	a	a	DET
ejpam-4200	335	22	sum	sum	NOUN
ejpam-4200	335	23	of	of	ADP
ejpam-4200	335	24	three	three	NUM
ejpam-4200	335	25	parts	part	NOUN
ejpam-4200	335	26	a(x	a(x	NOUN
ejpam-4200	335	27	,	,	PUNCT
ejpam-4200	335	28	ξ	ξ	NOUN
ejpam-4200	335	29	)	)	PUNCT
ejpam-4200	335	30	=	=	SYM
ejpam-4200	336	1	∑	∑	PUNCT
ejpam-4200	336	2	j≥0	j≥0	PROPN
ejpam-4200	336	3	j−4∑	j−4∑	ADP
ejpam-4200	336	4	k=0	k=0	PROPN
ejpam-4200	336	5	akj(x	akj(x	PROPN
ejpam-4200	336	6	)	)	PUNCT
ejpam-4200	336	7	+	+	CCONJ
ejpam-4200	336	8	j+3∑	j+3∑	PROPN
ejpam-4200	336	9	k	k	PROPN
ejpam-4200	336	10	=	=	PROPN
ejpam-4200	336	11	j−3	j−3	PROPN
ejpam-4200	336	12	akj(x	akj(x	PROPN
ejpam-4200	336	13	)	)	PUNCT
ejpam-4200	336	14	+	+	CCONJ
ejpam-4200	337	1	∞∑	∞∑	NUM
ejpam-4200	337	2	k	k	X
ejpam-4200	337	3	=	=	SYM
ejpam-4200	337	4	j+4	j+4	NUM
ejpam-4200	337	5	akj(x	akj(x	NOUN
ejpam-4200	337	6	)	)	PUNCT
ejpam-4200	337	7	ψj(ξ	ψj(ξ	PUNCT
ejpam-4200	337	8	)	)	PUNCT
ejpam-4200	338	1	=	=	PUNCT
ejpam-4200	338	2	a1(x	a1(x	PROPN
ejpam-4200	338	3	,	,	PUNCT
ejpam-4200	338	4	ξ	ξ	NOUN
ejpam-4200	338	5	)	)	PUNCT
ejpam-4200	338	6	+	+	CCONJ
ejpam-4200	338	7	a2(x	a2(x	PROPN
ejpam-4200	338	8	,	,	PUNCT
ejpam-4200	338	9	ξ	ξ	X
ejpam-4200	338	10	)	)	PUNCT
ejpam-4200	338	11	+	+	CCONJ
ejpam-4200	338	12	a3(x	a3(x	PROPN
ejpam-4200	338	13	,	,	PUNCT
ejpam-4200	338	14	ξ	ξ	NOUN
ejpam-4200	338	15	)	)	PUNCT
ejpam-4200	338	16	where	where	SCONJ
ejpam-4200	338	17	a1(x	a1(x	NOUN
ejpam-4200	338	18	,	,	PUNCT
ejpam-4200	338	19	d)f	d)f	X
ejpam-4200	338	20	=	=	PUNCT
ejpam-4200	339	1	+	+	ADJ
ejpam-4200	339	2	∞∑	∞∑	NUM
ejpam-4200	339	3	j=0	j=0	PROPN
ejpam-4200	339	4	(	(	PUNCT
ejpam-4200	339	5	j−4∑	j−4∑	ADV
ejpam-4200	339	6	k=0	k=0	PROPN
ejpam-4200	339	7	akjψj(d)f	akjψj(d)f	NUM
ejpam-4200	339	8	)	)	PUNCT
ejpam-4200	339	9	,	,	PUNCT
ejpam-4200	339	10	a2(x	a2(x	PROPN
ejpam-4200	339	11	,	,	PUNCT
ejpam-4200	339	12	d)f	d)f	X
ejpam-4200	339	13	=	=	PUNCT
ejpam-4200	340	1	+	+	ADP
ejpam-4200	340	2	∞∑	∞∑	NUM
ejpam-4200	340	3	j=0	j=0	ADJ
ejpam-4200	340	4			PROPN
ejpam-4200	340	5	j+3∑	j+3∑	PROPN
ejpam-4200	340	6	k	k	PROPN
ejpam-4200	340	7	=	=	PROPN
ejpam-4200	340	8	j−3	j−3	NOUN
ejpam-4200	340	9	akjψj(d)f	akjψj(d)f	NOUN
ejpam-4200	341	1			PROPN
ejpam-4200	341	2	,	,	PUNCT
ejpam-4200	341	3	a3(x	a3(x	PROPN
ejpam-4200	341	4	,	,	PUNCT
ejpam-4200	341	5	d)f	d)f	X
ejpam-4200	341	6	=	=	PUNCT
ejpam-4200	342	1	+	+	ADP
ejpam-4200	342	2	∞∑	∞∑	NUM
ejpam-4200	342	3	j=0	j=0	PRON
ejpam-4200	342	4			PROPN
ejpam-4200	342	5	∞∑	∞∑	ADJ
ejpam-4200	342	6	k	k	X
ejpam-4200	342	7	=	=	X
ejpam-4200	342	8	j+4	j+4	PRON
ejpam-4200	342	9	akjψj(d)f	akjψj(d)f	NOUN
ejpam-4200	343	1			PROPN
ejpam-4200	343	2	.	.	PUNCT
ejpam-4200	343	3	•we	•we	PROPN
ejpam-4200	343	4	have	have	VERB
ejpam-4200	343	5	f	f	PROPN
ejpam-4200	343	6	(	(	PUNCT
ejpam-4200	343	7	j−4∑	j−4∑	ADV
ejpam-4200	343	8	k=0	k=0	PROPN
ejpam-4200	343	9	akjfj	akjfj	NOUN
ejpam-4200	343	10	)	)	PUNCT
ejpam-4200	344	1	=	=	PUNCT
ejpam-4200	344	2	j−4∑	j−4∑	X
ejpam-4200	344	3	k=0	k=0	PROPN
ejpam-4200	344	4	f	f	PROPN
ejpam-4200	344	5	(	(	PUNCT
ejpam-4200	344	6	ψk(d)σj	ψk(d)σj	CCONJ
ejpam-4200	344	7	)	)	PUNCT
ejpam-4200	344	8	∗	∗	NOUN
ejpam-4200	344	9	f	f	PROPN
ejpam-4200	344	10	(	(	PUNCT
ejpam-4200	344	11	ψj(d)f	ψj(d)f	PROPN
ejpam-4200	344	12	)	)	PUNCT
ejpam-4200	345	1	=	=	PUNCT
ejpam-4200	346	1	j−4∑	j−4∑	NOUN
ejpam-4200	346	2	k=0	k=0	PROPN
ejpam-4200	346	3	(	(	PUNCT
ejpam-4200	346	4	ψkfσj	ψkfσj	NOUN
ejpam-4200	346	5	)	)	PUNCT
ejpam-4200	346	6	∗	∗	NOUN
ejpam-4200	346	7	(	(	PUNCT
ejpam-4200	346	8	ψjff	ψjff	PROPN
ejpam-4200	346	9	)	)	PUNCT
ejpam-4200	346	10	.	.	PUNCT
ejpam-4200	347	1	using	use	VERB
ejpam-4200	347	2	the	the	DET
ejpam-4200	347	3	fact	fact	NOUN
ejpam-4200	347	4	that	that	SCONJ
ejpam-4200	347	5	supp(f	supp(f	PROPN
ejpam-4200	347	6	∗	∗	VERB
ejpam-4200	347	7	g	g	NOUN
ejpam-4200	347	8	)	)	PUNCT
ejpam-4200	348	1	⊂	⊂	PROPN
ejpam-4200	348	2	suppf+suppg	suppf+suppg	PROPN
ejpam-4200	348	3	for	for	ADP
ejpam-4200	348	4	all	all	PRON
ejpam-4200	348	5	compactly	compactly	ADV
ejpam-4200	348	6	supported	support	VERB
ejpam-4200	348	7	distributions	distribution	NOUN
ejpam-4200	348	8	f	f	NOUN
ejpam-4200	348	9	,	,	PUNCT
ejpam-4200	348	10	g	g	PROPN
ejpam-4200	348	11	∈	∈	PROPN
ejpam-4200	348	12	s	s	PART
ejpam-4200	348	13	′	′	NOUN
ejpam-4200	348	14	,	,	PUNCT
ejpam-4200	348	15	we	we	PRON
ejpam-4200	348	16	have	have	VERB
ejpam-4200	348	17	suppf	suppf	NOUN
ejpam-4200	348	18	(	(	PUNCT
ejpam-4200	348	19	j−4∑	j−4∑	ADV
ejpam-4200	348	20	k=0	k=0	PROPN
ejpam-4200	348	21	akjfj	akjfj	PROPN
ejpam-4200	348	22	)	)	PUNCT
ejpam-4200	349	1	⊂	⊂	PROPN
ejpam-4200	349	2	{	{	PUNCT
ejpam-4200	349	3	ξ	ξ	PROPN
ejpam-4200	349	4	∈	∈	PROPN
ejpam-4200	349	5	rn	rn	PROPN
ejpam-4200	349	6	:	:	PUNCT
ejpam-4200	349	7	c12	c12	PROPN
ejpam-4200	349	8	j−1	j−1	PROPN
ejpam-4200	349	9	≤	≤	PROPN
ejpam-4200	349	10	|ξ|	|ξ|	PROPN
ejpam-4200	349	11	≤	≤	PROPN
ejpam-4200	349	12	c22	c22	NOUN
ejpam-4200	349	13	j+1	j+1	PROPN
ejpam-4200	349	14	}	}	PUNCT
ejpam-4200	349	15	with	with	ADP
ejpam-4200	349	16	c1	c1	PROPN
ejpam-4200	349	17	,	,	PUNCT
ejpam-4200	349	18	c2	c2	PROPN
ejpam-4200	349	19	>	>	X
ejpam-4200	349	20	0	0	PROPN
ejpam-4200	349	21	.	.	PUNCT
ejpam-4200	350	1	then	then	ADV
ejpam-4200	350	2	lemma	lemma	PROPN
ejpam-4200	350	3	7	7	NUM
ejpam-4200	350	4	yields	yield	NOUN
ejpam-4200	350	5	m.	m.	NOUN
ejpam-4200	350	6	congo	congo	PROPN
ejpam-4200	350	7	,	,	PUNCT
ejpam-4200	350	8	m.	m.	PROPN
ejpam-4200	350	9	f.	f.	PROPN
ejpam-4200	350	10	ouedraogo	ouedraogo	PROPN
ejpam-4200	350	11	/	/	SYM
ejpam-4200	350	12	eur	eur	PROPN
ejpam-4200	350	13	.	.	PUNCT
ejpam-4200	351	1	j.	j.	PROPN
ejpam-4200	351	2	pure	pure	PROPN
ejpam-4200	351	3	appl	appl	PROPN
ejpam-4200	351	4	.	.	PROPN
ejpam-4200	351	5	math	math	PROPN
ejpam-4200	351	6	,	,	PUNCT
ejpam-4200	351	7	15	15	NUM
ejpam-4200	351	8	(	(	PUNCT
ejpam-4200	351	9	1	1	NUM
ejpam-4200	351	10	)	)	PUNCT
ejpam-4200	351	11	(	(	PUNCT
ejpam-4200	351	12	2022	2022	NUM
ejpam-4200	351	13	)	)	PUNCT
ejpam-4200	351	14	,	,	PUNCT
ejpam-4200	351	15	47	47	NUM
ejpam-4200	351	16	-	-	SYM
ejpam-4200	351	17	63	63	NUM
ejpam-4200	351	18	60	60	NUM
ejpam-4200	351	19	∥a1(x	∥a1(x	NUM
ejpam-4200	351	20	,	,	PUNCT
ejpam-4200	351	21	d)f∥es	d)f∥e	NOUN
ejpam-4200	351	22	(	(	PUNCT
ejpam-4200	351	23	·	·	PUNCT
ejpam-4200	351	24	)	)	PUNCT
ejpam-4200	351	25	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	351	26	(	(	PUNCT
ejpam-4200	351	27	·	·	PUNCT
ejpam-4200	351	28	)	)	PUNCT
ejpam-4200	351	29	=	=	SYM
ejpam-4200	351	30	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	352	1	+	+	ADJ
ejpam-4200	352	2	∞∑	∞∑	NUM
ejpam-4200	352	3	j=0	j=0	PROPN
ejpam-4200	352	4	(	(	PUNCT
ejpam-4200	352	5	j−4∑	j−4∑	ADV
ejpam-4200	352	6	k=0	k=0	PROPN
ejpam-4200	352	7	akjψj(d)f	akjψj(d)f	NUM
ejpam-4200	352	8	)	)	PUNCT
ejpam-4200	352	9	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	352	10	es	es	PRON
ejpam-4200	352	11	(	(	PUNCT
ejpam-4200	352	12	·	·	PUNCT
ejpam-4200	352	13	)	)	PUNCT
ejpam-4200	352	14	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	352	15	(	(	PUNCT
ejpam-4200	352	16	·	·	PUNCT
ejpam-4200	352	17	)	)	PUNCT
ejpam-4200	352	18	≲	≲	PROPN
ejpam-4200	352	19	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	353	1	(	(	PUNCT
ejpam-4200	353	2	2js	2js	NOUN
ejpam-4200	353	3	(	(	PUNCT
ejpam-4200	353	4	·	·	PUNCT
ejpam-4200	353	5	)	)	PUNCT
ejpam-4200	353	6	j−4∑	j−4∑	ADP
ejpam-4200	354	1	k=0	k=0	PROPN
ejpam-4200	354	2	akjψj(d)f	akjψj(d)f	PROPN
ejpam-4200	354	3	)	)	PUNCT
ejpam-4200	355	1	j	j	PROPN
ejpam-4200	355	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	356	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	356	2	(	(	PUNCT
ejpam-4200	356	3	·	·	PUNCT
ejpam-4200	356	4	)	)	PUNCT
ejpam-4200	356	5	)	)	PUNCT
ejpam-4200	357	1	≲	≲	PROPN
ejpam-4200	357	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	357	3	(	(	PUNCT
ejpam-4200	357	4	j−4∑	j−4∑	X
ejpam-4200	357	5	k=0	k=0	PUNCT
ejpam-4200	357	6	∥σj∥l∞	∥σj∥l∞	X
ejpam-4200	357	7	2js(·)ψj(d)f	2js(·)ψj(d)f	NUM
ejpam-4200	357	8	)	)	PUNCT
ejpam-4200	357	9	j	j	PROPN
ejpam-4200	357	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	358	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	358	2	(	(	PUNCT
ejpam-4200	358	3	·	·	PUNCT
ejpam-4200	358	4	)	)	PUNCT
ejpam-4200	358	5	)	)	PUNCT
ejpam-4200	359	1	≲	≲	PROPN
ejpam-4200	359	2	∥∥∥∥(2js(·)ψj(d)f	∥∥∥∥(2js(·)ψj(d)f	NUM
ejpam-4200	359	3	)	)	PUNCT
ejpam-4200	359	4	j	j	PROPN
ejpam-4200	359	5	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4200	359	6	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	359	7	(	(	PUNCT
ejpam-4200	359	8	·	·	PUNCT
ejpam-4200	359	9	)	)	PUNCT
ejpam-4200	359	10	)	)	PUNCT
ejpam-4200	359	11	.	.	PUNCT
ejpam-4200	360	1	then	then	ADV
ejpam-4200	360	2	∥a1(x	∥a1(x	NOUN
ejpam-4200	360	3	,	,	PUNCT
ejpam-4200	360	4	d)f∥es	d)f∥e	NOUN
ejpam-4200	360	5	(	(	PUNCT
ejpam-4200	360	6	·	·	PUNCT
ejpam-4200	360	7	)	)	PUNCT
ejpam-4200	360	8	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	360	9	(	(	PUNCT
ejpam-4200	360	10	·	·	PUNCT
ejpam-4200	360	11	)	)	PUNCT
ejpam-4200	360	12	≲	≲	PROPN
ejpam-4200	360	13	∥f∥es	∥f∥es	PROPN
ejpam-4200	360	14	(	(	PUNCT
ejpam-4200	360	15	·	·	PUNCT
ejpam-4200	360	16	)	)	PUNCT
ejpam-4200	360	17	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	360	18	(	(	PUNCT
ejpam-4200	360	19	·	·	PUNCT
ejpam-4200	360	20	)	)	PUNCT
ejpam-4200	360	21	.	.	PUNCT
ejpam-4200	361	1	•for	•for	ADP
ejpam-4200	361	2	the	the	DET
ejpam-4200	361	3	second	second	ADJ
ejpam-4200	361	4	part	part	NOUN
ejpam-4200	361	5	∥a2(x	∥a2(x	PROPN
ejpam-4200	361	6	,	,	PUNCT
ejpam-4200	361	7	d)f∥es	d)f∥e	NOUN
ejpam-4200	361	8	(	(	PUNCT
ejpam-4200	361	9	·	·	PUNCT
ejpam-4200	361	10	)	)	PUNCT
ejpam-4200	361	11	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	361	12	(	(	PUNCT
ejpam-4200	361	13	·	·	PUNCT
ejpam-4200	361	14	)	)	PUNCT
ejpam-4200	361	15	=	=	SYM
ejpam-4200	361	16	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	362	1	+	+	ADJ
ejpam-4200	362	2	∞∑	∞∑	NUM
ejpam-4200	362	3	j=0	j=0	PRON
ejpam-4200	362	4			PROPN
ejpam-4200	362	5	j+3∑	j+3∑	PROPN
ejpam-4200	362	6	k	k	PROPN
ejpam-4200	362	7	=	=	NOUN
ejpam-4200	362	8	j−3	j−3	NUM
ejpam-4200	362	9	akjfj	akjfj	NOUN
ejpam-4200	362	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	363	1	es	es	PROPN
ejpam-4200	364	1	(	(	PUNCT
ejpam-4200	364	2	·	·	PUNCT
ejpam-4200	364	3	)	)	PUNCT
ejpam-4200	364	4	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	364	5	(	(	PUNCT
ejpam-4200	364	6	·	·	PUNCT
ejpam-4200	364	7	)	)	PUNCT
ejpam-4200	365	1	,	,	PUNCT
ejpam-4200	365	2	we	we	PRON
ejpam-4200	365	3	observe	observe	VERB
ejpam-4200	365	4	that	that	SCONJ
ejpam-4200	365	5	f	f	PROPN
ejpam-4200	365	6			PROPN
ejpam-4200	365	7	j+3∑	j+3∑	PROPN
ejpam-4200	366	1	k	k	PROPN
ejpam-4200	366	2	=	=	ADJ
ejpam-4200	366	3	j−3	j−3	ADJ
ejpam-4200	366	4	akjfj	akjfj	NOUN
ejpam-4200	366	5			PROPN
ejpam-4200	366	6	=	=	SYM
ejpam-4200	366	7	j+3∑	j+3∑	PROPN
ejpam-4200	367	1	k	k	PROPN
ejpam-4200	367	2	=	=	PROPN
ejpam-4200	367	3	j−3	j−3	PROPN
ejpam-4200	367	4	f	f	X
ejpam-4200	367	5	(	(	PUNCT
ejpam-4200	367	6	ψk(d)σj	ψk(d)σj	CCONJ
ejpam-4200	367	7	)	)	PUNCT
ejpam-4200	367	8	∗	∗	NOUN
ejpam-4200	367	9	f	f	PROPN
ejpam-4200	367	10	(	(	PUNCT
ejpam-4200	367	11	ψj(d)f	ψj(d)f	PROPN
ejpam-4200	367	12	)	)	PUNCT
ejpam-4200	367	13	=	=	SYM
ejpam-4200	368	1	j+3∑	j+3∑	PROPN
ejpam-4200	369	1	k	k	X
ejpam-4200	369	2	=	=	X
ejpam-4200	369	3	j−3	j−3	X
ejpam-4200	369	4	(	(	PUNCT
ejpam-4200	369	5	ψkfσj	ψkfσj	NOUN
ejpam-4200	369	6	)	)	PUNCT
ejpam-4200	369	7	∗	∗	NOUN
ejpam-4200	369	8	(	(	PUNCT
ejpam-4200	369	9	ψjff	ψjff	PROPN
ejpam-4200	369	10	)	)	PUNCT
ejpam-4200	369	11	.	.	PUNCT
ejpam-4200	370	1	then	then	ADV
ejpam-4200	370	2	f	f	PROPN
ejpam-4200	370	3			PROPN
ejpam-4200	370	4	j+3∑	j+3∑	PROPN
ejpam-4200	370	5	k	k	PROPN
ejpam-4200	370	6	=	=	ADJ
ejpam-4200	370	7	j−3	j−3	PROPN
ejpam-4200	370	8	akjfj	akjfj	NOUN
ejpam-4200	370	9			PROPN
ejpam-4200	370	10	is	be	AUX
ejpam-4200	370	11	supported	support	VERB
ejpam-4200	370	12	on	on	ADP
ejpam-4200	370	13	the	the	DET
ejpam-4200	370	14	ball	ball	NOUN
ejpam-4200	370	15	b(0	b(0	NOUN
ejpam-4200	370	16	,	,	PUNCT
ejpam-4200	370	17	2j+4	2j+4	NOUN
ejpam-4200	370	18	)	)	PUNCT
ejpam-4200	370	19	.	.	PUNCT
ejpam-4200	371	1	by	by	ADP
ejpam-4200	371	2	lemma	lemma	PROPN
ejpam-4200	371	3	8	8	NUM
ejpam-4200	371	4	,	,	PUNCT
ejpam-4200	371	5	∥a2(x	∥a2(x	NOUN
ejpam-4200	371	6	,	,	PUNCT
ejpam-4200	371	7	d)f∥es	d)f∥e	NOUN
ejpam-4200	371	8	(	(	PUNCT
ejpam-4200	371	9	·	·	PUNCT
ejpam-4200	371	10	)	)	PUNCT
ejpam-4200	371	11	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	371	12	(	(	PUNCT
ejpam-4200	371	13	·	·	PUNCT
ejpam-4200	371	14	)	)	PUNCT
ejpam-4200	371	15	≲	≲	PROPN
ejpam-4200	371	16	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	371	17	2js	2js	ADP
ejpam-4200	371	18	(	(	PUNCT
ejpam-4200	371	19	·	·	PUNCT
ejpam-4200	371	20	)	)	PUNCT
ejpam-4200	371	21	j+3∑	j+3∑	PROPN
ejpam-4200	372	1	k	k	PROPN
ejpam-4200	372	2	=	=	PROPN
ejpam-4200	372	3	j−3	j−3	PROPN
ejpam-4200	372	4	akjfj	akjfj	NOUN
ejpam-4200	372	5			PROPN
ejpam-4200	372	6	j	j	PROPN
ejpam-4200	372	7	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	373	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	373	2	(	(	PUNCT
ejpam-4200	373	3	·	·	PUNCT
ejpam-4200	373	4	)	)	PUNCT
ejpam-4200	373	5	)	)	PUNCT
ejpam-4200	374	1	≤	≤	NUM
ejpam-4200	374	2	2−m	2−m	NUM
ejpam-4200	374	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	375	1			PROPN
ejpam-4200	375	2	j+3∑	j+3∑	PROPN
ejpam-4200	375	3	k	k	PROPN
ejpam-4200	375	4	=	=	PROPN
ejpam-4200	375	5	j−3	j−3	PROPN
ejpam-4200	375	6	∥akj∥l∞	∥akj∥l∞	NUM
ejpam-4200	375	7	2js(·)ψj(d)f	2js(·)ψj(d)f	NUM
ejpam-4200	375	8			PROPN
ejpam-4200	375	9	j	j	PROPN
ejpam-4200	375	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	375	11	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	375	12	(	(	PUNCT
ejpam-4200	375	13	·	·	PUNCT
ejpam-4200	375	14	)	)	PUNCT
ejpam-4200	375	15	)	)	PUNCT
ejpam-4200	375	16	.	.	PUNCT
ejpam-4200	376	1	m.	m.	NOUN
ejpam-4200	376	2	congo	congo	PROPN
ejpam-4200	376	3	,	,	PUNCT
ejpam-4200	376	4	m.	m.	PROPN
ejpam-4200	376	5	f.	f.	PROPN
ejpam-4200	376	6	ouedraogo	ouedraogo	PROPN
ejpam-4200	376	7	/	/	SYM
ejpam-4200	376	8	eur	eur	PROPN
ejpam-4200	376	9	.	.	PUNCT
ejpam-4200	377	1	j.	j.	PROPN
ejpam-4200	377	2	pure	pure	PROPN
ejpam-4200	377	3	appl	appl	PROPN
ejpam-4200	377	4	.	.	PROPN
ejpam-4200	377	5	math	math	PROPN
ejpam-4200	377	6	,	,	PUNCT
ejpam-4200	377	7	15	15	NUM
ejpam-4200	377	8	(	(	PUNCT
ejpam-4200	377	9	1	1	NUM
ejpam-4200	377	10	)	)	PUNCT
ejpam-4200	377	11	(	(	PUNCT
ejpam-4200	377	12	2022	2022	NUM
ejpam-4200	377	13	)	)	PUNCT
ejpam-4200	377	14	,	,	PUNCT
ejpam-4200	377	15	47	47	NUM
ejpam-4200	377	16	-	-	SYM
ejpam-4200	377	17	63	63	NUM
ejpam-4200	377	18	61	61	NUM
ejpam-4200	377	19	one	one	NUM
ejpam-4200	377	20	have	have	VERB
ejpam-4200	377	21	j+3∑	j+3∑	PROPN
ejpam-4200	377	22	k	k	PROPN
ejpam-4200	377	23	=	=	PROPN
ejpam-4200	377	24	j−3	j−3	NOUN
ejpam-4200	377	25	∥akj∥l∞	∥akj∥l∞	X
ejpam-4200	378	1	≲	≲	PROPN
ejpam-4200	378	2	3∑	3∑	PROPN
ejpam-4200	378	3	k=−3	k=−3	VERB
ejpam-4200	378	4	2−kℓ	2−kℓ	NUM
ejpam-4200	378	5	<	<	X
ejpam-4200	379	1	+	+	ADJ
ejpam-4200	379	2	∞	∞	PROPN
ejpam-4200	379	3	(	(	PUNCT
ejpam-4200	379	4	with	with	ADP
ejpam-4200	379	5	δ	δ	PROPN
ejpam-4200	379	6	=	=	SYM
ejpam-4200	379	7	1	1	NUM
ejpam-4200	379	8	)	)	PUNCT
ejpam-4200	379	9	.	.	PUNCT
ejpam-4200	380	1	then	then	ADV
ejpam-4200	380	2	∥a2(x	∥a2(x	ADV
ejpam-4200	380	3	,	,	PUNCT
ejpam-4200	380	4	d)f∥es	d)f∥e	NOUN
ejpam-4200	380	5	(	(	PUNCT
ejpam-4200	380	6	·	·	PUNCT
ejpam-4200	380	7	)	)	PUNCT
ejpam-4200	380	8	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	380	9	(	(	PUNCT
ejpam-4200	380	10	·	·	PUNCT
ejpam-4200	380	11	)	)	PUNCT
ejpam-4200	380	12	≲	≲	PROPN
ejpam-4200	380	13	∥∥∥∥(2js(·)ψj(d)f	∥∥∥∥(2js(·)ψj(d)f	NUM
ejpam-4200	380	14	)	)	PUNCT
ejpam-4200	381	1	j	j	PROPN
ejpam-4200	381	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-4200	381	3	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	381	4	(	(	PUNCT
ejpam-4200	381	5	·	·	PUNCT
ejpam-4200	381	6	)	)	PUNCT
ejpam-4200	381	7	)	)	PUNCT
ejpam-4200	382	1	≲	≲	PROPN
ejpam-4200	382	2	∥f∥es	∥f∥es	PROPN
ejpam-4200	382	3	(	(	PUNCT
ejpam-4200	382	4	·	·	PUNCT
ejpam-4200	382	5	)	)	PUNCT
ejpam-4200	382	6	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	382	7	(	(	PUNCT
ejpam-4200	382	8	·	·	PUNCT
ejpam-4200	382	9	)	)	PUNCT
ejpam-4200	382	10	.	.	PUNCT
ejpam-4200	383	1	•	•	ADV
ejpam-4200	383	2	now	now	ADV
ejpam-4200	383	3	let	let	VERB
ejpam-4200	383	4	us	we	PRON
ejpam-4200	383	5	estimate	estimate	VERB
ejpam-4200	383	6	last	last	ADJ
ejpam-4200	383	7	part	part	NOUN
ejpam-4200	383	8	.	.	PUNCT
ejpam-4200	384	1	since	since	SCONJ
ejpam-4200	384	2	f	f	PROPN
ejpam-4200	384	3			PROPN
ejpam-4200	384	4	+	+	PROPN
ejpam-4200	384	5	∞∑	∞∑	PROPN
ejpam-4200	384	6	k	k	X
ejpam-4200	384	7	=	=	SYM
ejpam-4200	384	8	j+4	j+4	NUM
ejpam-4200	384	9	akjfj	akjfj	NOUN
ejpam-4200	384	10			PROPN
ejpam-4200	384	11	is	be	AUX
ejpam-4200	384	12	not	not	PART
ejpam-4200	384	13	supported	support	VERB
ejpam-4200	384	14	on	on	ADP
ejpam-4200	384	15	any	any	DET
ejpam-4200	384	16	ball	ball	NOUN
ejpam-4200	384	17	or	or	CCONJ
ejpam-4200	384	18	shell	shell	NOUN
ejpam-4200	384	19	,	,	PUNCT
ejpam-4200	384	20	we	we	PRON
ejpam-4200	384	21	can	can	AUX
ejpam-4200	384	22	not	not	PART
ejpam-4200	384	23	directly	directly	ADV
ejpam-4200	384	24	use	use	VERB
ejpam-4200	384	25	neither	neither	DET
ejpam-4200	384	26	lemma7	lemma7	NOUN
ejpam-4200	384	27	nor	nor	CCONJ
ejpam-4200	384	28	lemma8	lemma8	NOUN
ejpam-4200	384	29	.	.	PUNCT
ejpam-4200	385	1	however	however	ADV
ejpam-4200	385	2	,	,	PUNCT
ejpam-4200	385	3	in	in	ADP
ejpam-4200	385	4	s	s	PRON
ejpam-4200	385	5	′	′	NOUN
ejpam-4200	385	6	we	we	PRON
ejpam-4200	385	7	can	can	AUX
ejpam-4200	385	8	write	write	VERB
ejpam-4200	385	9	+	+	NOUN
ejpam-4200	385	10	∞∑	∞∑	NUM
ejpam-4200	385	11	j=0	j=0	ADJ
ejpam-4200	386	1	+	+	PRON
ejpam-4200	386	2	∞∑	∞∑	ADJ
ejpam-4200	386	3	k	k	X
ejpam-4200	386	4	=	=	SYM
ejpam-4200	386	5	j+4	j+4	NUM
ejpam-4200	386	6	akjfj	akjfj	NOUN
ejpam-4200	386	7	=	=	PUNCT
ejpam-4200	387	1	+	+	ADP
ejpam-4200	387	2	∞∑	∞∑	ADJ
ejpam-4200	387	3	k=4	k=4	PROPN
ejpam-4200	387	4	k−4∑	k−4∑	PROPN
ejpam-4200	387	5	j=0	j=0	PROPN
ejpam-4200	387	6	akjfj	akjfj	PROPN
ejpam-4200	387	7	.	.	PUNCT
ejpam-4200	388	1	we	we	PRON
ejpam-4200	388	2	have	have	VERB
ejpam-4200	388	3	f	f	PROPN
ejpam-4200	388	4	k−4∑	k−4∑	VERB
ejpam-4200	388	5	j=0	j=0	PROPN
ejpam-4200	388	6	akjfj	akjfj	VERB
ejpam-4200	388	7			PROPN
ejpam-4200	388	8	=	=	SYM
ejpam-4200	388	9	k−4∑	k−4∑	PROPN
ejpam-4200	388	10	j=0	j=0	PROPN
ejpam-4200	388	11	(	(	PUNCT
ejpam-4200	388	12	ψkfaj	ψkfaj	NOUN
ejpam-4200	388	13	)	)	PUNCT
ejpam-4200	388	14	∗	∗	NOUN
ejpam-4200	388	15	(	(	PUNCT
ejpam-4200	388	16	ψjff	ψjff	PROPN
ejpam-4200	388	17	)	)	PUNCT
ejpam-4200	388	18	.	.	PUNCT
ejpam-4200	389	1	we	we	PRON
ejpam-4200	389	2	have	have	VERB
ejpam-4200	389	3	suppf	suppf	NOUN
ejpam-4200	389	4	(	(	PUNCT
ejpam-4200	389	5	j−4∑	j−4∑	ADV
ejpam-4200	389	6	k=0	k=0	PROPN
ejpam-4200	389	7	akjfj	akjfj	PROPN
ejpam-4200	389	8	)	)	PUNCT
ejpam-4200	390	1	⊂	⊂	PROPN
ejpam-4200	390	2	{	{	PUNCT
ejpam-4200	390	3	ξ	ξ	X
ejpam-4200	390	4	∈	∈	PROPN
ejpam-4200	390	5	rn|	rn|	PROPN
ejpam-4200	390	6	c12	c12	PROPN
ejpam-4200	390	7	j−1	j−1	PROPN
ejpam-4200	390	8	≤	≤	PROPN
ejpam-4200	390	9	|ξ|	|ξ|	PROPN
ejpam-4200	390	10	≤	≤	PROPN
ejpam-4200	390	11	c22	c22	NOUN
ejpam-4200	390	12	j+1	j+1	PROPN
ejpam-4200	390	13	}	}	PUNCT
ejpam-4200	390	14	with	with	ADP
ejpam-4200	390	15	c1	c1	PROPN
ejpam-4200	390	16	,	,	PUNCT
ejpam-4200	390	17	c2	c2	PROPN
ejpam-4200	390	18	>	>	X
ejpam-4200	390	19	0	0	PROPN
ejpam-4200	390	20	.	.	PUNCT
ejpam-4200	391	1	thus	thus	ADV
ejpam-4200	391	2	we	we	PRON
ejpam-4200	391	3	can	can	AUX
ejpam-4200	391	4	use	use	VERB
ejpam-4200	391	5	lemma	lemma	PROPN
ejpam-4200	391	6	7	7	NUM
ejpam-4200	391	7	.	.	PUNCT
ejpam-4200	391	8	∥a3(x	∥a3(x	PROPN
ejpam-4200	391	9	,	,	PUNCT
ejpam-4200	391	10	d)f∥es	d)f∥e	NOUN
ejpam-4200	391	11	(	(	PUNCT
ejpam-4200	391	12	·	·	PUNCT
ejpam-4200	391	13	)	)	PUNCT
ejpam-4200	391	14	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	391	15	(	(	PUNCT
ejpam-4200	391	16	·	·	PUNCT
ejpam-4200	391	17	)	)	PUNCT
ejpam-4200	391	18	=	=	SYM
ejpam-4200	391	19	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	392	1	+	+	PUNCT
ejpam-4200	392	2	∞∑	∞∑	PROPN
ejpam-4200	392	3	k=4	k=4	PROPN
ejpam-4200	392	4	k−4∑	k−4∑	VERB
ejpam-4200	392	5	j=0	j=0	PROPN
ejpam-4200	392	6	akjfj	akjfj	PROPN
ejpam-4200	392	7	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	393	1	es	es	PROPN
ejpam-4200	393	2	(	(	PUNCT
ejpam-4200	393	3	·	·	PUNCT
ejpam-4200	393	4	)	)	PUNCT
ejpam-4200	393	5	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	393	6	(	(	PUNCT
ejpam-4200	393	7	·	·	PUNCT
ejpam-4200	393	8	)	)	PUNCT
ejpam-4200	394	1	≲	≲	PROPN
ejpam-4200	394	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	394	3	2ks	2ks	X
ejpam-4200	394	4	(	(	PUNCT
ejpam-4200	394	5	·	·	PUNCT
ejpam-4200	394	6	)	)	PUNCT
ejpam-4200	394	7	k−4∑	k−4∑	PROPN
ejpam-4200	394	8	j=0	j=0	PROPN
ejpam-4200	394	9	akjfj	akjfj	NOUN
ejpam-4200	394	10			PROPN
ejpam-4200	394	11	k	k	X
ejpam-4200	394	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	395	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	395	2	(	(	PUNCT
ejpam-4200	395	3	·	·	PUNCT
ejpam-4200	395	4	)	)	PUNCT
ejpam-4200	395	5	)	)	PUNCT
ejpam-4200	396	1	≲	≲	PROPN
ejpam-4200	396	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	396	3	k−4∑	k−4∑	VERB
ejpam-4200	396	4	j=0	j=0	PROPN
ejpam-4200	396	5	∥akj∥l∞	∥akj∥l∞	PROPN
ejpam-4200	396	6	2ks(·)ψj(d)f	2ks(·)ψj(d)f	NUM
ejpam-4200	397	1			PROPN
ejpam-4200	397	2	k	k	X
ejpam-4200	397	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	398	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	398	2	(	(	PUNCT
ejpam-4200	398	3	·	·	PUNCT
ejpam-4200	398	4	)	)	PUNCT
ejpam-4200	398	5	)	)	PUNCT
ejpam-4200	398	6	.	.	PUNCT
ejpam-4200	399	1	if	if	SCONJ
ejpam-4200	399	2	we	we	PRON
ejpam-4200	399	3	use(13	use(13	VERB
ejpam-4200	399	4	)	)	PUNCT
ejpam-4200	399	5	with	with	ADP
ejpam-4200	399	6	δ	δ	PROPN
ejpam-4200	399	7	=	=	SYM
ejpam-4200	399	8	1	1	NUM
ejpam-4200	399	9	,	,	PUNCT
ejpam-4200	399	10	we	we	PRON
ejpam-4200	399	11	have	have	VERB
ejpam-4200	399	12	∥a3(x	∥a3(x	PROPN
ejpam-4200	399	13	,	,	PUNCT
ejpam-4200	399	14	d)f∥es	d)f∥e	NOUN
ejpam-4200	399	15	(	(	PUNCT
ejpam-4200	399	16	·	·	PUNCT
ejpam-4200	399	17	)	)	PUNCT
ejpam-4200	399	18	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	399	19	(	(	PUNCT
ejpam-4200	399	20	·	·	PUNCT
ejpam-4200	399	21	)	)	PUNCT
ejpam-4200	400	1	≲	≲	PROPN
ejpam-4200	400	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	400	3	k−4∑	k−4∑	VERB
ejpam-4200	400	4	j=0	j=0	PROPN
ejpam-4200	401	1	2jℓ2−kℓ2ks(·)ψj(d)f	2jℓ2−kℓ2ks(·)ψj(d)f	PROPN
ejpam-4200	401	2			PROPN
ejpam-4200	401	3	k	k	X
ejpam-4200	401	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	402	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	402	2	(	(	PUNCT
ejpam-4200	402	3	·	·	PUNCT
ejpam-4200	402	4	)	)	PUNCT
ejpam-4200	402	5	)	)	PUNCT
ejpam-4200	402	6	references	reference	VERB
ejpam-4200	402	7	62	62	NUM
ejpam-4200	402	8	=	=	SYM
ejpam-4200	402	9	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	402	10	k−4∑	k−4∑	VERB
ejpam-4200	402	11	j=0	j=0	PROPN
ejpam-4200	403	1	2(k−j)(s(·)−ℓ)2js(·)ψj(d)f	2(k−j)(s(·)−ℓ)2js(·)ψj(d)f	PROPN
ejpam-4200	403	2			PROPN
ejpam-4200	403	3	k	k	X
ejpam-4200	403	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	404	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	404	2	(	(	PUNCT
ejpam-4200	404	3	·	·	PUNCT
ejpam-4200	404	4	)	)	PUNCT
ejpam-4200	404	5	)	)	PUNCT
ejpam-4200	405	1	≤	≤	NOUN
ejpam-4200	405	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4200	405	3	k−4∑	k−4∑	VERB
ejpam-4200	405	4	j=0	j=0	PROPN
ejpam-4200	405	5	2−|k−j||s−−ℓ|2js(·)ψj(d)f	2−|k−j||s−−ℓ|2js(·)ψj(d)f	PROPN
ejpam-4200	405	6			PROPN
ejpam-4200	405	7	k	k	X
ejpam-4200	405	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	406	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	406	2	(	(	PUNCT
ejpam-4200	406	3	·	·	PUNCT
ejpam-4200	406	4	)	)	PUNCT
ejpam-4200	406	5	)	)	PUNCT
ejpam-4200	407	1	≤	≤	NUM
ejpam-4200	407	2	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4200	408	1	+∞∑	+∞∑	PROPN
ejpam-4200	408	2	j=0	j=0	PROPN
ejpam-4200	408	3	2−|k−j||s−−ℓ|2js(·)ψj(d)f	2−|k−j||s−−ℓ|2js(·)ψj(d)f	PROPN
ejpam-4200	408	4			PROPN
ejpam-4200	408	5	k	k	X
ejpam-4200	408	6	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	409	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	409	2	(	(	PUNCT
ejpam-4200	409	3	·	·	PUNCT
ejpam-4200	409	4	)	)	PUNCT
ejpam-4200	409	5	)	)	PUNCT
ejpam-4200	409	6	.	.	PUNCT
ejpam-4200	410	1	by	by	ADP
ejpam-4200	410	2	hypothesis	hypothesis	NOUN
ejpam-4200	410	3	|s−	|s−	VERB
ejpam-4200	410	4	−	−	PROPN
ejpam-4200	410	5	ℓ|	ℓ|	PROPN
ejpam-4200	410	6	>	>	X
ejpam-4200	410	7	0	0	X
ejpam-4200	410	8	.	.	PUNCT
ejpam-4200	411	1	therefore	therefore	ADV
ejpam-4200	411	2	,	,	PUNCT
ejpam-4200	411	3	by	by	ADP
ejpam-4200	411	4	lemma	lemma	PROPN
ejpam-4200	411	5	5∥∥∥∥∥∥	5∥∥∥∥∥∥	NUM
ejpam-4200	411	6	k−4∑	k−4∑	VERB
ejpam-4200	411	7	j=0	j=0	PROPN
ejpam-4200	411	8	2−|k−j||s−−ℓ|2js(·)ψj(d)f	2−|k−j||s−−ℓ|2js(·)ψj(d)f	PROPN
ejpam-4200	412	1			PROPN
ejpam-4200	412	2	j	j	PROPN
ejpam-4200	412	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4200	413	1	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	413	2	(	(	PUNCT
ejpam-4200	413	3	·	·	PUNCT
ejpam-4200	413	4	)	)	PUNCT
ejpam-4200	413	5	)	)	PUNCT
ejpam-4200	414	1	≲	≲	PROPN
ejpam-4200	414	2	∥∥∥(2js(·)ψj(d)f	∥∥∥(2js(·)ψj(d)f	NUM
ejpam-4200	414	3	)	)	PUNCT
ejpam-4200	415	1	k	k	PROPN
ejpam-4200	415	2	∥∥∥	∥∥∥	PROPN
ejpam-4200	415	3	mp(·),u(·)(ℓq	mp(·),u(·)(ℓq	PROPN
ejpam-4200	415	4	(	(	PUNCT
ejpam-4200	415	5	·	·	PUNCT
ejpam-4200	415	6	)	)	PUNCT
ejpam-4200	415	7	)	)	PUNCT
ejpam-4200	415	8	.	.	PUNCT
ejpam-4200	416	1	then	then	ADV
ejpam-4200	416	2	∥a3(x	∥a3(x	PROPN
ejpam-4200	416	3	,	,	PUNCT
ejpam-4200	416	4	d)f∥es	d)f∥es	X
ejpam-4200	416	5	(	(	PUNCT
ejpam-4200	416	6	·	·	PUNCT
ejpam-4200	416	7	)	)	PUNCT
ejpam-4200	416	8	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	416	9	(	(	PUNCT
ejpam-4200	416	10	·	·	PUNCT
ejpam-4200	416	11	)	)	PUNCT
ejpam-4200	416	12	≲	≲	PROPN
ejpam-4200	416	13	∥f∥es	∥f∥es	PROPN
ejpam-4200	416	14	(	(	PUNCT
ejpam-4200	416	15	·	·	PUNCT
ejpam-4200	416	16	)	)	PUNCT
ejpam-4200	416	17	p(·),u(·),q	p(·),u(·),q	PROPN
ejpam-4200	416	18	(	(	PUNCT
ejpam-4200	416	19	·	·	PUNCT
ejpam-4200	416	20	)	)	PUNCT
ejpam-4200	416	21	.	.	PUNCT
ejpam-4200	417	1	the	the	DET
ejpam-4200	417	2	proof	proof	NOUN
ejpam-4200	417	3	is	be	AUX
ejpam-4200	417	4	completed	complete	VERB
ejpam-4200	417	5	.	.	PUNCT
ejpam-4200	418	1	□	□	PUNCT
ejpam-4200	418	2	references	reference	NOUN
ejpam-4200	418	3	[	[	X
ejpam-4200	418	4	1	1	NUM
ejpam-4200	418	5	]	]	PUNCT
ejpam-4200	418	6	a.	a.	PROPN
ejpam-4200	418	7	almeida	almeida	PROPN
ejpam-4200	418	8	and	and	CCONJ
ejpam-4200	418	9	a.	a.	PROPN
ejpam-4200	418	10	caetano	caetano	PROPN
ejpam-4200	418	11	.	.	PUNCT
ejpam-4200	419	1	variable	variable	ADJ
ejpam-4200	419	2	exponent	exponent	PROPN
ejpam-4200	419	3	besov	besov	PROPN
ejpam-4200	419	4	-	-	PUNCT
ejpam-4200	419	5	morrey	morrey	NOUN
ejpam-4200	419	6	spaces	space	NOUN
ejpam-4200	419	7	.	.	PUNCT
ejpam-4200	420	1	fourier	fouri	ADJ
ejpam-4200	420	2	anal	anal	PROPN
ejpam-4200	420	3	.	.	PUNCT
ejpam-4200	421	1	appl	appl	PROPN
ejpam-4200	421	2	.	.	PROPN
ejpam-4200	421	3	,	,	PUNCT
ejpam-4200	421	4	26(5	26(5	PROPN
ejpam-4200	421	5	)	)	PUNCT
ejpam-4200	421	6	,	,	PUNCT
ejpam-4200	421	7	2020	2020	NUM
ejpam-4200	421	8	.	.	PUNCT
ejpam-4200	422	1	[	[	X
ejpam-4200	422	2	2	2	NUM
ejpam-4200	422	3	]	]	X
ejpam-4200	422	4	g.	g.	PROPN
ejpam-4200	422	5	bourdaud	bourdaud	PROPN
ejpam-4200	422	6	.	.	PUNCT
ejpam-4200	423	1	une	une	AUX
ejpam-4200	423	2	algèbre	algèbre	PROPN
ejpam-4200	423	3	maximale	maximale	PROPN
ejpam-4200	423	4	d’opérateurs	d’opérateur	VERB
ejpam-4200	423	5	pseudo	pseudo	NOUN
ejpam-4200	423	6	-	-	PUNCT
ejpam-4200	423	7	différentiels	différentiel	NOUN
ejpam-4200	423	8	.	.	PUNCT
ejpam-4200	423	9	comm	comm	NOUN
ejpam-4200	423	10	.	.	PUNCT
ejpam-4200	424	1	partial	partial	ADJ
ejpam-4200	424	2	differential	differential	NOUN
ejpam-4200	424	3	equations	equation	NOUN
ejpam-4200	424	4	,	,	PUNCT
ejpam-4200	424	5	13(9):1059–1083	13(9):1059–1083	NUM
ejpam-4200	424	6	,	,	PUNCT
ejpam-4200	424	7	1988	1988	NUM
ejpam-4200	424	8	.	.	PUNCT
ejpam-4200	425	1	[	[	X
ejpam-4200	425	2	3	3	NUM
ejpam-4200	425	3	]	]	PUNCT
ejpam-4200	425	4	a.	a.	NOUN
ejpam-4200	425	5	caetano	caetano	PROPN
ejpam-4200	425	6	and	and	CCONJ
ejpam-4200	425	7	h.	h.	PROPN
ejpam-4200	425	8	kempka	kempka	PROPN
ejpam-4200	425	9	.	.	PUNCT
ejpam-4200	426	1	besov	besov	NOUN
ejpam-4200	426	2	spaces	space	NOUN
ejpam-4200	426	3	with	with	ADP
ejpam-4200	426	4	variable	variable	ADJ
ejpam-4200	426	5	smoothness	smoothness	NOUN
ejpam-4200	426	6	and	and	CCONJ
ejpam-4200	426	7	integrability	integrability	NOUN
ejpam-4200	426	8	.	.	PUNCT
ejpam-4200	427	1	mathematical	mathematical	ADJ
ejpam-4200	427	2	.	.	PUNCT
ejpam-4200	428	1	anal	anal	PROPN
ejpam-4200	428	2	.	.	PUNCT
ejpam-4200	429	1	and	and	CCONJ
ejpam-4200	429	2	appl	appl	PROPN
ejpam-4200	429	3	.	.	PROPN
ejpam-4200	429	4	,	,	PUNCT
ejpam-4200	429	5	484	484	NUM
ejpam-4200	429	6	,	,	PUNCT
ejpam-4200	429	7	2020	2020	NUM
ejpam-4200	429	8	.	.	PUNCT
ejpam-4200	430	1	[	[	X
ejpam-4200	430	2	4	4	NUM
ejpam-4200	430	3	]	]	PUNCT
ejpam-4200	430	4	a.	a.	NOUN
ejpam-4200	430	5	caetano	caetano	PROPN
ejpam-4200	430	6	and	and	CCONJ
ejpam-4200	430	7	h.	h.	PROPN
ejpam-4200	430	8	kempka	kempka	PROPN
ejpam-4200	430	9	.	.	PUNCT
ejpam-4200	431	1	variable	variable	ADJ
ejpam-4200	431	2	exponent	exponent	NOUN
ejpam-4200	431	3	triebel	triebel	NOUN
ejpam-4200	431	4	-	-	PUNCT
ejpam-4200	431	5	lizorkin	lizorkin	NOUN
ejpam-4200	431	6	-	-	PUNCT
ejpam-4200	431	7	morrey	morrey	NOUN
ejpam-4200	431	8	spaces	space	NOUN
ejpam-4200	431	9	.	.	PUNCT
ejpam-4200	432	1	math	math	NOUN
ejpam-4200	432	2	.	.	PUNCT
ejpam-4200	433	1	anal	anal	PROPN
ejpam-4200	433	2	.	.	PUNCT
ejpam-4200	433	3	appl	appl	PROPN
ejpam-4200	433	4	.	.	PROPN
ejpam-4200	433	5	,	,	PUNCT
ejpam-4200	433	6	484(123712	484(123712	NOUN
ejpam-4200	433	7	)	)	PUNCT
ejpam-4200	433	8	,	,	PUNCT
ejpam-4200	433	9	2020	2020	NUM
ejpam-4200	433	10	.	.	PUNCT
ejpam-4200	434	1	[	[	X
ejpam-4200	434	2	5	5	NUM
ejpam-4200	434	3	]	]	PUNCT
ejpam-4200	434	4	a.	a.	NOUN
ejpam-4200	434	5	caetano	caetano	PROPN
ejpam-4200	434	6	and	and	CCONJ
ejpam-4200	434	7	h.	h.	PROPN
ejpam-4200	434	8	kempka	kempka	PROPN
ejpam-4200	434	9	.	.	PUNCT
ejpam-4200	435	1	decompositions	decomposition	NOUN
ejpam-4200	435	2	with	with	ADP
ejpam-4200	435	3	atoms	atom	NOUN
ejpam-4200	435	4	and	and	CCONJ
ejpam-4200	435	5	molecules	molecule	NOUN
ejpam-4200	435	6	for	for	ADP
ejpam-4200	435	7	variable	variable	ADJ
ejpam-4200	435	8	exponent	exponent	NOUN
ejpam-4200	435	9	triebel	triebel	NOUN
ejpam-4200	435	10	-	-	PUNCT
ejpam-4200	435	11	lizorkin	lizorkin	NOUN
ejpam-4200	435	12	-	-	PUNCT
ejpam-4200	435	13	morrey	morrey	NOUN
ejpam-4200	435	14	spaces	space	NOUN
ejpam-4200	435	15	.	.	PUNCT
ejpam-4200	436	1	constructive	constructive	ADJ
ejpam-4200	436	2	approximation	approximation	NOUN
ejpam-4200	436	3	,	,	PUNCT
ejpam-4200	436	4	53:201–234	53:201–234	NUM
ejpam-4200	436	5	,	,	PUNCT
ejpam-4200	436	6	2021	2021	NUM
ejpam-4200	436	7	.	.	PUNCT
ejpam-4200	437	1	[	[	X
ejpam-4200	437	2	6	6	NUM
ejpam-4200	437	3	]	]	PUNCT
ejpam-4200	437	4	r.	r.	PROPN
ejpam-4200	437	5	coifman	coifman	PROPN
ejpam-4200	437	6	and	and	CCONJ
ejpam-4200	437	7	y.	y.	PROPN
ejpam-4200	437	8	meyer	meyer	PROPN
ejpam-4200	437	9	.	.	PROPN
ejpam-4200	437	10	au	au	PROPN
ejpam-4200	437	11	delà	delà	PROPN
ejpam-4200	437	12	des	des	X
ejpam-4200	437	13	opérateurs	opérateurs	X
ejpam-4200	437	14	pseudo	pseudo	NOUN
ejpam-4200	437	15	-	-	PUNCT
ejpam-4200	437	16	différentiels	différentiel	NOUN
ejpam-4200	437	17	.	.	NOUN
ejpam-4200	437	18	1978	1978	NUM
ejpam-4200	437	19	.	.	PUNCT
ejpam-4200	438	1	[	[	X
ejpam-4200	438	2	7	7	X
ejpam-4200	438	3	]	]	X
ejpam-4200	438	4	d.	d.	PROPN
ejpam-4200	438	5	cruz	cruz	PROPN
ejpam-4200	438	6	-	-	PUNCT
ejpam-4200	438	7	uribe	uribe	PROPN
ejpam-4200	438	8	and	and	CCONJ
ejpam-4200	438	9	a.	a.	NOUN
ejpam-4200	438	10	fiorenza	fiorenza	PROPN
ejpam-4200	438	11	.	.	PUNCT
ejpam-4200	439	1	variable	variable	ADJ
ejpam-4200	439	2	lebesgue	lebesgue	PROPN
ejpam-4200	439	3	spaces	space	NOUN
ejpam-4200	439	4	.	.	PUNCT
ejpam-4200	440	1	birkhäuser	birkhäuser	NOUN
ejpam-4200	440	2	,	,	PUNCT
ejpam-4200	440	3	basel	basel	PROPN
ejpam-4200	440	4	,	,	PUNCT
ejpam-4200	440	5	2013	2013	NUM
ejpam-4200	440	6	.	.	PUNCT
ejpam-4200	441	1	references	reference	NOUN
ejpam-4200	441	2	63	63	NUM
ejpam-4200	442	1	[	[	SYM
ejpam-4200	442	2	8	8	NUM
ejpam-4200	442	3	]	]	X
ejpam-4200	442	4	h.	h.	PROPN
ejpam-4200	442	5	kempka	kempka	PROPN
ejpam-4200	442	6	and	and	CCONJ
ejpam-4200	442	7	j.	j.	PROPN
ejpam-4200	442	8	vyb́ıral	vyb́ıral	PROPN
ejpam-4200	442	9	.	.	PUNCT
ejpam-4200	442	10	spaces	space	NOUN
ejpam-4200	442	11	of	of	ADP
ejpam-4200	442	12	variable	variable	ADJ
ejpam-4200	442	13	smoothness	smoothness	NOUN
ejpam-4200	442	14	and	and	CCONJ
ejpam-4200	442	15	integrability	integrability	NOUN
ejpam-4200	442	16	:	:	PUNCT
ejpam-4200	442	17	characterizations	characterization	NOUN
ejpam-4200	442	18	by	by	ADP
ejpam-4200	442	19	local	local	ADJ
ejpam-4200	442	20	means	mean	NOUN
ejpam-4200	442	21	and	and	CCONJ
ejpam-4200	442	22	ball	ball	NOUN
ejpam-4200	442	23	means	mean	NOUN
ejpam-4200	442	24	of	of	ADP
ejpam-4200	442	25	differences	difference	NOUN
ejpam-4200	442	26	.	.	PUNCT
ejpam-4200	443	1	fourier	fouri	ADJ
ejpam-4200	443	2	anal	anal	PROPN
ejpam-4200	443	3	.	.	PUNCT
ejpam-4200	444	1	appl	appl	PROPN
ejpam-4200	444	2	.	.	PROPN
ejpam-4200	444	3	,	,	PUNCT
ejpam-4200	444	4	18(4):852–891	18(4):852–891	PROPN
ejpam-4200	444	5	,	,	PUNCT
ejpam-4200	444	6	2012	2012	NUM
ejpam-4200	444	7	.	.	PUNCT
ejpam-4200	445	1	[	[	X
ejpam-4200	445	2	9	9	NUM
ejpam-4200	445	3	]	]	X
ejpam-4200	445	4	h.	h.	PROPN
ejpam-4200	445	5	kozono	kozono	PROPN
ejpam-4200	445	6	and	and	CCONJ
ejpam-4200	445	7	m.	m.	PROPN
ejpam-4200	445	8	yamazaki	yamazaki	PROPN
ejpam-4200	445	9	.	.	PUNCT
ejpam-4200	446	1	semilinear	semilinear	PROPN
ejpam-4200	446	2	heat	heat	NOUN
ejpam-4200	446	3	equations	equation	NOUN
ejpam-4200	446	4	and	and	CCONJ
ejpam-4200	446	5	the	the	DET
ejpam-4200	446	6	navier	navier	NOUN
ejpam-4200	446	7	-	-	PUNCT
ejpam-4200	446	8	stokes	stoke	NOUN
ejpam-4200	446	9	equation	equation	NOUN
ejpam-4200	446	10	with	with	ADP
ejpam-4200	446	11	distributions	distribution	NOUN
ejpam-4200	446	12	in	in	ADP
ejpam-4200	446	13	new	new	ADJ
ejpam-4200	446	14	function	function	NOUN
ejpam-4200	446	15	spaces	space	NOUN
ejpam-4200	446	16	as	as	ADP
ejpam-4200	446	17	initial	initial	ADJ
ejpam-4200	446	18	data	datum	NOUN
ejpam-4200	446	19	.	.	PUNCT
ejpam-4200	447	1	comm	comm	NOUN
ejpam-4200	447	2	.	.	PUNCT
ejpam-4200	448	1	partial	partial	ADJ
ejpam-4200	448	2	differential	differential	NOUN
ejpam-4200	448	3	equations	equation	NOUN
ejpam-4200	448	4	,	,	PUNCT
ejpam-4200	448	5	19:959–1014	19:959–1014	NUM
ejpam-4200	448	6	,	,	PUNCT
ejpam-4200	448	7	1994	1994	NUM
ejpam-4200	448	8	.	.	PUNCT
ejpam-4200	449	1	[	[	X
ejpam-4200	449	2	10	10	NUM
ejpam-4200	449	3	]	]	PUNCT
ejpam-4200	449	4	p.	p.	NOUN
ejpam-4200	449	5	hästö	hästö	VERB
ejpam-4200	449	6	l.	l.	PROPN
ejpam-4200	449	7	diening	diening	PROPN
ejpam-4200	449	8	and	and	CCONJ
ejpam-4200	449	9	s.	s.	PROPN
ejpam-4200	449	10	roudenko	roudenko	PROPN
ejpam-4200	449	11	.	.	PUNCT
ejpam-4200	450	1	function	function	NOUN
ejpam-4200	450	2	spaces	space	NOUN
ejpam-4200	450	3	of	of	ADP
ejpam-4200	450	4	variable	variable	ADJ
ejpam-4200	450	5	smoothness	smoothness	NOUN
ejpam-4200	450	6	and	and	CCONJ
ejpam-4200	450	7	integrability	integrability	NOUN
ejpam-4200	450	8	.	.	PUNCT
ejpam-4200	451	1	funct	funct	PROPN
ejpam-4200	451	2	.	.	PUNCT
ejpam-4200	452	1	anal	anal	PROPN
ejpam-4200	452	2	.	.	PUNCT
ejpam-4200	452	3	,	,	PUNCT
ejpam-4200	452	4	256(6):1731–1768	256(6):1731–1768	NOUN
ejpam-4200	452	5	,	,	PUNCT
ejpam-4200	452	6	2009	2009	NUM
ejpam-4200	452	7	.	.	PUNCT
ejpam-4200	453	1	[	[	X
ejpam-4200	453	2	11	11	NUM
ejpam-4200	453	3	]	]	PUNCT
ejpam-4200	453	4	p.	p.	NOUN
ejpam-4200	453	5	hästö	hästö	VERB
ejpam-4200	453	6	l.	l.	PROPN
ejpam-4200	453	7	diening	diening	PROPN
ejpam-4200	453	8	,	,	PUNCT
ejpam-4200	453	9	p.	p.	NOUN
ejpam-4200	453	10	harjulehto	harjulehto	NOUN
ejpam-4200	453	11	and	and	CCONJ
ejpam-4200	453	12	m.	m.	PROPN
ejpam-4200	453	13	ruzicka	ruzicka	PROPN
ejpam-4200	453	14	.	.	PUNCT
ejpam-4200	454	1	lebesgue	lebesgue	PROPN
ejpam-4200	454	2	and	and	CCONJ
ejpam-4200	454	3	sobolev	sobolev	NOUN
ejpam-4200	454	4	spaces	space	NOUN
ejpam-4200	454	5	with	with	ADP
ejpam-4200	454	6	variable	variable	ADJ
ejpam-4200	454	7	exponents	exponent	NOUN
ejpam-4200	454	8	.	.	PUNCT
ejpam-4200	454	9	,	,	PUNCT
ejpam-4200	454	10	volume	volume	NOUN
ejpam-4200	454	11	2017	2017	NUM
ejpam-4200	454	12	.	.	PUNCT
ejpam-4200	455	1	springer	springer	NOUN
ejpam-4200	455	2	-	-	PUNCT
ejpam-4200	455	3	verlag	verlag	PROPN
ejpam-4200	455	4	,	,	PUNCT
ejpam-4200	455	5	berlin	berlin	PROPN
ejpam-4200	455	6	,	,	PUNCT
ejpam-4200	455	7	2011	2011	NUM
ejpam-4200	455	8	.	.	PUNCT
ejpam-4200	456	1	[	[	X
ejpam-4200	456	2	12	12	NUM
ejpam-4200	456	3	]	]	PUNCT
ejpam-4200	456	4	j.	j.	PROPN
ejpam-4200	456	5	marschall	marschall	PROPN
ejpam-4200	456	6	.	.	PUNCT
ejpam-4200	457	1	pseudodifferential	pseudodifferential	ADJ
ejpam-4200	457	2	operators	operator	NOUN
ejpam-4200	457	3	with	with	ADP
ejpam-4200	457	4	coefficients	coefficient	NOUN
ejpam-4200	457	5	in	in	ADP
ejpam-4200	457	6	sobolev	sobolev	NOUN
ejpam-4200	457	7	spaces	space	NOUN
ejpam-4200	457	8	.	.	PUNCT
ejpam-4200	458	1	trans	trans	PROPN
ejpam-4200	458	2	.	.	PUNCT
ejpam-4200	459	1	amer	amer	PROPN
ejpam-4200	459	2	.	.	PUNCT
ejpam-4200	459	3	math	math	PROPN
ejpam-4200	459	4	.	.	PUNCT
ejpam-4200	460	1	soc	soc	PROPN
ejpam-4200	460	2	.	.	PUNCT
ejpam-4200	460	3	,	,	PUNCT
ejpam-4200	460	4	307(1):335–361	307(1):335–361	NUM
ejpam-4200	460	5	,	,	PUNCT
ejpam-4200	460	6	1988	1988	NUM
ejpam-4200	460	7	.	.	PUNCT
ejpam-4200	461	1	[	[	X
ejpam-4200	461	2	13	13	NUM
ejpam-4200	461	3	]	]	PUNCT
ejpam-4200	461	4	j.	j.	PROPN
ejpam-4200	461	5	marschall	marschall	PROPN
ejpam-4200	461	6	.	.	PUNCT
ejpam-4200	462	1	nonregular	nonregular	ADJ
ejpam-4200	462	2	pseudo	pseudo	NOUN
ejpam-4200	462	3	-	-	ADJ
ejpam-4200	462	4	differential	differential	ADJ
ejpam-4200	462	5	operators	operator	NOUN
ejpam-4200	462	6	.	.	PUNCT
ejpam-4200	463	1	z.	z.	PROPN
ejpam-4200	463	2	anal	anal	PROPN
ejpam-4200	463	3	.	.	PUNCT
ejpam-4200	464	1	anwend	anwend	PROPN
ejpam-4200	464	2	,	,	PUNCT
ejpam-4200	464	3	15(1):109	15(1):109	NUM
ejpam-4200	464	4	–	–	PUNCT
ejpam-4200	464	5	148	148	NUM
ejpam-4200	464	6	,	,	PUNCT
ejpam-4200	464	7	1996	1996	NUM
ejpam-4200	464	8	.	.	PUNCT
ejpam-4200	465	1	[	[	X
ejpam-4200	465	2	14	14	NUM
ejpam-4200	465	3	]	]	PUNCT
ejpam-4200	465	4	a.	a.	NOUN
ejpam-4200	465	5	mazzucato	mazzucato	PROPN
ejpam-4200	465	6	.	.	PUNCT
ejpam-4200	466	1	besov	besov	NOUN
ejpam-4200	466	2	-	-	PUNCT
ejpam-4200	466	3	morrey	morrey	NOUN
ejpam-4200	466	4	spaces	space	NOUN
ejpam-4200	466	5	:	:	PUNCT
ejpam-4200	466	6	function	function	NOUN
ejpam-4200	466	7	space	space	NOUN
ejpam-4200	466	8	theory	theory	NOUN
ejpam-4200	466	9	and	and	CCONJ
ejpam-4200	466	10	applications	application	NOUN
ejpam-4200	466	11	to	to	ADP
ejpam-4200	466	12	nonlinear	nonlinear	ADJ
ejpam-4200	466	13	pde	pde	NOUN
ejpam-4200	466	14	.	.	PUNCT
ejpam-4200	467	1	trans	trans	PROPN
ejpam-4200	467	2	.	.	PUNCT
ejpam-4200	468	1	amer	amer	PROPN
ejpam-4200	468	2	.	.	PUNCT
ejpam-4200	468	3	math	math	PROPN
ejpam-4200	468	4	.	.	PUNCT
ejpam-4200	469	1	soc	soc	PROPN
ejpam-4200	469	2	.	.	PUNCT
ejpam-4200	469	3	,	,	PUNCT
ejpam-4200	469	4	355:1297–1364	355:1297–1364	NUM
ejpam-4200	469	5	,	,	PUNCT
ejpam-4200	469	6	2003	2003	NUM
ejpam-4200	469	7	.	.	PUNCT
ejpam-4200	470	1	[	[	X
ejpam-4200	470	2	15	15	NUM
ejpam-4200	470	3	]	]	X
ejpam-4200	470	4	y.	y.	PROPN
ejpam-4200	470	5	sawano	sawano	PROPN
ejpam-4200	470	6	.	.	PUNCT
ejpam-4200	471	1	a	a	DET
ejpam-4200	471	2	note	note	NOUN
ejpam-4200	471	3	on	on	ADP
ejpam-4200	471	4	besov	besov	NOUN
ejpam-4200	471	5	-	-	PUNCT
ejpam-4200	471	6	morrey	morrey	NOUN
ejpam-4200	471	7	spaces	space	NOUN
ejpam-4200	471	8	and	and	CCONJ
ejpam-4200	471	9	triebel	triebel	NOUN
ejpam-4200	471	10	-	-	PUNCT
ejpam-4200	471	11	lizorkin	lizorkin	NOUN
ejpam-4200	471	12	-	-	PUNCT
ejpam-4200	471	13	morrey	morrey	NOUN
ejpam-4200	471	14	spaces	space	NOUN
ejpam-4200	471	15	.	.	PUNCT
ejpam-4200	472	1	acta	acta	PROPN
ejpam-4200	472	2	math	math	PROPN
ejpam-4200	472	3	.	.	PUNCT
ejpam-4200	473	1	sin	sin	NOUN
ejpam-4200	473	2	.	.	PUNCT
ejpam-4200	473	3	,	,	PUNCT
ejpam-4200	473	4	25:1223–1242	25:1223–1242	PROPN
ejpam-4200	473	5	,	,	PUNCT
ejpam-4200	473	6	2009	2009	NUM
ejpam-4200	473	7	.	.	PUNCT
ejpam-4200	474	1	[	[	X
ejpam-4200	474	2	16	16	NUM
ejpam-4200	474	3	]	]	PUNCT
ejpam-4200	474	4	m.	m.	PROPN
ejpam-4200	474	5	e.	e.	PROPN
ejpam-4200	474	6	taylor	taylor	PROPN
ejpam-4200	474	7	.	.	PUNCT
ejpam-4200	475	1	pseudodifferential	pseudodifferential	ADJ
ejpam-4200	475	2	operators	operator	NOUN
ejpam-4200	475	3	and	and	CCONJ
ejpam-4200	475	4	nonlinear	nonlinear	ADJ
ejpam-4200	475	5	pde	pde	NOUN
ejpam-4200	475	6	.	.	PUNCT
ejpam-4200	476	1	progress	progress	NOUN
ejpam-4200	476	2	in	in	ADP
ejpam-4200	476	3	mathematics	mathematics	PROPN
ejpam-4200	476	4	100	100	NUM
ejpam-4200	476	5	,	,	PUNCT
ejpam-4200	476	6	birkhäuser	birkhäuser	NOUN
ejpam-4200	476	7	,	,	PUNCT
ejpam-4200	476	8	boston	boston	PROPN
ejpam-4200	476	9	,	,	PUNCT
ejpam-4200	476	10	ma	ma	PROPN
ejpam-4200	476	11	,	,	PUNCT
ejpam-4200	476	12	,	,	PUNCT
ejpam-4200	476	13	1991	1991	NUM
ejpam-4200	476	14	.	.	PUNCT
ejpam-4200	477	1	[	[	X
ejpam-4200	477	2	17	17	NUM
ejpam-4200	477	3	]	]	X
ejpam-4200	477	4	h.	h.	PROPN
ejpam-4200	477	5	triebel	triebel	PROPN
ejpam-4200	477	6	.	.	PUNCT
ejpam-4200	478	1	besov	besov	NOUN
ejpam-4200	478	2	spaces	space	NOUN
ejpam-4200	478	3	with	with	ADP
ejpam-4200	478	4	variable	variable	ADJ
ejpam-4200	478	5	smoothness	smoothness	NOUN
ejpam-4200	478	6	and	and	CCONJ
ejpam-4200	478	7	integrability	integrability	NOUN
ejpam-4200	478	8	.	.	PUNCT
ejpam-4200	479	1	birkhauser	birkhauser	PROPN
ejpam-4200	479	2	verlag	verlag	PROPN
ejpam-4200	479	3	,	,	PUNCT
ejpam-4200	479	4	basel	basel	PROPN
ejpam-4200	479	5	and	and	CCONJ
ejpam-4200	479	6	al	al	PROPN
ejpam-4200	479	7	.	.	PROPN
ejpam-4200	479	8	,	,	PUNCT
ejpam-4200	479	9	1983	1983	NUM
ejpam-4200	479	10	.	.	PUNCT
ejpam-4200	480	1	[	[	X
ejpam-4200	480	2	18	18	NUM
ejpam-4200	480	3	]	]	PUNCT
ejpam-4200	480	4	w.	w.	PROPN
ejpam-4200	480	5	sickel	sickel	PROPN
ejpam-4200	480	6	w.	w.	PROPN
ejpam-4200	480	7	yuan	yuan	PROPN
ejpam-4200	480	8	and	and	CCONJ
ejpam-4200	480	9	d.	d.	PROPN
ejpam-4200	480	10	yang	yang	PROPN
ejpam-4200	480	11	.	.	PUNCT
ejpam-4200	481	1	morrey	morrey	PROPN
ejpam-4200	481	2	and	and	CCONJ
ejpam-4200	481	3	campanato	campanato	PROPN
ejpam-4200	481	4	meet	meet	NOUN
ejpam-4200	481	5	besov	besov	NOUN
ejpam-4200	481	6	,	,	PUNCT
ejpam-4200	481	7	lizorkin	lizorkin	NOUN
ejpam-4200	481	8	and	and	CCONJ
ejpam-4200	481	9	triebel	triebel	NOUN
ejpam-4200	481	10	.	.	PUNCT
ejpam-4200	482	1	2005	2005	NUM
ejpam-4200	482	2	,	,	PUNCT
ejpam-4200	482	3	2010	2010	NUM
ejpam-4200	482	4	.	.	PUNCT