id	sid	tid	token	lemma	pos
ma-260	1	1	2024	2024	NUM
ma-260	1	2	ada	ada	PROPN
ma-260	1	3	academica	academica	PROPN
ma-260	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-260	1	5	.	.	PUNCT
ma-260	2	1	j.	j.	PROPN
ma-260	2	2	math	math	PROPN
ma-260	2	3	.	.	PUNCT
ma-260	3	1	anal	anal	ADJ
ma-260	3	2	.	.	PUNCT
ma-260	4	1	4	4	NUM
ma-260	4	2	(	(	PUNCT
ma-260	4	3	2024	2024	NUM
ma-260	4	4	)	)	PUNCT
ma-260	4	5	22doi	22doi	NOUN
ma-260	4	6	:	:	PUNCT
ma-260	4	7	10.28924	10.28924	NUM
ma-260	4	8	/	/	SYM
ma-260	4	9	ada	ada	PROPN
ma-260	4	10	/	/	SYM
ma-260	4	11	ma.4.22	ma.4.22	PROPN
ma-260	4	12	boundedness	boundedness	NOUN
ma-260	4	13	of	of	ADP
ma-260	4	14	some	some	DET
ma-260	4	15	commutators	commutator	NOUN
ma-260	4	16	in	in	ADP
ma-260	4	17	total	total	ADJ
ma-260	4	18	fofana	fofana	PROPN
ma-260	4	19	spaces	space	VERB
ma-260	4	20	pokou	pokou	PROPN
ma-260	4	21	nagacy	nagacy	PROPN
ma-260	4	22	laboratoire	laboratoire	PROPN
ma-260	4	23	des	des	PROPN
ma-260	4	24	sciences	sciences	PROPN
ma-260	4	25	et	et	PROPN
ma-260	4	26	technologies	technologies	PROPN
ma-260	4	27	de	de	PROPN
ma-260	4	28	l’environnement	l’environnement	PROPN
ma-260	4	29	,	,	PUNCT
ma-260	4	30	ufr	ufr	PROPN
ma-260	4	31	environnement	environnement	PROPN
ma-260	4	32	,	,	PUNCT
ma-260	4	33	université	université	PROPN
ma-260	4	34	jean	jean	PROPN
ma-260	4	35	lorougnon	lorougnon	PROPN
ma-260	4	36	guede	guede	PROPN
ma-260	4	37	,	,	PUNCT
ma-260	4	38	bp	bp	PROPN
ma-260	4	39	150	150	NUM
ma-260	4	40	daloa	daloa	PROPN
ma-260	4	41	,	,	PUNCT
ma-260	4	42	côte	côte	NOUN
ma-260	4	43	d’ivoire	d’ivoire	NOUN
ma-260	4	44	pokounagacy@yahoo.com	pokounagacy@yahoo.com	NOUN
ma-260	5	1	abstract	abstract	ADJ
ma-260	5	2	.	.	PUNCT
ma-260	6	1	in	in	ADP
ma-260	6	2	this	this	DET
ma-260	6	3	paper	paper	NOUN
ma-260	6	4	,	,	PUNCT
ma-260	6	5	we	we	PRON
ma-260	6	6	find	find	VERB
ma-260	6	7	necessary	necessary	ADJ
ma-260	6	8	and	and	CCONJ
ma-260	6	9	sufficient	sufficient	ADJ
ma-260	6	10	conditions	condition	NOUN
ma-260	6	11	for	for	ADP
ma-260	6	12	the	the	DET
ma-260	6	13	boundedness	boundedness	NOUN
ma-260	6	14	of	of	ADP
ma-260	6	15	the	the	DET
ma-260	6	16	com	com	NOUN
ma-260	6	17	-	-	PUNCT
ma-260	6	18	mutator	mutator	NOUN
ma-260	6	19	of	of	ADP
ma-260	6	20	the	the	DET
ma-260	6	21	hardy	hardy	ADJ
ma-260	6	22	-	-	PUNCT
ma-260	6	23	littlewood	littlewood	NOUN
ma-260	6	24	maximal	maximal	ADJ
ma-260	6	25	operator	operator	NOUN
ma-260	6	26	in	in	ADP
ma-260	6	27	total	total	ADJ
ma-260	6	28	fofana	fofana	PROPN
ma-260	6	29	spaces	space	NOUN
ma-260	6	30	.	.	PUNCT
ma-260	7	1	we	we	PRON
ma-260	7	2	also	also	ADV
ma-260	7	3	give	give	VERB
ma-260	7	4	in	in	ADP
ma-260	7	5	thesespaces	thesespace	NOUN
ma-260	7	6	the	the	DET
ma-260	7	7	boundedness	boundedness	NOUN
ma-260	7	8	of	of	ADP
ma-260	7	9	some	some	DET
ma-260	7	10	sublinear	sublinear	NOUN
ma-260	7	11	operators	operator	NOUN
ma-260	7	12	and	and	CCONJ
ma-260	7	13	their	their	PRON
ma-260	7	14	commutators	commutator	NOUN
ma-260	7	15	.	.	PUNCT
ma-260	8	1	1	1	X
ma-260	8	2	.	.	X
ma-260	8	3	introduction	introduction	NOUN
ma-260	8	4	and	and	CCONJ
ma-260	8	5	main	main	ADJ
ma-260	8	6	results	result	NOUN
ma-260	8	7	let	let	VERB
ma-260	8	8	d	d	PRON
ma-260	8	9	be	be	AUX
ma-260	8	10	a	a	DET
ma-260	8	11	fixed	fix	VERB
ma-260	8	12	positive	positive	ADJ
ma-260	8	13	integer	integer	NOUN
ma-260	8	14	and	and	CCONJ
ma-260	8	15	rd	rd	VERB
ma-260	8	16	the	the	DET
ma-260	8	17	d	d	ADJ
ma-260	8	18	-	-	ADJ
ma-260	8	19	dimensional	dimensional	ADJ
ma-260	8	20	euclidean	euclidean	ADJ
ma-260	8	21	space	space	NOUN
ma-260	8	22	.	.	PUNCT
ma-260	9	1	the	the	DET
ma-260	9	2	estimation	estimation	NOUN
ma-260	9	3	ofcommutators	ofcommutator	NOUN
ma-260	9	4	plays	play	VERB
ma-260	9	5	an	an	DET
ma-260	9	6	important	important	ADJ
ma-260	9	7	role	role	NOUN
ma-260	9	8	in	in	ADP
ma-260	9	9	studying	study	VERB
ma-260	9	10	the	the	DET
ma-260	9	11	regularity	regularity	NOUN
ma-260	9	12	of	of	ADP
ma-260	9	13	solutions	solution	NOUN
ma-260	9	14	of	of	ADP
ma-260	9	15	elliptic	elliptic	ADJ
ma-260	9	16	,	,	PUNCT
ma-260	9	17	parabolicand	parabolicand	NOUN
ma-260	9	18	ultraparabolic	ultraparabolic	VERB
ma-260	9	19	partial	partial	ADJ
ma-260	9	20	differential	differential	NOUN
ma-260	9	21	equations	equation	NOUN
ma-260	9	22	of	of	ADP
ma-260	9	23	second	second	ADJ
ma-260	9	24	order	order	NOUN
ma-260	9	25	,	,	PUNCT
ma-260	9	26	and	and	CCONJ
ma-260	9	27	their	their	PRON
ma-260	9	28	boundedness	boundedness	NOUN
ma-260	9	29	can	can	AUX
ma-260	9	30	beused	beuse	VERB
ma-260	9	31	to	to	PART
ma-260	9	32	characterize	characterize	VERB
ma-260	9	33	certain	certain	ADJ
ma-260	9	34	function	function	NOUN
ma-260	9	35	spaces	space	NOUN
ma-260	9	36	(	(	PUNCT
ma-260	9	37	see	see	VERB
ma-260	9	38	,	,	PUNCT
ma-260	9	39	for	for	ADP
ma-260	9	40	instance	instance	NOUN
ma-260	9	41	[	[	X
ma-260	9	42	3	3	NUM
ma-260	9	43	,	,	PUNCT
ma-260	9	44	18,20]).we	18,20]).we	NUM
ma-260	9	45	denote	denote	VERB
ma-260	9	46	by	by	ADP
ma-260	9	47	l0(rd	l0(rd	NOUN
ma-260	9	48	)	)	PUNCT
ma-260	9	49	the	the	DET
ma-260	9	50	complex	complex	ADJ
ma-260	9	51	vector	vector	NOUN
ma-260	9	52	space	space	NOUN
ma-260	9	53	of	of	ADP
ma-260	9	54	equivalent	equivalent	ADJ
ma-260	9	55	classes	class	NOUN
ma-260	9	56	(	(	PUNCT
ma-260	9	57	modulo	modulo	NOUN
ma-260	9	58	equality	equality	NOUN
ma-260	9	59	lebesguealmost	lebesguealmost	VERB
ma-260	9	60	everywhere	everywhere	ADV
ma-260	9	61	)	)	PUNCT
ma-260	9	62	of	of	ADP
ma-260	9	63	lebesgue	lebesgue	PROPN
ma-260	9	64	measurable	measurable	ADJ
ma-260	9	65	complex	complex	ADV
ma-260	9	66	-	-	PUNCT
ma-260	9	67	valued	value	VERB
ma-260	9	68	functions	function	NOUN
ma-260	9	69	on	on	ADP
ma-260	9	70	rd	rd	PROPN
ma-260	9	71	.	.	PUNCT
ma-260	10	1	for	for	ADP
ma-260	10	2	f	f	PROPN
ma-260	10	3	∈	∈	PROPN
ma-260	10	4	l0(rd	l0(rd	PROPN
ma-260	10	5	)	)	PUNCT
ma-260	10	6	and	and	CCONJ
ma-260	10	7	x	x	PUNCT
ma-260	10	8	∈	∈	PROPN
ma-260	10	9	rd	rd	PROPN
ma-260	10	10	,	,	PUNCT
ma-260	10	11	the	the	DET
ma-260	10	12	hardy	hardy	ADJ
ma-260	10	13	-	-	PUNCT
ma-260	10	14	littlewood	littlewood	NOUN
ma-260	10	15	maximal	maximal	ADJ
ma-260	10	16	function	function	NOUN
ma-260	10	17	is	be	AUX
ma-260	10	18	defined	define	VERB
ma-260	10	19	by	by	ADP
ma-260	10	20	the	the	DET
ma-260	10	21	formula	formula	NOUN
ma-260	10	22	mf	mf	X
ma-260	10	23	(	(	PUNCT
ma-260	10	24	x	x	NOUN
ma-260	10	25	)	)	PUNCT
ma-260	10	26	=	=	SYM
ma-260	10	27	sup	sup	NUM
ma-260	10	28	r>0	r>0	PROPN
ma-260	10	29	|b(x	|b(x	PROPN
ma-260	10	30	,	,	PUNCT
ma-260	10	31	r)|−1	r)|−1	VERB
ma-260	10	32	∫	∫	PROPN
ma-260	10	33	b(x	b(x	PROPN
ma-260	10	34	,	,	PUNCT
ma-260	10	35	r	r	NOUN
ma-260	10	36	)	)	PUNCT
ma-260	10	37	|f	|f	PROPN
ma-260	11	1	(	(	PUNCT
ma-260	11	2	y)|	y)|	PROPN
ma-260	11	3	dy	dy	NOUN
ma-260	11	4	,	,	PUNCT
ma-260	11	5	(	(	PUNCT
ma-260	11	6	1.1	1.1	NUM
ma-260	11	7	)	)	PUNCT
ma-260	11	8	where	where	SCONJ
ma-260	11	9	|b(x	|b(x	PROPN
ma-260	11	10	,	,	PUNCT
ma-260	11	11	r)|	r)|	PROPN
ma-260	11	12	is	be	AUX
ma-260	11	13	the	the	DET
ma-260	11	14	lebesgue	lebesgue	ADJ
ma-260	11	15	measure	measure	NOUN
ma-260	11	16	of	of	ADP
ma-260	11	17	the	the	DET
ma-260	11	18	ball	ball	NOUN
ma-260	11	19	b(x	b(x	NOUN
ma-260	11	20	,	,	PUNCT
ma-260	11	21	r	r	NOUN
ma-260	11	22	)	)	PUNCT
ma-260	11	23	=	=	SYM
ma-260	11	24	{	{	PUNCT
ma-260	11	25	y	y	PROPN
ma-260	11	26	∈	∈	PROPN
ma-260	11	27	rd	rd	PROPN
ma-260	11	28	:	:	PUNCT
ma-260	11	29	|x	|x	NOUN
ma-260	11	30	−	−	PROPN
ma-260	12	1	y	y	NOUN
ma-260	13	1	|	|	ADV
ma-260	13	2	<	<	X
ma-260	13	3	r	r	X
ma-260	13	4	}	}	PUNCT
ma-260	13	5	.	.	PUNCT
ma-260	14	1	the	the	DET
ma-260	14	2	maximal	maximal	ADJ
ma-260	14	3	commutatormb	commutatormb	NOUN
ma-260	14	4	generated	generate	VERB
ma-260	14	5	by	by	ADP
ma-260	14	6	the	the	DET
ma-260	14	7	maximal	maximal	ADJ
ma-260	14	8	operatorm	operatorm	NOUN
ma-260	14	9	and	and	CCONJ
ma-260	14	10	a	a	DET
ma-260	14	11	locally	locally	ADV
ma-260	14	12	integrable	integrable	ADJ
ma-260	14	13	function	function	NOUN
ma-260	14	14	b	b	PROPN
ma-260	14	15	is	be	AUX
ma-260	14	16	defined	define	VERB
ma-260	14	17	by	by	ADP
ma-260	14	18	mb(f	mb(f	NOUN
ma-260	14	19	)	)	PUNCT
ma-260	14	20	(	(	PUNCT
ma-260	14	21	x	x	X
ma-260	14	22	)	)	PUNCT
ma-260	14	23	=	=	SYM
ma-260	14	24	sup	sup	NUM
ma-260	14	25	r>0	r>0	PROPN
ma-260	14	26	|b(x	|b(x	PROPN
ma-260	14	27	,	,	PUNCT
ma-260	14	28	r)|−1	r)|−1	VERB
ma-260	14	29	∫	∫	PROPN
ma-260	14	30	b(x	b(x	PROPN
ma-260	14	31	,	,	PUNCT
ma-260	14	32	r	r	NOUN
ma-260	14	33	)	)	PUNCT
ma-260	14	34	|b(x)−	|b(x)−	NOUN
ma-260	14	35	b(y)||f	b(y)||f	PROPN
ma-260	14	36	(	(	PUNCT
ma-260	14	37	y)|dy	y)|dy	NOUN
ma-260	14	38	.	.	PUNCT
ma-260	15	1	furthermore	furthermore	ADV
ma-260	15	2	the	the	DET
ma-260	15	3	commutator	commutator	NOUN
ma-260	15	4	generated	generate	VERB
ma-260	15	5	by	by	ADP
ma-260	15	6	the	the	DET
ma-260	15	7	operator	operator	NOUN
ma-260	15	8	m	m	PROPN
ma-260	15	9	and	and	CCONJ
ma-260	15	10	a	a	DET
ma-260	15	11	suitable	suitable	ADJ
ma-260	15	12	function	function	NOUN
ma-260	15	13	b	b	NOUN
ma-260	15	14	is	be	AUX
ma-260	15	15	defined	define	VERB
ma-260	15	16	by	by	ADP
ma-260	15	17	[	[	X
ma-260	15	18	b	b	NOUN
ma-260	15	19	,	,	PUNCT
ma-260	15	20	m]f	m]f	NOUN
ma-260	15	21	(	(	PUNCT
ma-260	15	22	x	x	NOUN
ma-260	15	23	)	)	PUNCT
ma-260	15	24	=	=	NOUN
ma-260	15	25	b(x)m(f	b(x)m(f	NOUN
ma-260	15	26	)	)	PUNCT
ma-260	15	27	(	(	PUNCT
ma-260	15	28	x)−m(bf	x)−m(bf	NOUN
ma-260	15	29	)	)	PUNCT
ma-260	15	30	(	(	PUNCT
ma-260	15	31	x	x	NOUN
ma-260	15	32	)	)	PUNCT
ma-260	15	33	.	.	PUNCT
ma-260	16	1	recall	recall	VERB
ma-260	16	2	that	that	SCONJ
ma-260	16	3	the	the	DET
ma-260	16	4	operators	operator	NOUN
ma-260	16	5	mb	mb	ADP
ma-260	16	6	and	and	CCONJ
ma-260	16	7	[	[	X
ma-260	16	8	b	b	X
ma-260	16	9	,	,	PUNCT
ma-260	16	10	m	m	VERB
ma-260	16	11	]	]	PUNCT
ma-260	16	12	essentially	essentially	ADV
ma-260	16	13	differ	differ	VERB
ma-260	16	14	from	from	ADP
ma-260	16	15	each	each	DET
ma-260	16	16	other	other	ADJ
ma-260	16	17	since	since	SCONJ
ma-260	16	18	mb	mb	PROPN
ma-260	16	19	is	be	AUX
ma-260	16	20	positiveand	positiveand	ADV
ma-260	16	21	sublinear	sublinear	NOUN
ma-260	16	22	and	and	CCONJ
ma-260	16	23	[	[	X
ma-260	16	24	b	b	X
ma-260	16	25	,	,	PUNCT
ma-260	16	26	m	m	VERB
ma-260	16	27	]	]	X
ma-260	16	28	is	be	AUX
ma-260	16	29	neither	neither	CCONJ
ma-260	16	30	positive	positive	ADJ
ma-260	16	31	nor	nor	CCONJ
ma-260	16	32	sublinear	sublinear	ADJ
ma-260	16	33	.	.	PUNCT
ma-260	17	1	the	the	DET
ma-260	17	2	operators	operator	NOUN
ma-260	17	3	m	m	VERB
ma-260	17	4	,	,	PUNCT
ma-260	18	1	[	[	X
ma-260	18	2	b	b	X
ma-260	18	3	,	,	PUNCT
ma-260	18	4	m	m	NOUN
ma-260	18	5	]	]	PUNCT
ma-260	18	6	and	and	CCONJ
ma-260	18	7	mb	mb	ADP
ma-260	18	8	play	play	NOUN
ma-260	18	9	received	receive	VERB
ma-260	18	10	:	:	PUNCT
ma-260	18	11	28	28	NUM
ma-260	18	12	jul	jul	PROPN
ma-260	18	13	2024	2024	NUM
ma-260	18	14	.	.	PUNCT
ma-260	19	1	key	key	ADJ
ma-260	19	2	words	word	NOUN
ma-260	19	3	and	and	CCONJ
ma-260	19	4	phrases	phrase	NOUN
ma-260	19	5	.	.	PUNCT
ma-260	20	1	total	total	ADJ
ma-260	20	2	fofana	fofana	PROPN
ma-260	20	3	spaces	space	NOUN
ma-260	20	4	;	;	PUNCT
ma-260	20	5	maximal	maximal	ADJ
ma-260	20	6	operator	operator	NOUN
ma-260	20	7	;	;	PUNCT
ma-260	20	8	commutator	commutator	NOUN
ma-260	20	9	;	;	PUNCT
ma-260	20	10	sublinear	sublinear	NOUN
ma-260	20	11	operators	operator	NOUN
ma-260	20	12	;	;	PUNCT
ma-260	20	13	bmo	bmo	PROPN
ma-260	20	14	spaces.1	spaces.1	PROPN
ma-260	20	15	https://adac.ee	https://adac.ee	PROPN
ma-260	20	16	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	20	17	eur	eur	PROPN
ma-260	20	18	.	.	PUNCT
ma-260	21	1	j.	j.	PROPN
ma-260	21	2	math	math	PROPN
ma-260	21	3	.	.	PUNCT
ma-260	22	1	anal	anal	PROPN
ma-260	22	2	.	.	PUNCT
ma-260	23	1	10.28924	10.28924	NUM
ma-260	23	2	/	/	SYM
ma-260	23	3	ada	ada	PROPN
ma-260	23	4	/	/	SYM
ma-260	23	5	ma.4.22	ma.4.22	PROPN
ma-260	23	6	2an	2an	ADJ
ma-260	23	7	important	important	ADJ
ma-260	23	8	role	role	NOUN
ma-260	23	9	in	in	ADP
ma-260	23	10	real	real	ADJ
ma-260	23	11	and	and	CCONJ
ma-260	23	12	harmonic	harmonic	ADJ
ma-260	23	13	analysis	analysis	NOUN
ma-260	23	14	and	and	CCONJ
ma-260	23	15	applications	application	NOUN
ma-260	23	16	(	(	PUNCT
ma-260	23	17	see	see	VERB
ma-260	23	18	for	for	ADP
ma-260	23	19	example	example	NOUN
ma-260	23	20	[	[	X
ma-260	23	21	1	1	NUM
ma-260	23	22	,	,	PUNCT
ma-260	23	23	2	2	NUM
ma-260	23	24	,	,	PUNCT
ma-260	23	25	10	10	NUM
ma-260	23	26	,	,	PUNCT
ma-260	23	27	15	15	NUM
ma-260	23	28	,	,	PUNCT
ma-260	23	29	16]and	16]and	NUM
ma-260	23	30	the	the	DET
ma-260	23	31	references	reference	NOUN
ma-260	23	32	therein	therein	ADV
ma-260	23	33	)	)	PUNCT
ma-260	23	34	.	.	PUNCT
ma-260	24	1	the	the	DET
ma-260	24	2	boundedness	boundedness	NOUN
ma-260	24	3	of	of	ADP
ma-260	24	4	these	these	DET
ma-260	24	5	operators	operator	NOUN
ma-260	24	6	on	on	ADP
ma-260	24	7	lebesgue	lebesgue	NOUN
ma-260	24	8	spaces	space	NOUN
ma-260	24	9	has	have	AUX
ma-260	24	10	beenextended	beenextende	VERB
ma-260	24	11	to	to	ADP
ma-260	24	12	several	several	ADJ
ma-260	24	13	other	other	ADJ
ma-260	24	14	spaces	space	NOUN
ma-260	24	15	.	.	PUNCT
ma-260	25	1	for	for	ADP
ma-260	25	2	example	example	NOUN
ma-260	25	3	,	,	PUNCT
ma-260	25	4	on	on	ADP
ma-260	25	5	morrey	morrey	PROPN
ma-260	25	6	spaces	space	NOUN
ma-260	25	7	(	(	PUNCT
ma-260	25	8	[	[	X
ma-260	25	9	4	4	NUM
ma-260	25	10	]	]	PUNCT
ma-260	25	11	,	,	PUNCT
ma-260	25	12	[	[	X
ma-260	25	13	11	11	NUM
ma-260	25	14	]	]	NUM
ma-260	25	15	)	)	PUNCT
ma-260	25	16	,	,	PUNCT
ma-260	25	17	modified	modify	VERB
ma-260	25	18	morreyspaces	morreyspace	NOUN
ma-260	25	19	(	(	PUNCT
ma-260	25	20	[	[	X
ma-260	25	21	14	14	NUM
ma-260	25	22	]	]	NUM
ma-260	25	23	)	)	PUNCT
ma-260	25	24	,	,	PUNCT
ma-260	25	25	total	total	ADJ
ma-260	25	26	morrey	morrey	NOUN
ma-260	25	27	spaces	space	NOUN
ma-260	25	28	(	(	PUNCT
ma-260	25	29	[	[	X
ma-260	25	30	13	13	NUM
ma-260	25	31	]	]	NUM
ma-260	25	32	)	)	PUNCT
ma-260	25	33	,	,	PUNCT
ma-260	25	34	fofana	fofana	PROPN
ma-260	25	35	spaces	space	VERB
ma-260	25	36	(	(	PUNCT
ma-260	25	37	[	[	X
ma-260	25	38	6	6	NUM
ma-260	25	39	]	]	PUNCT
ma-260	25	40	)	)	PUNCT
ma-260	25	41	to	to	PART
ma-260	25	42	name	name	VERB
ma-260	25	43	but	but	CCONJ
ma-260	25	44	a	a	DET
ma-260	25	45	few.recently	few.recently	ADV
ma-260	25	46	,	,	PUNCT
ma-260	25	47	p.	p.	NOUN
ma-260	25	48	nagacy	nagacy	NOUN
ma-260	25	49	and	and	CCONJ
ma-260	25	50	b.	b.	PROPN
ma-260	25	51	a.	a.	PROPN
ma-260	25	52	kpata	kpata	PROPN
ma-260	26	1	[	[	X
ma-260	26	2	17	17	NUM
ma-260	26	3	]	]	PUNCT
ma-260	26	4	introduced	introduce	VERB
ma-260	26	5	the	the	DET
ma-260	26	6	total	total	ADJ
ma-260	26	7	fofana	fofana	NOUN
ma-260	26	8	spaces	space	NOUN
ma-260	26	9	and	and	CCONJ
ma-260	26	10	established	establish	VERB
ma-260	26	11	inthese	inthese	ADJ
ma-260	26	12	spaces	space	NOUN
ma-260	26	13	,	,	PUNCT
ma-260	26	14	under	under	ADP
ma-260	26	15	certain	certain	ADJ
ma-260	26	16	conditions	condition	NOUN
ma-260	26	17	,	,	PUNCT
ma-260	26	18	the	the	DET
ma-260	26	19	boundedness	boundedness	NOUN
ma-260	26	20	of	of	ADP
ma-260	26	21	the	the	DET
ma-260	26	22	hardy	hardy	ADJ
ma-260	26	23	-	-	PUNCT
ma-260	26	24	littlewood	littlewood	NOUN
ma-260	26	25	maximal	maximal	ADJ
ma-260	26	26	operators	operator	NOUN
ma-260	26	27	,	,	PUNCT
ma-260	26	28	the	the	DET
ma-260	26	29	riesz	riesz	NOUN
ma-260	26	30	potential	potential	NOUN
ma-260	26	31	and	and	CCONJ
ma-260	26	32	fractional	fractional	ADJ
ma-260	26	33	maximal	maximal	ADJ
ma-260	26	34	operators.the	operators.the	DET
ma-260	26	35	main	main	ADJ
ma-260	26	36	purpose	purpose	NOUN
ma-260	26	37	of	of	ADP
ma-260	26	38	the	the	DET
ma-260	26	39	present	present	ADJ
ma-260	26	40	paper	paper	NOUN
ma-260	26	41	is	be	AUX
ma-260	26	42	to	to	PART
ma-260	26	43	establish	establish	VERB
ma-260	26	44	the	the	DET
ma-260	26	45	boundedness	boundedness	NOUN
ma-260	26	46	of	of	ADP
ma-260	26	47	the	the	DET
ma-260	26	48	commutators	commutator	NOUN
ma-260	26	49	of	of	ADP
ma-260	26	50	thehardy	thehardy	ADJ
ma-260	26	51	-	-	PUNCT
ma-260	26	52	littlewood	littlewood	NOUN
ma-260	26	53	maximal	maximal	ADJ
ma-260	26	54	operator	operator	NOUN
ma-260	26	55	and	and	CCONJ
ma-260	26	56	some	some	DET
ma-260	26	57	sublinear	sublinear	NOUN
ma-260	26	58	operators	operator	NOUN
ma-260	26	59	in	in	ADP
ma-260	26	60	total	total	ADJ
ma-260	26	61	fofana	fofana	PROPN
ma-260	26	62	spaces	space	NOUN
ma-260	26	63	.	.	PUNCT
ma-260	27	1	beforestating	beforestate	VERB
ma-260	27	2	our	our	PRON
ma-260	27	3	main	main	ADJ
ma-260	27	4	results	result	NOUN
ma-260	27	5	,	,	PUNCT
ma-260	27	6	let	let	VERB
ma-260	27	7	us	we	PRON
ma-260	27	8	start	start	VERB
ma-260	27	9	with	with	ADP
ma-260	27	10	some	some	DET
ma-260	27	11	notations	notation	NOUN
ma-260	27	12	and	and	CCONJ
ma-260	27	13	basic	basic	ADJ
ma-260	27	14	definitions	definition	NOUN
ma-260	27	15	.	.	PUNCT
ma-260	28	1	let	let	VERB
ma-260	28	2	1	1	NUM
ma-260	28	3	≤	≤	NOUN
ma-260	28	4	q	q	NOUN
ma-260	28	5	,	,	PUNCT
ma-260	28	6	p	p	ADJ
ma-260	28	7	≤	≤	NOUN
ma-260	28	8	∞and	∞and	ADP
ma-260	28	9	r	r	NOUN
ma-260	28	10	>	>	X
ma-260	28	11	0	0	NUM
ma-260	28	12	.	.	PUNCT
ma-260	29	1	for	for	ADP
ma-260	29	2	f	f	PROPN
ma-260	29	3	∈	∈	PROPN
ma-260	29	4	l0(rd	l0(rd	PROPN
ma-260	29	5	)	)	PUNCT
ma-260	29	6	we	we	PRON
ma-260	29	7	define	define	VERB
ma-260	29	8	r	r	NOUN
ma-260	29	9	‖f	‖f	ADJ
ma-260	30	1	‖q	‖q	NOUN
ma-260	30	2	,	,	PUNCT
ma-260	30	3	p	p	X
ma-260	30	4	:	:	PUNCT
ma-260	30	5	=	=	SYM
ma-260	30	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-260	31	1	[	[	X
ma-260	31	2	∫	∫	PROPN
ma-260	31	3	rd	rd	PROPN
ma-260	31	4	|f	|f	PROPN
ma-260	31	5	χb(y	χb(y	PUNCT
ma-260	31	6	,	,	PUNCT
ma-260	31	7	r)|q(x)dx	r)|q(x)dx	VERB
ma-260	31	8	]	]	PUNCT
ma-260	31	9	1	1	NUM
ma-260	31	10	q	q	SYM
ma-260	31	11	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-260	31	12	pwith	pwith	NOUN
ma-260	31	13	the	the	DET
ma-260	31	14	lp(rd)-norm	lp(rd)-norm	NOUN
ma-260	31	15	taken	take	VERB
ma-260	31	16	with	with	ADP
ma-260	31	17	respect	respect	NOUN
ma-260	31	18	to	to	ADP
ma-260	31	19	the	the	DET
ma-260	31	20	variable	variable	ADJ
ma-260	31	21	y	y	PROPN
ma-260	31	22	.	.	PUNCT
ma-260	32	1	we	we	PRON
ma-260	32	2	adopt	adopt	VERB
ma-260	32	3	the	the	DET
ma-260	32	4	usual	usual	ADJ
ma-260	32	5	convention	convention	NOUN
ma-260	32	6	1	1	NUM
ma-260	32	7	∞	∞	NUM
ma-260	32	8	=	=	SYM
ma-260	32	9	0.in	0.in	NUM
ma-260	32	10	1988	1988	NUM
ma-260	32	11	,	,	PUNCT
ma-260	32	12	fofana	fofana	PROPN
ma-260	33	1	[	[	X
ma-260	33	2	7	7	X
ma-260	33	3	]	]	PUNCT
ma-260	33	4	introduced	introduce	VERB
ma-260	33	5	the	the	DET
ma-260	33	6	functions	function	NOUN
ma-260	33	7	spaces	space	NOUN
ma-260	33	8	(	(	PUNCT
ma-260	33	9	lq	lq	PROPN
ma-260	33	10	,	,	PUNCT
ma-260	33	11	lp)α	lp)α	PROPN
ma-260	33	12	(	(	PUNCT
ma-260	33	13	rd	rd	NOUN
ma-260	33	14	)	)	PUNCT
ma-260	33	15	,	,	PUNCT
ma-260	33	16	1	1	NUM
ma-260	33	17	≤	≤	NUM
ma-260	33	18	q	q	ADJ
ma-260	33	19	≤	≤	NUM
ma-260	33	20	α	α	NOUN
ma-260	33	21	≤	≤	NOUN
ma-260	33	22	p	p	NOUN
ma-260	33	23	≤	≤	NUM
ma-260	33	24	∞	∞	PROPN
ma-260	33	25	,	,	PUNCT
ma-260	33	26	whichconsists	whichconsist	NOUN
ma-260	33	27	of	of	ADP
ma-260	33	28	the	the	DET
ma-260	33	29	set	set	NOUN
ma-260	33	30	of	of	ADP
ma-260	33	31	all	all	DET
ma-260	33	32	functions	function	NOUN
ma-260	33	33	f	f	PROPN
ma-260	33	34	∈	∈	PROPN
ma-260	33	35	l0(rd	l0(rd	PROPN
ma-260	33	36	)	)	PUNCT
ma-260	33	37	satisfying	satisfying	NOUN
ma-260	33	38	‖f	‖f	ADP
ma-260	33	39	‖q	‖q	NOUN
ma-260	33	40	,	,	PUNCT
ma-260	33	41	p	p	X
ma-260	33	42	,	,	PUNCT
ma-260	33	43	α	α	X
ma-260	33	44	<	<	X
ma-260	33	45	∞	∞	PROPN
ma-260	33	46	,	,	PUNCT
ma-260	33	47	where	where	SCONJ
ma-260	33	48	‖f	‖f	ADP
ma-260	33	49	‖q	‖q	NOUN
ma-260	33	50	,	,	PUNCT
ma-260	33	51	p	p	X
ma-260	33	52	,	,	PUNCT
ma-260	33	53	α	α	NOUN
ma-260	33	54	=	=	NOUN
ma-260	33	55	sup	sup	PROPN
ma-260	33	56	r>0	r>0	PROPN
ma-260	33	57	rd	rd	PROPN
ma-260	33	58	(	(	PUNCT
ma-260	33	59	1	1	NUM
ma-260	33	60	α	α	NOUN
ma-260	33	61	−	−	PROPN
ma-260	33	62	1	1	NUM
ma-260	33	63	q	q	NOUN
ma-260	33	64	−	−	PROPN
ma-260	33	65	1	1	NUM
ma-260	33	66	p	p	NOUN
ma-260	33	67	)	)	PUNCT
ma-260	33	68	r	r	NOUN
ma-260	33	69	‖f	‖f	ADJ
ma-260	33	70	‖q	‖q	NOUN
ma-260	33	71	,	,	PUNCT
ma-260	33	72	p	p	NOUN
ma-260	33	73	.	.	PUNCT
ma-260	34	1	it	it	PRON
ma-260	34	2	is	be	AUX
ma-260	34	3	proved	prove	VERB
ma-260	34	4	in	in	ADP
ma-260	34	5	[	[	X
ma-260	34	6	7	7	X
ma-260	34	7	]	]	X
ma-260	34	8	the	the	DET
ma-260	34	9	following	follow	VERB
ma-260	34	10	properties	property	NOUN
ma-260	34	11	:	:	PUNCT
ma-260	34	12	•	•	NOUN
ma-260	34	13	for	for	ADP
ma-260	34	14	1	1	NUM
ma-260	34	15	≤	≤	NOUN
ma-260	34	16	q	q	NOUN
ma-260	34	17	<	<	X
ma-260	34	18	α	α	X
ma-260	34	19	fixed	fix	VERB
ma-260	34	20	and	and	CCONJ
ma-260	34	21	p	p	NOUN
ma-260	34	22	going	go	VERB
ma-260	34	23	from	from	ADP
ma-260	34	24	α	α	PRON
ma-260	34	25	to	to	ADP
ma-260	34	26	∞	∞	PROPN
ma-260	34	27	,	,	PUNCT
ma-260	34	28	the	the	DET
ma-260	34	29	spaces	space	NOUN
ma-260	34	30	(	(	PUNCT
ma-260	34	31	lq	lq	PROPN
ma-260	34	32	,	,	PUNCT
ma-260	34	33	lp)α	lp)α	PROPN
ma-260	34	34	(	(	PUNCT
ma-260	34	35	rd	rd	NOUN
ma-260	34	36	)	)	PUNCT
ma-260	34	37	form	form	VERB
ma-260	34	38	a	a	DET
ma-260	34	39	chain	chain	NOUN
ma-260	34	40	of	of	ADP
ma-260	34	41	distinctbanach	distinctbanach	PROPN
ma-260	34	42	spaces	space	NOUN
ma-260	34	43	beginning	begin	VERB
ma-260	34	44	with	with	ADP
ma-260	34	45	the	the	DET
ma-260	34	46	lebesgue	lebesgue	NOUN
ma-260	34	47	space	space	NOUN
ma-260	34	48	lα(rd	lα(rd	PROPN
ma-260	34	49	)	)	PUNCT
ma-260	34	50	and	and	CCONJ
ma-260	34	51	ending	end	VERB
ma-260	34	52	by	by	ADP
ma-260	34	53	the	the	DET
ma-260	34	54	classical	classical	ADJ
ma-260	34	55	morreyspace	morreyspace	NOUN
ma-260	34	56	lq	lq	VERB
ma-260	34	57	,	,	PUNCT
ma-260	34	58	d(1−	d(1−	X
ma-260	34	59	q	q	PROPN
ma-260	34	60	α	α	NOUN
ma-260	34	61	)	)	PUNCT
ma-260	34	62	(	(	PUNCT
ma-260	34	63	rd	rd	NOUN
ma-260	34	64	)	)	PUNCT
ma-260	34	65	=	=	PRON
ma-260	34	66	(	(	PUNCT
ma-260	34	67	lq	lq	PROPN
ma-260	34	68	,	,	PUNCT
ma-260	34	69	l∞)α	l∞)α	X
ma-260	34	70	(	(	PUNCT
ma-260	34	71	rd	rd	NOUN
ma-260	34	72	)	)	PUNCT
ma-260	35	1	;	;	PUNCT
ma-260	35	2	•	•	X
ma-260	35	3	there	there	PRON
ma-260	35	4	exists	exist	VERB
ma-260	35	5	a	a	DET
ma-260	35	6	constant	constant	ADJ
ma-260	35	7	c	c	NOUN
ma-260	35	8	>	>	X
ma-260	35	9	0	0	NUM
ma-260	35	10	such	such	ADJ
ma-260	35	11	that	that	SCONJ
ma-260	35	12	‖f	‖f	ADP
ma-260	35	13	‖q	‖q	NOUN
ma-260	35	14	,	,	PUNCT
ma-260	35	15	p	p	X
ma-260	35	16	,	,	PUNCT
ma-260	35	17	α	α	NOUN
ma-260	35	18	≤	≤	NOUN
ma-260	35	19	c	c	NOUN
ma-260	35	20	‖f	‖f	PRON
ma-260	35	21	‖α	‖α	PROPN
ma-260	35	22	.	.	PUNCT
ma-260	36	1	(	(	PUNCT
ma-260	36	2	1.2	1.2	NUM
ma-260	36	3	)	)	PUNCT
ma-260	36	4	for	for	ADP
ma-260	36	5	an	an	DET
ma-260	36	6	in	in	ADP
ma-260	36	7	-	-	PUNCT
ma-260	36	8	depth	depth	NOUN
ma-260	36	9	study	study	NOUN
ma-260	36	10	of	of	ADP
ma-260	36	11	fofana	fofana	PROPN
ma-260	36	12	spaces	space	NOUN
ma-260	36	13	,	,	PUNCT
ma-260	36	14	please	please	INTJ
ma-260	36	15	consult	consult	VERB
ma-260	36	16	the	the	DET
ma-260	36	17	following	following	ADJ
ma-260	36	18	references	reference	NOUN
ma-260	36	19	(	(	PUNCT
ma-260	36	20	see	see	VERB
ma-260	36	21	[	[	X
ma-260	36	22	6	6	NUM
ma-260	36	23	,	,	PUNCT
ma-260	36	24	8	8	NUM
ma-260	36	25	,	,	PUNCT
ma-260	36	26	9]).let	9]).let	NUM
ma-260	36	27	1	1	NUM
ma-260	36	28	≤	≤	NOUN
ma-260	36	29	q	q	PROPN
ma-260	36	30	≤	≤	NUM
ma-260	36	31	α	α	NOUN
ma-260	36	32	,	,	PUNCT
ma-260	36	33	λ	λ	PROPN
ma-260	36	34	≤	≤	NOUN
ma-260	36	35	p	p	NOUN
ma-260	36	36	≤	≤	NOUN
ma-260	36	37	∞	∞	PROPN
ma-260	36	38	and	and	CCONJ
ma-260	37	1	[	[	X
ma-260	37	2	r	r	X
ma-260	37	3	]	]	SYM
ma-260	37	4	1	1	NUM
ma-260	37	5	=	=	SYM
ma-260	37	6	min{1	min{1	PROPN
ma-260	37	7	,	,	PUNCT
ma-260	37	8	r	r	NOUN
ma-260	37	9	}	}	PUNCT
ma-260	37	10	,	,	PUNCT
ma-260	37	11	r	r	NOUN
ma-260	37	12	>	>	X
ma-260	37	13	0	0	NUM
ma-260	37	14	.	.	PUNCT
ma-260	38	1	the	the	DET
ma-260	38	2	total	total	ADJ
ma-260	38	3	fofana	fofana	NOUN
ma-260	38	4	spaces	space	NOUN
ma-260	38	5	(	(	PUNCT
ma-260	38	6	lq	lq	PROPN
ma-260	38	7	,	,	PUNCT
ma-260	38	8	lp)α	lp)α	PROPN
ma-260	38	9	,	,	PUNCT
ma-260	38	10	λ(rd)are	λ(rd)are	PROPN
ma-260	38	11	defined	define	VERB
ma-260	38	12	by	by	ADP
ma-260	38	13	(	(	PUNCT
ma-260	38	14	lq	lq	PROPN
ma-260	38	15	,	,	PUNCT
ma-260	38	16	lp)α	lp)α	PROPN
ma-260	38	17	,	,	PUNCT
ma-260	38	18	λ(rd	λ(rd	X
ma-260	38	19	)	)	PUNCT
ma-260	38	20	=	=	SYM
ma-260	38	21	{	{	PUNCT
ma-260	38	22	f	f	PROPN
ma-260	38	23	∈	∈	PROPN
ma-260	38	24	l0(rd	l0(rd	PROPN
ma-260	38	25	)	)	PUNCT
ma-260	38	26	:	:	PUNCT
ma-260	38	27	‖f	‖f	ADP
ma-260	38	28	‖(lq	‖(lq	CCONJ
ma-260	38	29	,	,	PUNCT
ma-260	38	30	lp)α	lp)α	PROPN
ma-260	38	31	,	,	PUNCT
ma-260	38	32	λ(rd	λ(rd	ADV
ma-260	38	33	)	)	PUNCT
ma-260	38	34	<	<	X
ma-260	38	35	∞	∞	NUM
ma-260	38	36	}	}	PUNCT
ma-260	38	37	where	where	SCONJ
ma-260	38	38	‖f	‖f	ADJ
ma-260	38	39	‖(lq	‖(lq	NUM
ma-260	38	40	,	,	PUNCT
ma-260	38	41	lp)α	lp)α	PROPN
ma-260	38	42	,	,	PUNCT
ma-260	38	43	λ(rd	λ(rd	ADV
ma-260	38	44	)	)	PUNCT
ma-260	38	45	=	=	SYM
ma-260	38	46	sup	sup	NUM
ma-260	38	47	r>0	r>0	PROPN
ma-260	39	1	[	[	X
ma-260	39	2	r	r	X
ma-260	39	3	]	]	X
ma-260	39	4	d	d	X
ma-260	39	5	(	(	PUNCT
ma-260	39	6	1	1	NUM
ma-260	39	7	α	α	NOUN
ma-260	39	8	−	−	PROPN
ma-260	39	9	1	1	NUM
ma-260	39	10	q	q	NOUN
ma-260	39	11	−	−	PROPN
ma-260	39	12	1	1	NUM
ma-260	39	13	p	p	NOUN
ma-260	39	14	)	)	PUNCT
ma-260	39	15	1	1	NUM
ma-260	40	1	[	[	X
ma-260	40	2	1	1	NUM
ma-260	40	3	/	/	SYM
ma-260	40	4	r	r	NOUN
ma-260	40	5	]	]	PUNCT
ma-260	40	6	d(−	d(−	PROPN
ma-260	40	7	1	1	NUM
ma-260	40	8	λ	λ	NOUN
ma-260	40	9	+	+	NOUN
ma-260	40	10	1	1	NUM
ma-260	40	11	q	q	NOUN
ma-260	40	12	+	+	NUM
ma-260	40	13	1	1	NUM
ma-260	40	14	p	p	NOUN
ma-260	40	15	)	)	PUNCT
ma-260	40	16	1	1	NUM
ma-260	40	17	r	r	NOUN
ma-260	40	18	‖f	‖f	ADJ
ma-260	40	19	‖q	‖q	NOUN
ma-260	40	20	,	,	PUNCT
ma-260	40	21	p	p	NOUN
ma-260	40	22	.note	.note	PUNCT
ma-260	40	23	that(1	that(1	NOUN
ma-260	40	24	)	)	PUNCT
ma-260	41	1	the	the	DET
ma-260	41	2	space	space	NOUN
ma-260	41	3	(	(	PUNCT
ma-260	41	4	lq	lq	PROPN
ma-260	41	5	,	,	PUNCT
ma-260	41	6	lp)α	lp)α	PROPN
ma-260	41	7	,	,	PUNCT
ma-260	41	8	λ(rd	λ(rd	NUM
ma-260	41	9	)	)	PUNCT
ma-260	41	10	is	be	AUX
ma-260	41	11	a	a	DET
ma-260	41	12	complex	complex	ADJ
ma-260	41	13	vector	vector	NOUN
ma-260	41	14	subspace	subspace	NOUN
ma-260	41	15	of	of	ADP
ma-260	41	16	l0(rd).(2	l0(rd).(2	PROPN
ma-260	41	17	)	)	PUNCT
ma-260	41	18	from	from	ADP
ma-260	41	19	the	the	DET
ma-260	41	20	definition	definition	NOUN
ma-260	41	21	of	of	ADP
ma-260	41	22	(	(	PUNCT
ma-260	41	23	lq	lq	PROPN
ma-260	41	24	,	,	PUNCT
ma-260	41	25	lp)α	lp)α	PROPN
ma-260	41	26	,	,	PUNCT
ma-260	41	27	λ(rd	λ(rd	NUM
ma-260	41	28	)	)	PUNCT
ma-260	41	29	spaces	space	VERB
ma-260	41	30	we	we	PRON
ma-260	41	31	deduce	deduce	VERB
ma-260	41	32	that	that	SCONJ
ma-260	41	33	the	the	DET
ma-260	41	34	map	map	NOUN
ma-260	41	35	l0(rd	l0(rd	PROPN
ma-260	41	36	)	)	PUNCT
ma-260	41	37	3	3	NUM
ma-260	41	38	f	f	SYM
ma-260	41	39	7→	7→	NUM
ma-260	41	40	‖f	‖f	ADJ
ma-260	41	41	‖(lq	‖(lq	CCONJ
ma-260	41	42	,	,	PUNCT
ma-260	41	43	lp)α	lp)α	PROPN
ma-260	41	44	,	,	PUNCT
ma-260	41	45	λ(rd	λ(rd	ADJ
ma-260	41	46	)	)	PUNCT
ma-260	41	47	defines	define	VERB
ma-260	41	48	a	a	DET
ma-260	41	49	norm	norm	NOUN
ma-260	41	50	on	on	ADP
ma-260	41	51	(	(	PUNCT
ma-260	41	52	lq	lq	PROPN
ma-260	41	53	,	,	PUNCT
ma-260	41	54	lp)α	lp)α	PROPN
ma-260	41	55	,	,	PUNCT
ma-260	41	56	λ(rd	λ(rd	NOUN
ma-260	41	57	)	)	PUNCT
ma-260	41	58	.	.	PUNCT
ma-260	42	1	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	42	2	eur	eur	PROPN
ma-260	42	3	.	.	PUNCT
ma-260	43	1	j.	j.	PROPN
ma-260	43	2	math	math	PROPN
ma-260	43	3	.	.	PUNCT
ma-260	44	1	anal	anal	PROPN
ma-260	44	2	.	.	PUNCT
ma-260	45	1	10.28924	10.28924	NUM
ma-260	45	2	/	/	SYM
ma-260	45	3	ada	ada	PROPN
ma-260	45	4	/	/	SYM
ma-260	45	5	ma.4.22	ma.4.22	PROPN
ma-260	45	6	3	3	NUM
ma-260	45	7	(	(	PUNCT
ma-260	45	8	3	3	NUM
ma-260	45	9	)	)	PUNCT
ma-260	45	10	for	for	ADP
ma-260	45	11	1	1	NUM
ma-260	45	12	≤	≤	NUM
ma-260	45	13	q	q	PROPN
ma-260	45	14	≤	≤	NUM
ma-260	45	15	α	α	NOUN
ma-260	45	16	,	,	PUNCT
ma-260	45	17	λ	λ	X
ma-260	45	18	<	<	X
ma-260	45	19	∞	∞	PROPN
ma-260	45	20	,	,	PUNCT
ma-260	45	21	the	the	DET
ma-260	45	22	space	space	NOUN
ma-260	45	23	(	(	PUNCT
ma-260	45	24	lq	lq	PROPN
ma-260	45	25	,	,	PUNCT
ma-260	45	26	l∞)α	l∞)α	NOUN
ma-260	45	27	,	,	PUNCT
ma-260	45	28	λ(rd	λ(rd	NUM
ma-260	45	29	)	)	PUNCT
ma-260	45	30	is	be	AUX
ma-260	45	31	the	the	DET
ma-260	45	32	total	total	ADJ
ma-260	45	33	morrey	morrey	PROPN
ma-260	45	34	space	space	NOUN
ma-260	45	35	lq	lq	VERB
ma-260	45	36	,	,	PUNCT
ma-260	45	37	d(1−	d(1−	X
ma-260	45	38	q	q	PROPN
ma-260	45	39	α	α	PROPN
ma-260	45	40	)	)	PUNCT
ma-260	45	41	,	,	PUNCT
ma-260	45	42	d(1−	d(1−	X
ma-260	45	43	q	q	PROPN
ma-260	45	44	λ	λ	PROPN
ma-260	45	45	)	)	PUNCT
ma-260	45	46	(	(	PUNCT
ma-260	45	47	rd)defined	rd)define	VERB
ma-260	45	48	in	in	ADP
ma-260	45	49	[	[	X
ma-260	45	50	13	13	NUM
ma-260	45	51	]	]	PUNCT
ma-260	45	52	and	and	CCONJ
ma-260	45	53	lq	lq	NOUN
ma-260	45	54	,	,	PUNCT
ma-260	45	55	d(1−	d(1−	X
ma-260	45	56	q	q	PROPN
ma-260	45	57	α	α	PROPN
ma-260	45	58	)	)	PUNCT
ma-260	45	59	,	,	PUNCT
ma-260	45	60	d(1−	d(1−	X
ma-260	45	61	q	q	PROPN
ma-260	45	62	λ	λ	PROPN
ma-260	45	63	)	)	PUNCT
ma-260	45	64	(	(	PUNCT
ma-260	45	65	rd	rd	NOUN
ma-260	45	66	)	)	PUNCT
ma-260	46	1	=	=	SYM
ma-260	46	2	lq	lq	NOUN
ma-260	46	3	,	,	PUNCT
ma-260	46	4	d(1−	d(1−	X
ma-260	46	5	q	q	PROPN
ma-260	46	6	α	α	NOUN
ma-260	46	7	)	)	PUNCT
ma-260	46	8	(	(	PUNCT
ma-260	46	9	rd	rd	NOUN
ma-260	46	10	)	)	PUNCT
ma-260	46	11	∩	∩	NOUN
ma-260	46	12	lq	lq	NOUN
ma-260	46	13	,	,	PUNCT
ma-260	46	14	d(1−	d(1−	ADJ
ma-260	46	15	q	q	PROPN
ma-260	46	16	λ	λ	PROPN
ma-260	46	17	)	)	PUNCT
ma-260	46	18	(	(	PUNCT
ma-260	46	19	rd	rd	NOUN
ma-260	46	20	)	)	PUNCT
ma-260	46	21	with	with	ADP
ma-260	46	22	λ	λ	PROPN
ma-260	46	23	≤	≤	NUM
ma-260	46	24	α.we	α.we	NOUN
ma-260	46	25	define	define	VERB
ma-260	46	26	the	the	DET
ma-260	46	27	space	space	NOUN
ma-260	46	28	bmo(rd	bmo(rd	NOUN
ma-260	46	29	)	)	PUNCT
ma-260	46	30	as	as	ADP
ma-260	46	31	the	the	DET
ma-260	46	32	set	set	NOUN
ma-260	46	33	of	of	ADP
ma-260	46	34	all	all	DET
ma-260	46	35	locally	locally	ADV
ma-260	46	36	integrable	integrable	ADJ
ma-260	46	37	functions	function	NOUN
ma-260	46	38	b	b	NOUN
ma-260	46	39	with	with	ADP
ma-260	46	40	finite	finite	ADJ
ma-260	46	41	norm	norm	NOUN
ma-260	46	42	‖b‖bmo(rd	‖b‖bmo(rd	NOUN
ma-260	46	43	)	)	PUNCT
ma-260	47	1	=	=	SYM
ma-260	47	2	sup	sup	NOUN
ma-260	47	3	r>0,x∈rd	r>0,x∈rd	NOUN
ma-260	47	4	|b(x	|b(x	NOUN
ma-260	47	5	,	,	PUNCT
ma-260	47	6	r)|−1	r)|−1	VERB
ma-260	47	7	∫	∫	PROPN
ma-260	47	8	b(x	b(x	PROPN
ma-260	47	9	,	,	PUNCT
ma-260	47	10	r	r	NOUN
ma-260	47	11	)	)	PUNCT
ma-260	47	12	|b(y)−	|b(y)−	ADJ
ma-260	47	13	bb(x	bb(x	PROPN
ma-260	47	14	,	,	PUNCT
ma-260	47	15	r)|dy	r)|dy	NOUN
ma-260	48	1	where	where	SCONJ
ma-260	48	2	bb(x	bb(x	ADJ
ma-260	48	3	,	,	PUNCT
ma-260	48	4	r	r	NOUN
ma-260	48	5	)	)	PUNCT
ma-260	48	6	=	=	SYM
ma-260	48	7	|b(x	|b(x	PROPN
ma-260	48	8	,	,	PUNCT
ma-260	48	9	r)|−1	r)|−1	VERB
ma-260	48	10	∫	∫	PROPN
ma-260	48	11	b(x	b(x	PROPN
ma-260	48	12	,	,	PUNCT
ma-260	48	13	r	r	NOUN
ma-260	48	14	)	)	PUNCT
ma-260	48	15	b(y)dy.for	b(y)dy.for	ADP
ma-260	48	16	a	a	DET
ma-260	48	17	function	function	NOUN
ma-260	48	18	b	b	NOUN
ma-260	48	19	defined	define	VERB
ma-260	48	20	on	on	ADP
ma-260	48	21	rd	rd	PROPN
ma-260	48	22	,	,	PUNCT
ma-260	48	23	we	we	PRON
ma-260	48	24	denote	denote	VERB
ma-260	48	25	by	by	ADP
ma-260	48	26	b−(x	b−(x	PROPN
ma-260	48	27	)	)	PUNCT
ma-260	48	28	:	:	PUNCT
ma-260	49	1	=	=	SYM
ma-260	49	2	{	{	PUNCT
ma-260	49	3	0	0	NUM
ma-260	49	4	if	if	SCONJ
ma-260	49	5	b(x	b(x	VERB
ma-260	49	6	)	)	PUNCT
ma-260	49	7	≥	≥	NOUN
ma-260	49	8	0	0	NUM
ma-260	49	9	|b(x)|	|b(x)|	PROPN
ma-260	49	10	if	if	SCONJ
ma-260	49	11	b(x	b(x	VERB
ma-260	49	12	)	)	PUNCT
ma-260	49	13	<	<	X
ma-260	49	14	0	0	PUNCT
ma-260	49	15	and	and	CCONJ
ma-260	49	16	b+(x	b+(x	ADJ
ma-260	49	17	)	)	PUNCT
ma-260	49	18	=	=	PUNCT
ma-260	49	19	|b(x)|	|b(x)|	PROPN
ma-260	49	20	−	−	PROPN
ma-260	49	21	b−(x	b−(x	NOUN
ma-260	49	22	)	)	PUNCT
ma-260	49	23	.	.	PUNCT
ma-260	50	1	obviously	obviously	ADV
ma-260	50	2	b+(x)−	b+(x)−	PROPN
ma-260	50	3	b−(x	b−(x	PROPN
ma-260	50	4	)	)	PUNCT
ma-260	51	1	=	=	PUNCT
ma-260	52	1	b(x).our	b(x).our	PRON
ma-260	52	2	first	first	ADJ
ma-260	52	3	result	result	NOUN
ma-260	52	4	reads	read	VERB
ma-260	52	5	as	as	SCONJ
ma-260	52	6	follows	follow	NOUN
ma-260	52	7	theorem	theorem	VERB
ma-260	52	8	1.1	1.1	NUM
ma-260	52	9	.	.	PUNCT
ma-260	53	1	let	let	VERB
ma-260	53	2	1	1	NUM
ma-260	53	3	<	<	X
ma-260	53	4	q	q	X
ma-260	53	5	≤	≤	NUM
ma-260	53	6	λ	λ	NOUN
ma-260	53	7	≤	≤	NUM
ma-260	53	8	α	α	NOUN
ma-260	53	9	<	<	X
ma-260	53	10	p	p	X
ma-260	53	11	<	<	X
ma-260	53	12	∞	∞	NUM
ma-260	53	13	such	such	ADJ
ma-260	53	14	that	that	SCONJ
ma-260	53	15	1q	1q	NUM
ma-260	53	16	+	+	NOUN
ma-260	53	17	2	2	NUM
ma-260	53	18	p	p	NOUN
ma-260	53	19	<	<	X
ma-260	53	20	1	1	NUM
ma-260	53	21	α	α	NOUN
ma-260	53	22	+	+	NOUN
ma-260	53	23	1	1	NUM
ma-260	53	24	λ	λ	NOUN
ma-260	53	25	.	.	PUNCT
ma-260	54	1	then	then	ADV
ma-260	54	2	the	the	DET
ma-260	54	3	operator	operator	NOUN
ma-260	54	4	[	[	X
ma-260	54	5	b	b	X
ma-260	54	6	,	,	PUNCT
ma-260	54	7	m	m	VERB
ma-260	54	8	]	]	X
ma-260	54	9	is	be	AUX
ma-260	54	10	bounded	bound	VERB
ma-260	54	11	on	on	ADP
ma-260	54	12	(	(	PUNCT
ma-260	54	13	lq	lq	PROPN
ma-260	54	14	,	,	PUNCT
ma-260	54	15	lp)α	lp)α	PROPN
ma-260	54	16	,	,	PUNCT
ma-260	54	17	λ(rd	λ(rd	NOUN
ma-260	54	18	)	)	PUNCT
ma-260	54	19	if	if	SCONJ
ma-260	54	20	and	and	CCONJ
ma-260	54	21	only	only	ADV
ma-260	54	22	if	if	SCONJ
ma-260	54	23	b	b	PROPN
ma-260	54	24	∈	∈	PROPN
ma-260	54	25	bmo(rd	bmo(rd	NOUN
ma-260	54	26	)	)	PUNCT
ma-260	54	27	such	such	ADJ
ma-260	54	28	that	that	SCONJ
ma-260	54	29	b−	b−	PROPN
ma-260	54	30	∈	∈	PROPN
ma-260	54	31	l∞(rd	l∞(rd	NOUN
ma-260	54	32	)	)	PUNCT
ma-260	54	33	.	.	PUNCT
ma-260	55	1	the	the	DET
ma-260	55	2	last	last	ADJ
ma-260	55	3	two	two	NUM
ma-260	55	4	theorems	theorem	NOUN
ma-260	55	5	concern	concern	NOUN
ma-260	55	6	the	the	DET
ma-260	55	7	sublinear	sublinear	NOUN
ma-260	55	8	operators	operator	NOUN
ma-260	55	9	t	t	X
ma-260	55	10	satisfying	satisfy	VERB
ma-260	55	11	the	the	DET
ma-260	55	12	condition	condition	NOUN
ma-260	55	13	|t	|t	PROPN
ma-260	55	14	(	(	PUNCT
ma-260	55	15	x)|	x)|	PROPN
ma-260	55	16	≤	≤	PROPN
ma-260	56	1	c	c	PROPN
ma-260	56	2	∫	∫	PROPN
ma-260	56	3	rd	rd	PROPN
ma-260	56	4	|f	|f	PROPN
ma-260	57	1	(	(	PUNCT
ma-260	57	2	y)|	y)|	NOUN
ma-260	57	3	|x	|x	VERB
ma-260	57	4	−	−	PROPN
ma-260	57	5	y	y	PROPN
ma-260	57	6	|d	|d	NOUN
ma-260	57	7	dy	dy	X
ma-260	57	8	x	x	NOUN
ma-260	57	9	/∈	/∈	PUNCT
ma-260	57	10	supp	supp	PROPN
ma-260	57	11	f	f	PROPN
ma-260	57	12	,	,	PUNCT
ma-260	57	13	(	(	PUNCT
ma-260	57	14	1.3	1.3	NUM
ma-260	57	15	)	)	PUNCT
ma-260	57	16	for	for	ADP
ma-260	57	17	any	any	DET
ma-260	57	18	f	f	PROPN
ma-260	57	19	∈	∈	PROPN
ma-260	57	20	l1(rd	l1(rd	PROPN
ma-260	57	21	)	)	PUNCT
ma-260	57	22	with	with	ADP
ma-260	57	23	compact	compact	ADJ
ma-260	57	24	support	support	NOUN
ma-260	57	25	.	.	PUNCT
ma-260	58	1	we	we	PRON
ma-260	58	2	point	point	VERB
ma-260	58	3	out	out	ADP
ma-260	58	4	that	that	SCONJ
ma-260	58	5	the	the	DET
ma-260	58	6	condition	condition	NOUN
ma-260	58	7	(	(	PUNCT
ma-260	58	8	1.3	1.3	NUM
ma-260	58	9	)	)	PUNCT
ma-260	58	10	was	be	AUX
ma-260	58	11	first	first	ADJ
ma-260	58	12	introducedby	introducedby	ADJ
ma-260	58	13	soria	soria	PROPN
ma-260	58	14	and	and	CCONJ
ma-260	58	15	weiss	weiss	PROPN
ma-260	59	1	[	[	X
ma-260	59	2	19	19	NUM
ma-260	59	3	]	]	PUNCT
ma-260	59	4	.	.	PUNCT
ma-260	60	1	this	this	DET
ma-260	60	2	condition	condition	NOUN
ma-260	60	3	is	be	AUX
ma-260	60	4	satisfied	satisfied	ADJ
ma-260	60	5	by	by	ADP
ma-260	60	6	many	many	ADJ
ma-260	60	7	operators	operator	NOUN
ma-260	60	8	such	such	ADJ
ma-260	60	9	as	as	ADP
ma-260	60	10	the	the	DET
ma-260	60	11	hardy	hardy	ADJ
ma-260	60	12	-	-	PUNCT
ma-260	60	13	littewoodmaximal	littewoodmaximal	ADJ
ma-260	60	14	operator	operator	NOUN
ma-260	60	15	,	,	PUNCT
ma-260	60	16	calderón	calderón	NOUN
ma-260	60	17	-	-	PUNCT
ma-260	60	18	zygmund	zygmund	ADJ
ma-260	60	19	singular	singular	ADJ
ma-260	60	20	integral	integral	ADJ
ma-260	60	21	operators	operator	NOUN
ma-260	60	22	,	,	PUNCT
ma-260	60	23	bochner	bochner	NOUN
ma-260	60	24	-	-	PUNCT
ma-260	60	25	riesz	riesz	NOUN
ma-260	60	26	operators	operator	NOUN
ma-260	60	27	at	at	ADP
ma-260	60	28	thecritical	thecritical	ADJ
ma-260	60	29	index	index	NOUN
ma-260	60	30	,	,	PUNCT
ma-260	60	31	c.	c.	PROPN
ma-260	60	32	fefferman	fefferman	PROPN
ma-260	60	33	’s	’s	PART
ma-260	60	34	singular	singular	PROPN
ma-260	60	35	multiplier	multiplier	ADV
ma-260	60	36	.	.	PUNCT
ma-260	61	1	it	it	PRON
ma-260	61	2	is	be	AUX
ma-260	61	3	proved	prove	VERB
ma-260	61	4	in	in	ADP
ma-260	61	5	[	[	X
ma-260	61	6	5	5	NUM
ma-260	61	7	]	]	PUNCT
ma-260	61	8	that	that	SCONJ
ma-260	61	9	t	t	PROPN
ma-260	61	10	is	be	AUX
ma-260	61	11	bounded	bound	VERB
ma-260	61	12	on	on	ADP
ma-260	61	13	morreyspaces	morreyspace	NOUN
ma-260	61	14	.	.	PUNCT
ma-260	62	1	it	it	PRON
ma-260	62	2	is	be	AUX
ma-260	62	3	also	also	ADV
ma-260	62	4	bounded	bound	VERB
ma-260	62	5	on	on	ADP
ma-260	62	6	classical	classical	ADJ
ma-260	62	7	fofana	fofana	NOUN
ma-260	62	8	spaces	space	NOUN
ma-260	62	9	(	(	PUNCT
ma-260	62	10	see	see	VERB
ma-260	62	11	[	[	X
ma-260	62	12	6	6	NUM
ma-260	62	13	]	]	NUM
ma-260	62	14	)	)	PUNCT
ma-260	62	15	.	.	PUNCT
ma-260	63	1	in	in	ADP
ma-260	63	2	the	the	DET
ma-260	63	3	setting	setting	NOUN
ma-260	63	4	of	of	ADP
ma-260	63	5	total	total	ADJ
ma-260	63	6	fofana	fofana	PROPN
ma-260	63	7	spaces	space	NOUN
ma-260	63	8	,	,	PUNCT
ma-260	63	9	we	we	PRON
ma-260	63	10	have	have	VERB
ma-260	63	11	the	the	DET
ma-260	63	12	following	follow	VERB
ma-260	63	13	result	result	NOUN
ma-260	63	14	holds	hold	VERB
ma-260	63	15	true	true	ADJ
ma-260	63	16	.	.	PUNCT
ma-260	64	1	theorem	theorem	VERB
ma-260	64	2	1.2	1.2	NUM
ma-260	64	3	.	.	PUNCT
ma-260	65	1	let	let	VERB
ma-260	65	2	1	1	NUM
ma-260	65	3	<	<	X
ma-260	65	4	q	q	X
ma-260	65	5	≤	≤	PROPN
ma-260	65	6	λ	λ	PROPN
ma-260	65	7	,	,	PUNCT
ma-260	65	8	α	α	X
ma-260	65	9	<	<	X
ma-260	65	10	p	p	X
ma-260	65	11	<	<	X
ma-260	65	12	∞	∞	NUM
ma-260	66	1	such	such	ADJ
ma-260	66	2	that	that	SCONJ
ma-260	66	3	1q	1q	NUM
ma-260	66	4	+	+	NOUN
ma-260	66	5	2	2	NUM
ma-260	66	6	p	p	NOUN
ma-260	66	7	<	<	X
ma-260	66	8	1	1	NUM
ma-260	66	9	α	α	NOUN
ma-260	66	10	+	+	NOUN
ma-260	66	11	1	1	NUM
ma-260	66	12	λ	λ	NOUN
ma-260	66	13	.	.	PUNCT
ma-260	67	1	if	if	SCONJ
ma-260	67	2	t	t	PROPN
ma-260	67	3	is	be	AUX
ma-260	67	4	sublinear	sublinear	ADJ
ma-260	67	5	operator	operator	NOUN
ma-260	67	6	with	with	ADP
ma-260	67	7	is	be	AUX
ma-260	67	8	bounded	bound	VERB
ma-260	67	9	on	on	ADP
ma-260	67	10	lq	lq	NOUN
ma-260	67	11	and	and	CCONJ
ma-260	67	12	satisfies	satisfy	VERB
ma-260	67	13	the	the	DET
ma-260	67	14	condition	condition	NOUN
ma-260	67	15	(	(	PUNCT
ma-260	67	16	1.3	1.3	NUM
ma-260	67	17	)	)	PUNCT
ma-260	67	18	then	then	ADV
ma-260	67	19	t	t	PROPN
ma-260	67	20	is	be	AUX
ma-260	67	21	also	also	ADV
ma-260	67	22	bounded	bound	VERB
ma-260	67	23	on	on	ADP
ma-260	67	24	(	(	PUNCT
ma-260	67	25	lq	lq	PROPN
ma-260	67	26	,	,	PUNCT
ma-260	67	27	lp)α	lp)α	PROPN
ma-260	67	28	,	,	PUNCT
ma-260	67	29	λ(rd	λ(rd	NOUN
ma-260	67	30	)	)	PUNCT
ma-260	67	31	.	.	PUNCT
ma-260	68	1	if	if	SCONJ
ma-260	68	2	t	t	PROPN
ma-260	68	3	is	be	AUX
ma-260	68	4	a	a	DET
ma-260	68	5	linear	linear	ADJ
ma-260	68	6	operator	operator	NOUN
ma-260	68	7	and	and	CCONJ
ma-260	68	8	b	b	NOUN
ma-260	68	9	∈	∈	NOUN
ma-260	68	10	bmo(rd	bmo(rd	NUM
ma-260	68	11	)	)	PUNCT
ma-260	68	12	,	,	PUNCT
ma-260	68	13	we	we	PRON
ma-260	68	14	define	define	VERB
ma-260	68	15	the	the	DET
ma-260	68	16	linear	linear	ADJ
ma-260	68	17	commutator	commutator	NOUN
ma-260	69	1	[	[	X
ma-260	69	2	b	b	X
ma-260	69	3	,	,	PUNCT
ma-260	69	4	t	t	X
ma-260	69	5	]	]	PUNCT
ma-260	69	6	by	by	ADP
ma-260	69	7	[	[	X
ma-260	69	8	b	b	PROPN
ma-260	69	9	,	,	PUNCT
ma-260	69	10	t	t	X
ma-260	69	11	]	]	X
ma-260	69	12	f	f	X
ma-260	69	13	(	(	PUNCT
ma-260	69	14	x	x	X
ma-260	69	15	)	)	PUNCT
ma-260	69	16	=	=	SYM
ma-260	69	17	t	t	PROPN
ma-260	69	18	(	(	PUNCT
ma-260	69	19	bf	bf	NOUN
ma-260	69	20	)	)	PUNCT
ma-260	69	21	(	(	PUNCT
ma-260	69	22	x)−	x)−	PROPN
ma-260	69	23	b(x)t	b(x)t	PROPN
ma-260	69	24	(	(	PUNCT
ma-260	69	25	f	f	NOUN
ma-260	69	26	)	)	PUNCT
ma-260	69	27	(	(	PUNCT
ma-260	69	28	x	x	X
ma-260	69	29	)	)	PUNCT
ma-260	69	30	x	x	SYM
ma-260	69	31	∈	∈	PROPN
ma-260	69	32	rd	rd	NOUN
ma-260	69	33	,	,	PUNCT
ma-260	69	34	with	with	ADP
ma-260	69	35	locally	locally	ADV
ma-260	69	36	integrable	integrable	ADJ
ma-260	69	37	functions	function	NOUN
ma-260	69	38	f	f	PROPN
ma-260	69	39	on	on	ADP
ma-260	69	40	rd	rd	PROPN
ma-260	69	41	.	.	PUNCT
ma-260	70	1	it	it	PRON
ma-260	70	2	is	be	AUX
ma-260	70	3	also	also	ADV
ma-260	70	4	proved	prove	VERB
ma-260	70	5	in	in	ADP
ma-260	70	6	[	[	X
ma-260	70	7	6	6	NUM
ma-260	70	8	]	]	PUNCT
ma-260	70	9	that	that	SCONJ
ma-260	70	10	[	[	X
ma-260	70	11	b	b	X
ma-260	70	12	,	,	PUNCT
ma-260	70	13	t	t	PROPN
ma-260	70	14	]	]	PUNCT
ma-260	70	15	is	be	AUX
ma-260	70	16	bounded	bound	VERB
ma-260	70	17	on	on	ADP
ma-260	70	18	classicalfofana	classicalfofana	PROPN
ma-260	70	19	spaces	space	NOUN
ma-260	70	20	and	and	CCONJ
ma-260	70	21	bounded	bound	VERB
ma-260	70	22	on	on	ADP
ma-260	70	23	morrey	morrey	PROPN
ma-260	70	24	spaces	space	NOUN
ma-260	70	25	in	in	ADP
ma-260	70	26	[	[	X
ma-260	70	27	5	5	NUM
ma-260	70	28	]	]	PUNCT
ma-260	70	29	.	.	PUNCT
ma-260	71	1	the	the	DET
ma-260	71	2	next	next	ADJ
ma-260	71	3	result	result	NOUN
ma-260	71	4	shows	show	VERB
ma-260	71	5	the	the	DET
ma-260	71	6	boundedness	boundedness	PROPN
ma-260	71	7	ontotal	ontotal	ADJ
ma-260	71	8	fofana	fofana	PROPN
ma-260	71	9	spaces	space	NOUN
ma-260	71	10	of	of	ADP
ma-260	71	11	[	[	X
ma-260	71	12	b	b	PROPN
ma-260	71	13	,	,	PUNCT
ma-260	71	14	t	t	X
ma-260	71	15	]	]	PUNCT
ma-260	71	16	.	.	PUNCT
ma-260	72	1	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	72	2	eur	eur	PROPN
ma-260	72	3	.	.	PUNCT
ma-260	73	1	j.	j.	PROPN
ma-260	73	2	math	math	PROPN
ma-260	73	3	.	.	PUNCT
ma-260	74	1	anal	anal	PROPN
ma-260	74	2	.	.	PUNCT
ma-260	75	1	10.28924	10.28924	NUM
ma-260	75	2	/	/	SYM
ma-260	75	3	ada	ada	PROPN
ma-260	75	4	/	/	SYM
ma-260	75	5	ma.4.22	ma.4.22	PROPN
ma-260	75	6	4	4	NUM
ma-260	75	7	theorem	theorem	VERB
ma-260	75	8	1.3	1.3	NUM
ma-260	75	9	.	.	PUNCT
ma-260	76	1	let	let	VERB
ma-260	76	2	1	1	NUM
ma-260	76	3	<	<	X
ma-260	76	4	q	q	X
ma-260	76	5	≤	≤	PROPN
ma-260	76	6	λ	λ	PROPN
ma-260	76	7	,	,	PUNCT
ma-260	76	8	α	α	X
ma-260	76	9	<	<	X
ma-260	76	10	p	p	X
ma-260	76	11	<	<	X
ma-260	76	12	∞	∞	NUM
ma-260	76	13	such	such	ADJ
ma-260	76	14	that	that	SCONJ
ma-260	76	15	1q	1q	NUM
ma-260	76	16	+	+	NOUN
ma-260	76	17	2	2	NUM
ma-260	76	18	p	p	NOUN
ma-260	76	19	<	<	X
ma-260	76	20	1	1	NUM
ma-260	76	21	α	α	NOUN
ma-260	76	22	+	+	NOUN
ma-260	76	23	1	1	NUM
ma-260	76	24	λ	λ	NOUN
ma-260	76	25	and	and	CCONJ
ma-260	76	26	b	b	NOUN
ma-260	76	27	∈	∈	NOUN
ma-260	76	28	bmo(rd	bmo(rd	NUM
ma-260	76	29	)	)	PUNCT
ma-260	76	30	.	.	PUNCT
ma-260	77	1	if	if	SCONJ
ma-260	77	2	a	a	DET
ma-260	77	3	linear	linear	ADJ
ma-260	77	4	operator	operator	NOUN
ma-260	77	5	t	t	NOUN
ma-260	77	6	satisfies	satisfie	NOUN
ma-260	77	7	(	(	PUNCT
ma-260	77	8	1.3	1.3	NUM
ma-260	77	9	)	)	PUNCT
ma-260	77	10	and	and	CCONJ
ma-260	77	11	[	[	X
ma-260	77	12	b	b	X
ma-260	77	13	,	,	PUNCT
ma-260	77	14	t	t	PROPN
ma-260	77	15	]	]	PUNCT
ma-260	77	16	is	be	AUX
ma-260	77	17	bounded	bound	VERB
ma-260	77	18	on	on	ADP
ma-260	77	19	lq	lq	INTJ
ma-260	77	20	,	,	PUNCT
ma-260	77	21	then	then	ADV
ma-260	77	22	t	t	PROPN
ma-260	77	23	is	be	AUX
ma-260	77	24	also	also	ADV
ma-260	77	25	bounded	bound	VERB
ma-260	77	26	on	on	ADP
ma-260	77	27	(	(	PUNCT
ma-260	77	28	lq	lq	PROPN
ma-260	77	29	,	,	PUNCT
ma-260	77	30	lp)α	lp)α	PROPN
ma-260	77	31	,	,	PUNCT
ma-260	77	32	λ(rd	λ(rd	NOUN
ma-260	77	33	)	)	PUNCT
ma-260	77	34	.	.	PUNCT
ma-260	78	1	the	the	DET
ma-260	78	2	remainder	remainder	NOUN
ma-260	78	3	of	of	ADP
ma-260	78	4	this	this	DET
ma-260	78	5	note	note	NOUN
ma-260	78	6	is	be	AUX
ma-260	78	7	organized	organize	VERB
ma-260	78	8	as	as	SCONJ
ma-260	78	9	follows	follow	VERB
ma-260	78	10	:	:	PUNCT
ma-260	78	11	in	in	ADP
ma-260	78	12	section	section	NOUN
ma-260	78	13	2	2	NUM
ma-260	78	14	we	we	PRON
ma-260	78	15	recall	recall	VERB
ma-260	78	16	some	some	DET
ma-260	78	17	properties	property	NOUN
ma-260	78	18	oftotal	oftotal	ADJ
ma-260	78	19	fofana	fofana	PROPN
ma-260	78	20	spaces	space	NOUN
ma-260	78	21	.	.	PUNCT
ma-260	79	1	section	section	NOUN
ma-260	79	2	3	3	NUM
ma-260	79	3	is	be	AUX
ma-260	79	4	devoted	devote	VERB
ma-260	79	5	to	to	ADP
ma-260	79	6	the	the	DET
ma-260	79	7	proofs	proof	NOUN
ma-260	79	8	of	of	ADP
ma-260	79	9	theorem	theorem	ADJ
ma-260	79	10	1.1	1.1	NUM
ma-260	79	11	and	and	CCONJ
ma-260	79	12	section	section	NOUN
ma-260	79	13	4	4	NUM
ma-260	79	14	deals	deal	NOUN
ma-260	79	15	withthe	withthe	ADJ
ma-260	79	16	proofs	proof	NOUN
ma-260	79	17	of	of	ADP
ma-260	79	18	theorem	theorem	ADJ
ma-260	79	19	1.2	1.2	NUM
ma-260	79	20	and	and	CCONJ
ma-260	79	21	theorem	theorem	VERB
ma-260	79	22	1.3	1.3	NUM
ma-260	79	23	.	.	PUNCT
ma-260	80	1	the	the	DET
ma-260	80	2	letter	letter	NOUN
ma-260	80	3	c	c	PROPN
ma-260	80	4	will	will	AUX
ma-260	80	5	be	be	AUX
ma-260	80	6	used	use	VERB
ma-260	80	7	for	for	ADP
ma-260	80	8	positive	positive	ADJ
ma-260	80	9	constants	constant	NOUN
ma-260	80	10	not	not	PART
ma-260	80	11	depending	depend	VERB
ma-260	80	12	on	on	ADP
ma-260	80	13	the	the	DET
ma-260	80	14	relevant	relevant	ADJ
ma-260	80	15	variables	variable	NOUN
ma-260	80	16	,	,	PUNCT
ma-260	80	17	andtheses	andthese	VERB
ma-260	80	18	constants	constant	NOUN
ma-260	80	19	may	may	AUX
ma-260	80	20	change	change	VERB
ma-260	80	21	from	from	ADP
ma-260	80	22	one	one	NUM
ma-260	80	23	occurrence	occurrence	NOUN
ma-260	80	24	to	to	ADP
ma-260	80	25	another	another	PRON
ma-260	80	26	.	.	PUNCT
ma-260	81	1	we	we	PRON
ma-260	81	2	propose	propose	VERB
ma-260	81	3	the	the	DET
ma-260	81	4	following	follow	VERB
ma-260	81	5	abbreviation	abbreviation	NOUN
ma-260	81	6	a	a	DET
ma-260	81	7	<	<	X
ma-260	81	8	∼	∼	X
ma-260	81	9	b	b	NOUN
ma-260	81	10	for	for	ADP
ma-260	81	11	the	the	DET
ma-260	81	12	inequalities	inequality	NOUN
ma-260	81	13	a	a	DET
ma-260	81	14	≤	≤	NUM
ma-260	81	15	cb	cb	PROPN
ma-260	81	16	.	.	PUNCT
ma-260	82	1	if	if	SCONJ
ma-260	82	2	a	a	DET
ma-260	82	3	<	<	X
ma-260	82	4	∼	∼	X
ma-260	82	5	b	b	NOUN
ma-260	82	6	and	and	CCONJ
ma-260	82	7	b	b	NOUN
ma-260	82	8	<	<	X
ma-260	82	9	∼	∼	NOUN
ma-260	82	10	a	a	NOUN
ma-260	82	11	,	,	PUNCT
ma-260	82	12	then	then	ADV
ma-260	82	13	we	we	PRON
ma-260	82	14	write	write	VERB
ma-260	82	15	a	a	DET
ma-260	82	16	≈	≈	PROPN
ma-260	82	17	b.	b.	PROPN
ma-260	82	18	2	2	NUM
ma-260	82	19	.	.	PUNCT
ma-260	83	1	some	some	DET
ma-260	83	2	properties	property	NOUN
ma-260	83	3	of	of	ADP
ma-260	83	4	total	total	ADJ
ma-260	83	5	fofana	fofana	NOUN
ma-260	83	6	spaces	space	VERB
ma-260	83	7	the	the	DET
ma-260	83	8	results	result	NOUN
ma-260	83	9	of	of	ADP
ma-260	83	10	this	this	DET
ma-260	83	11	section	section	NOUN
ma-260	83	12	are	be	AUX
ma-260	83	13	proved	prove	VERB
ma-260	83	14	in	in	ADP
ma-260	83	15	[	[	PUNCT
ma-260	83	16	17].the	17].the	DET
ma-260	83	17	following	following	ADJ
ma-260	83	18	result	result	NOUN
ma-260	83	19	examines	examine	VERB
ma-260	83	20	the	the	DET
ma-260	83	21	relationship	relationship	NOUN
ma-260	83	22	between	between	ADP
ma-260	83	23	total	total	ADJ
ma-260	83	24	fofana	fofana	NOUN
ma-260	83	25	spaces	space	NOUN
ma-260	83	26	and	and	CCONJ
ma-260	83	27	fofana	fofana	PROPN
ma-260	83	28	spaces	space	NOUN
ma-260	83	29	.	.	PUNCT
ma-260	84	1	proposition	proposition	NOUN
ma-260	84	2	2.1	2.1	NUM
ma-260	84	3	.	.	PUNCT
ma-260	85	1	let	let	VERB
ma-260	85	2	1	1	NUM
ma-260	85	3	≤	≤	NOUN
ma-260	85	4	q	q	PROPN
ma-260	85	5	≤	≤	NUM
ma-260	85	6	α	α	NOUN
ma-260	85	7	,	,	PUNCT
ma-260	85	8	λ	λ	PROPN
ma-260	85	9	≤	≤	NOUN
ma-260	85	10	p	p	NOUN
ma-260	85	11	≤	≤	NOUN
ma-260	85	12	∞.	∞.	PROPN
ma-260	85	13	then	then	ADV
ma-260	85	14	(	(	PUNCT
ma-260	85	15	lq	lq	PROPN
ma-260	85	16	,	,	PUNCT
ma-260	85	17	lp)α(rd	lp)α(rd	ADJ
ma-260	85	18	)	)	PUNCT
ma-260	85	19	∩	∩	NOUN
ma-260	85	20	(	(	PUNCT
ma-260	85	21	lq	lq	PROPN
ma-260	85	22	,	,	PUNCT
ma-260	85	23	lp)λ(rd	lp)λ(rd	ADJ
ma-260	85	24	)	)	PUNCT
ma-260	85	25	↪	↪	PROPN
ma-260	85	26	→	→	SYM
ma-260	85	27	(	(	PUNCT
ma-260	85	28	lq	lq	PROPN
ma-260	85	29	,	,	PUNCT
ma-260	85	30	lp)α	lp)α	PROPN
ma-260	85	31	,	,	PUNCT
ma-260	85	32	λ(rd	λ(rd	NUM
ma-260	85	33	)	)	PUNCT
ma-260	85	34	and	and	CCONJ
ma-260	85	35	for	for	ADP
ma-260	85	36	f	f	PROPN
ma-260	85	37	∈	∈	PROPN
ma-260	85	38	(	(	PUNCT
ma-260	85	39	lq	lq	PROPN
ma-260	85	40	,	,	PUNCT
ma-260	85	41	lp)α(rd	lp)α(rd	ADJ
ma-260	85	42	)	)	PUNCT
ma-260	85	43	∩	∩	NOUN
ma-260	85	44	(	(	PUNCT
ma-260	85	45	lq	lq	PROPN
ma-260	85	46	,	,	PUNCT
ma-260	85	47	lp)λ(rd	lp)λ(rd	ADJ
ma-260	85	48	)	)	PUNCT
ma-260	85	49	‖f	‖f	PRON
ma-260	85	50	‖(lq	‖(lq	ADP
ma-260	85	51	,	,	PUNCT
ma-260	85	52	lp)α	lp)α	PROPN
ma-260	85	53	,	,	PUNCT
ma-260	85	54	λ(rd	λ(rd	ADJ
ma-260	85	55	)	)	PUNCT
ma-260	85	56	≤	≤	NOUN
ma-260	85	57	max{‖f	max{‖f	NOUN
ma-260	85	58	‖q	‖q	NOUN
ma-260	85	59	,	,	PUNCT
ma-260	85	60	p	p	X
ma-260	85	61	,	,	PUNCT
ma-260	85	62	α	α	NOUN
ma-260	85	63	,	,	PUNCT
ma-260	85	64	‖f	‖f	ADP
ma-260	85	65	‖q	‖q	ADP
ma-260	85	66	,	,	PUNCT
ma-260	85	67	p	p	X
ma-260	85	68	,	,	PUNCT
ma-260	85	69	λ	λ	NOUN
ma-260	85	70	}	}	PUNCT
ma-260	85	71	.	.	PUNCT
ma-260	86	1	proposition	proposition	NOUN
ma-260	86	2	2.2	2.2	NUM
ma-260	86	3	.	.	PUNCT
ma-260	87	1	let	let	VERB
ma-260	87	2	1	1	NUM
ma-260	87	3	≤	≤	NOUN
ma-260	87	4	q	q	ADJ
ma-260	87	5	≤	≤	NUM
ma-260	87	6	λ	λ	NOUN
ma-260	87	7	≤	≤	NUM
ma-260	87	8	α	α	PRON
ma-260	87	9	≤	≤	NOUN
ma-260	87	10	p	p	NOUN
ma-260	87	11	≤	≤	NOUN
ma-260	87	12	∞.	∞.	PROPN
ma-260	87	13	then	then	ADV
ma-260	87	14	(	(	PUNCT
ma-260	87	15	lq	lq	PROPN
ma-260	87	16	,	,	PUNCT
ma-260	87	17	lp)α	lp)α	PROPN
ma-260	87	18	,	,	PUNCT
ma-260	87	19	λ(rd	λ(rd	NOUN
ma-260	87	20	)	)	PUNCT
ma-260	87	21	=	=	SYM
ma-260	87	22	(	(	PUNCT
ma-260	87	23	lq	lq	PROPN
ma-260	87	24	,	,	PUNCT
ma-260	87	25	lp)α(rd	lp)α(rd	ADJ
ma-260	87	26	)	)	PUNCT
ma-260	87	27	∩	∩	NOUN
ma-260	87	28	(	(	PUNCT
ma-260	87	29	lq	lq	PROPN
ma-260	87	30	,	,	PUNCT
ma-260	87	31	lp)λ(rd	lp)λ(rd	ADJ
ma-260	87	32	)	)	PUNCT
ma-260	87	33	and	and	CCONJ
ma-260	87	34	for	for	ADP
ma-260	87	35	f	f	PROPN
ma-260	87	36	∈	∈	PROPN
ma-260	87	37	(	(	PUNCT
ma-260	87	38	lq	lq	PROPN
ma-260	87	39	,	,	PUNCT
ma-260	87	40	lp)α	lp)α	PROPN
ma-260	87	41	,	,	PUNCT
ma-260	87	42	λ(rd	λ(rd	NOUN
ma-260	87	43	)	)	PUNCT
ma-260	87	44	‖f	‖f	PRON
ma-260	87	45	‖(lq	‖(lq	CCONJ
ma-260	87	46	,	,	PUNCT
ma-260	87	47	lp)α	lp)α	PROPN
ma-260	87	48	,	,	PUNCT
ma-260	87	49	λ(rd	λ(rd	ADV
ma-260	87	50	)	)	PUNCT
ma-260	87	51	=	=	SYM
ma-260	87	52	max{‖f	max{‖f	NOUN
ma-260	87	53	‖q	‖q	NOUN
ma-260	87	54	,	,	PUNCT
ma-260	87	55	p	p	X
ma-260	87	56	,	,	PUNCT
ma-260	87	57	α	α	NOUN
ma-260	87	58	,	,	PUNCT
ma-260	87	59	‖f	‖f	ADP
ma-260	87	60	‖q	‖q	ADP
ma-260	87	61	,	,	PUNCT
ma-260	87	62	p	p	X
ma-260	87	63	,	,	PUNCT
ma-260	87	64	λ	λ	NOUN
ma-260	87	65	}	}	PUNCT
ma-260	87	66	.	.	PUNCT
ma-260	88	1	total	total	ADJ
ma-260	88	2	fofana	fofana	PROPN
ma-260	88	3	spaces	space	NOUN
ma-260	88	4	are	be	AUX
ma-260	88	5	generalizations	generalization	NOUN
ma-260	88	6	of	of	ADP
ma-260	88	7	classical	classical	ADJ
ma-260	88	8	fofana	fofana	NOUN
ma-260	88	9	spaces	space	NOUN
ma-260	88	10	since	since	SCONJ
ma-260	88	11	proposition	proposition	NOUN
ma-260	88	12	2.2	2.2	NUM
ma-260	88	13	assertsthat	assertsthat	NOUN
ma-260	88	14	(	(	PUNCT
ma-260	88	15	lq	lq	PROPN
ma-260	88	16	,	,	PUNCT
ma-260	88	17	lp)α	lp)α	PROPN
ma-260	88	18	,	,	PUNCT
ma-260	88	19	α(rd	α(rd	NOUN
ma-260	88	20	)	)	PUNCT
ma-260	88	21	=	=	PUNCT
ma-260	88	22	(	(	PUNCT
ma-260	88	23	lq	lq	PROPN
ma-260	88	24	,	,	PUNCT
ma-260	88	25	lp)α(rd).the	lp)α(rd).the	ADJ
ma-260	88	26	family	family	NOUN
ma-260	88	27	of	of	ADP
ma-260	88	28	spaces	space	NOUN
ma-260	88	29	(	(	PUNCT
ma-260	88	30	lq	lq	PROPN
ma-260	88	31	,	,	PUNCT
ma-260	88	32	lp)α	lp)α	PROPN
ma-260	88	33	,	,	PUNCT
ma-260	88	34	λ(rd	λ(rd	NUM
ma-260	88	35	)	)	PUNCT
ma-260	88	36	is	be	AUX
ma-260	88	37	increasing	increase	VERB
ma-260	88	38	with	with	ADP
ma-260	88	39	respect	respect	NOUN
ma-260	88	40	to	to	ADP
ma-260	88	41	the	the	DET
ma-260	88	42	p	p	PROPN
ma-260	88	43	power	power	NOUN
ma-260	88	44	.	.	PUNCT
ma-260	89	1	more	more	ADV
ma-260	89	2	precisely	precisely	ADV
ma-260	89	3	,	,	PUNCT
ma-260	89	4	we	we	PRON
ma-260	89	5	have	have	VERB
ma-260	89	6	the	the	DET
ma-260	89	7	following	following	NOUN
ma-260	89	8	.	.	PUNCT
ma-260	90	1	proposition	proposition	NOUN
ma-260	90	2	2.3	2.3	NUM
ma-260	90	3	.	.	PUNCT
ma-260	91	1	let	let	VERB
ma-260	91	2	1	1	NUM
ma-260	91	3	≤	≤	NOUN
ma-260	91	4	q	q	PROPN
ma-260	91	5	≤	≤	NUM
ma-260	91	6	α	α	NOUN
ma-260	91	7	,	,	PUNCT
ma-260	91	8	λ	λ	PROPN
ma-260	91	9	≤	≤	NOUN
ma-260	91	10	p1	p1	NOUN
ma-260	91	11	≤	≤	NUM
ma-260	91	12	p2	p2	NOUN
ma-260	91	13	≤	≤	PUNCT
ma-260	91	14	∞.	∞.	PROPN
ma-260	91	15	then	then	ADV
ma-260	91	16	:	:	PUNCT
ma-260	91	17	‖f	‖f	ADJ
ma-260	91	18	‖(lq	‖(lq	CCONJ
ma-260	91	19	,	,	PUNCT
ma-260	91	20	lp2)α	lp2)α	PROPN
ma-260	91	21	,	,	PUNCT
ma-260	91	22	λ(rd	λ(rd	ADV
ma-260	91	23	)	)	PUNCT
ma-260	91	24	<	<	X
ma-260	91	25	∼	∼	NOUN
ma-260	91	26	‖f	‖f	ADJ
ma-260	91	27	‖(lq	‖(lq	ADP
ma-260	91	28	,	,	PUNCT
ma-260	91	29	lp1)α	lp1)α	NOUN
ma-260	91	30	,	,	PUNCT
ma-260	91	31	λ(rd	λ(rd	PRON
ma-260	91	32	)	)	PUNCT
ma-260	91	33	,	,	PUNCT
ma-260	91	34	f	f	PROPN
ma-260	91	35	∈	∈	PROPN
ma-260	91	36	l0(rd	l0(rd	PROPN
ma-260	91	37	)	)	PUNCT
ma-260	91	38	and	and	CCONJ
ma-260	91	39	consequently	consequently	ADV
ma-260	91	40	,	,	PUNCT
ma-260	91	41	(	(	PUNCT
ma-260	91	42	lq	lq	INTJ
ma-260	91	43	,	,	PUNCT
ma-260	91	44	lp1)α	lp1)α	NOUN
ma-260	91	45	,	,	PUNCT
ma-260	91	46	λ(rd	λ(rd	X
ma-260	91	47	)	)	PUNCT
ma-260	92	1	⊂	⊂	PROPN
ma-260	92	2	(	(	PUNCT
ma-260	92	3	lq	lq	PROPN
ma-260	92	4	,	,	PUNCT
ma-260	92	5	lp2)α	lp2)α	PROPN
ma-260	92	6	,	,	PUNCT
ma-260	92	7	λ(rd	λ(rd	NOUN
ma-260	92	8	)	)	PUNCT
ma-260	92	9	.	.	PUNCT
ma-260	93	1	the	the	DET
ma-260	93	2	following	follow	VERB
ma-260	93	3	result	result	NOUN
ma-260	93	4	states	state	VERB
ma-260	93	5	the	the	DET
ma-260	93	6	boundedness	boundedness	PROPN
ma-260	93	7	property	property	NOUN
ma-260	93	8	of	of	ADP
ma-260	93	9	m	m	PROPN
ma-260	93	10	(	(	PUNCT
ma-260	93	11	the	the	DET
ma-260	93	12	hardy	hardy	ADJ
ma-260	93	13	-	-	PUNCT
ma-260	93	14	littlewood	littlewood	NOUN
ma-260	93	15	maximal	maximal	ADJ
ma-260	93	16	op	op	NOUN
ma-260	93	17	-	-	PUNCT
ma-260	93	18	erator	erator	NOUN
ma-260	93	19	)	)	PUNCT
ma-260	93	20	on	on	ADP
ma-260	93	21	total	total	ADJ
ma-260	93	22	fofana	fofana	PROPN
ma-260	93	23	spaces	space	NOUN
ma-260	93	24	.	.	PUNCT
ma-260	94	1	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	94	2	eur	eur	PROPN
ma-260	94	3	.	.	PUNCT
ma-260	95	1	j.	j.	PROPN
ma-260	95	2	math	math	PROPN
ma-260	95	3	.	.	PUNCT
ma-260	96	1	anal	anal	PROPN
ma-260	96	2	.	.	PUNCT
ma-260	97	1	10.28924	10.28924	NUM
ma-260	97	2	/	/	SYM
ma-260	97	3	ada	ada	PROPN
ma-260	97	4	/	/	SYM
ma-260	97	5	ma.4.22	ma.4.22	PROPN
ma-260	97	6	5	5	NUM
ma-260	97	7	theorem	theorem	VERB
ma-260	97	8	2.4	2.4	NUM
ma-260	97	9	.	.	PUNCT
ma-260	98	1	(	(	PUNCT
ma-260	98	2	1	1	X
ma-260	98	3	)	)	PUNCT
ma-260	98	4	let	let	VERB
ma-260	98	5	1	1	NUM
ma-260	98	6	<	<	X
ma-260	98	7	q	q	X
ma-260	98	8	≤	≤	NUM
ma-260	98	9	α	α	NOUN
ma-260	98	10	,	,	PUNCT
ma-260	98	11	λ	λ	X
ma-260	98	12	<	<	X
ma-260	98	13	p	p	X
ma-260	98	14	<	<	X
ma-260	98	15	∞	∞	NUM
ma-260	98	16	such	such	ADJ
ma-260	98	17	that	that	SCONJ
ma-260	98	18	1q	1q	NUM
ma-260	98	19	+	+	NOUN
ma-260	98	20	2	2	NUM
ma-260	98	21	p	p	NOUN
ma-260	98	22	<	<	X
ma-260	98	23	1	1	NUM
ma-260	98	24	α	α	NOUN
ma-260	98	25	+	+	NOUN
ma-260	98	26	1	1	NUM
ma-260	98	27	λ	λ	NOUN
ma-260	98	28	.	.	PUNCT
ma-260	99	1	then	then	ADV
ma-260	99	2	‖mf	‖mf	NUM
ma-260	99	3	‖(lq	‖(lq	NUM
ma-260	99	4	,	,	PUNCT
ma-260	99	5	lp)α	lp)α	PROPN
ma-260	99	6	,	,	PUNCT
ma-260	99	7	λ(rd	λ(rd	ADV
ma-260	99	8	)	)	PUNCT
ma-260	99	9	<	<	X
ma-260	99	10	∼	∼	NOUN
ma-260	99	11	‖f	‖f	ADJ
ma-260	99	12	‖(lq	‖(lq	CCONJ
ma-260	99	13	,	,	PUNCT
ma-260	99	14	lp)α	lp)α	PROPN
ma-260	99	15	,	,	PUNCT
ma-260	99	16	λ(rd	λ(rd	PRON
ma-260	99	17	)	)	PUNCT
ma-260	99	18	,	,	PUNCT
ma-260	99	19	f	f	PROPN
ma-260	99	20	∈	∈	PROPN
ma-260	99	21	(	(	PUNCT
ma-260	99	22	lq	lq	PROPN
ma-260	99	23	,	,	PUNCT
ma-260	99	24	lp)α	lp)α	PROPN
ma-260	99	25	,	,	PUNCT
ma-260	99	26	λ(rd	λ(rd	NOUN
ma-260	99	27	)	)	PUNCT
ma-260	99	28	.	.	PUNCT
ma-260	100	1	(	(	PUNCT
ma-260	100	2	2	2	X
ma-260	100	3	)	)	PUNCT
ma-260	100	4	let	let	VERB
ma-260	100	5	q	q	NOUN
ma-260	100	6	=	=	SYM
ma-260	100	7	1	1	NUM
ma-260	100	8	<	<	X
ma-260	100	9	α	α	NOUN
ma-260	100	10	,	,	PUNCT
ma-260	100	11	λ	λ	X
ma-260	100	12	<	<	X
ma-260	100	13	p	p	X
ma-260	100	14	<	<	X
ma-260	100	15	∞.	∞.	PROPN
ma-260	100	16	then	then	ADV
ma-260	100	17	‖mf	‖mf	NUM
ma-260	100	18	‖(l1,∞,lp)α	‖(l1,∞,lp)α	PROPN
ma-260	100	19	,	,	PUNCT
ma-260	100	20	λ(rd	λ(rd	ADV
ma-260	100	21	)	)	PUNCT
ma-260	100	22	<	<	X
ma-260	100	23	∼	∼	NOUN
ma-260	100	24	‖f	‖f	ADJ
ma-260	100	25	‖(l1,lp)α	‖(l1,lp)α	PROPN
ma-260	100	26	,	,	PUNCT
ma-260	100	27	λ(rd	λ(rd	PRON
ma-260	100	28	)	)	PUNCT
ma-260	100	29	,	,	PUNCT
ma-260	100	30	f	f	PROPN
ma-260	100	31	∈	∈	PROPN
ma-260	100	32	(	(	PUNCT
ma-260	100	33	l1	l1	PROPN
ma-260	100	34	,	,	PUNCT
ma-260	100	35	lp)α	lp)α	PROPN
ma-260	100	36	,	,	PUNCT
ma-260	100	37	λ(rd	λ(rd	NOUN
ma-260	100	38	)	)	PUNCT
ma-260	100	39	,	,	PUNCT
ma-260	100	40	where	where	SCONJ
ma-260	100	41	‖f	‖f	ADP
ma-260	100	42	‖(l1,∞,lp)α	‖(l1,∞,lp)α	NOUN
ma-260	100	43	,	,	PUNCT
ma-260	100	44	λ(rd	λ(rd	PRON
ma-260	100	45	)	)	PUNCT
ma-260	100	46	:	:	PUNCT
ma-260	100	47	=	=	PUNCT
ma-260	101	1	sup	sup	NUM
ma-260	101	2	r>0	r>0	PROPN
ma-260	101	3	[	[	X
ma-260	101	4	r	r	X
ma-260	101	5	]	]	X
ma-260	101	6	d	d	X
ma-260	101	7	(	(	PUNCT
ma-260	101	8	1	1	NUM
ma-260	101	9	α	α	NOUN
ma-260	101	10	−1−	−1−	NOUN
ma-260	101	11	1	1	NUM
ma-260	101	12	p	p	NOUN
ma-260	101	13	)	)	PUNCT
ma-260	101	14	1	1	NUM
ma-260	102	1	[	[	X
ma-260	102	2	1	1	NUM
ma-260	102	3	/	/	SYM
ma-260	102	4	r	r	NOUN
ma-260	102	5	]	]	PUNCT
ma-260	102	6	d(−	d(−	PROPN
ma-260	102	7	1	1	NUM
ma-260	102	8	λ	λ	X
ma-260	102	9	+1	+1	X
ma-260	102	10	+	+	PROPN
ma-260	102	11	1	1	NUM
ma-260	102	12	p	p	NOUN
ma-260	102	13	)	)	PUNCT
ma-260	102	14	1	1	NUM
ma-260	103	1	[	[	X
ma-260	103	2	∫	∫	PROPN
ma-260	103	3	rd	rd	PROPN
ma-260	103	4	(	(	PUNCT
ma-260	103	5	∥∥f	∥∥f	PROPN
ma-260	103	6	χb(y	χb(y	PROPN
ma-260	103	7	,	,	PUNCT
ma-260	103	8	r)∥∥∗1,∞)p	r)∥∥∗1,∞)p	PROPN
ma-260	103	9	dy	dy	X
ma-260	103	10	]	]	X
ma-260	103	11	1p	1p	NUM
ma-260	103	12	with	with	ADP
ma-260	103	13	∥∥f	∥∥f	PROPN
ma-260	103	14	χb(y	χb(y	NOUN
ma-260	103	15	,	,	PUNCT
ma-260	103	16	r)∥∥∗1,∞	r)∥∥∗1,∞	NOUN
ma-260	103	17	=	=	SYM
ma-260	103	18	sup	sup	NOUN
ma-260	103	19	r>0	r>0	NOUN
ma-260	103	20	r	r	NOUN
ma-260	103	21	|{x	|{x	SYM
ma-260	103	22	∈	∈	PROPN
ma-260	103	23	b(y	b(y	PROPN
ma-260	103	24	,	,	PUNCT
ma-260	103	25	r	r	NOUN
ma-260	103	26	)	)	PUNCT
ma-260	103	27	:	:	PUNCT
ma-260	103	28	|f	|f	PROPN
ma-260	103	29	(	(	PUNCT
ma-260	103	30	x)|	x)|	PROPN
ma-260	103	31	>	>	X
ma-260	103	32	r}|	r}|	PROPN
ma-260	103	33	.	.	PUNCT
ma-260	104	1	3	3	X
ma-260	104	2	.	.	X
ma-260	104	3	proof	proof	NOUN
ma-260	104	4	of	of	ADP
ma-260	104	5	theorem	theorem	ADJ
ma-260	104	6	1.1	1.1	NUM
ma-260	104	7	for	for	ADP
ma-260	104	8	the	the	DET
ma-260	104	9	proof	proof	NOUN
ma-260	104	10	of	of	ADP
ma-260	104	11	this	this	DET
ma-260	104	12	theorem	theorem	NOUN
ma-260	104	13	,	,	PUNCT
ma-260	104	14	we	we	PRON
ma-260	104	15	need	need	VERB
ma-260	104	16	some	some	DET
ma-260	104	17	results.the	results.the	DET
ma-260	104	18	following	following	ADJ
ma-260	104	19	result	result	NOUN
ma-260	104	20	(	(	PUNCT
ma-260	104	21	see	see	VERB
ma-260	104	22	[	[	X
ma-260	104	23	1	1	NUM
ma-260	104	24	,	,	PUNCT
ma-260	104	25	corollary	corollary	ADJ
ma-260	104	26	1.11	1.11	NUM
ma-260	104	27	]	]	PUNCT
ma-260	104	28	)	)	PUNCT
ma-260	104	29	will	will	AUX
ma-260	104	30	be	be	AUX
ma-260	104	31	useful	useful	ADJ
ma-260	104	32	in	in	ADP
ma-260	104	33	the	the	DET
ma-260	104	34	proof	proof	NOUN
ma-260	104	35	of	of	ADP
ma-260	104	36	theorem	theorem	ADJ
ma-260	104	37	1.1	1.1	NUM
ma-260	104	38	.	.	PUNCT
ma-260	105	1	lemma	lemma	PROPN
ma-260	105	2	3.1	3.1	NUM
ma-260	105	3	.	.	PUNCT
ma-260	106	1	if	if	SCONJ
ma-260	106	2	b	b	PROPN
ma-260	106	3	∈	∈	PROPN
ma-260	106	4	bmo(rd	bmo(rd	NUM
ma-260	106	5	)	)	PUNCT
ma-260	106	6	,	,	PUNCT
ma-260	106	7	then	then	ADV
ma-260	106	8	there	there	PRON
ma-260	106	9	exists	exist	VERB
ma-260	106	10	a	a	DET
ma-260	106	11	positive	positive	ADJ
ma-260	106	12	constant	constant	ADJ
ma-260	106	13	c	c	NOUN
ma-260	106	14	such	such	ADJ
ma-260	106	15	that	that	DET
ma-260	106	16	mbf	mbf	NOUN
ma-260	106	17	(	(	PUNCT
ma-260	106	18	x	x	NOUN
ma-260	106	19	)	)	PUNCT
ma-260	106	20	≤	≤	NOUN
ma-260	106	21	c	c	NOUN
ma-260	106	22	‖b‖bmo(rd	‖b‖bmo(rd	NOUN
ma-260	106	23	)	)	PUNCT
ma-260	106	24	m(mf	m(mf	PROPN
ma-260	106	25	)	)	PUNCT
ma-260	106	26	(	(	PUNCT
ma-260	106	27	x	x	X
ma-260	106	28	)	)	PUNCT
ma-260	106	29	for	for	ADP
ma-260	106	30	almost	almost	ADV
ma-260	106	31	every	every	PRON
ma-260	106	32	x	x	SYM
ma-260	106	33	∈	∈	PROPN
ma-260	106	34	rd	rd	PROPN
ma-260	106	35	and	and	CCONJ
ma-260	106	36	any	any	DET
ma-260	106	37	locally	locally	ADV
ma-260	106	38	integrable	integrable	ADJ
ma-260	106	39	functions	function	NOUN
ma-260	106	40	f	f	PROPN
ma-260	106	41	on	on	ADP
ma-260	106	42	rd	rd	PROPN
ma-260	106	43	.	.	PUNCT
ma-260	107	1	proposition	proposition	NOUN
ma-260	107	2	3.2	3.2	NUM
ma-260	107	3	.	.	PUNCT
ma-260	108	1	let	let	VERB
ma-260	108	2	1	1	NUM
ma-260	108	3	<	<	X
ma-260	108	4	q	q	X
ma-260	108	5	≤	≤	NUM
ma-260	108	6	α	α	NOUN
ma-260	108	7	,	,	PUNCT
ma-260	108	8	λ	λ	X
ma-260	108	9	<	<	X
ma-260	108	10	p	p	X
ma-260	108	11	<	<	X
ma-260	108	12	∞	∞	NUM
ma-260	108	13	such	such	ADJ
ma-260	108	14	that	that	SCONJ
ma-260	108	15	1q	1q	NUM
ma-260	108	16	+	+	NOUN
ma-260	108	17	2	2	NUM
ma-260	108	18	p	p	NOUN
ma-260	108	19	<	<	X
ma-260	108	20	1	1	NUM
ma-260	108	21	α	α	NOUN
ma-260	108	22	+	+	NOUN
ma-260	108	23	1	1	NUM
ma-260	108	24	λ	λ	NOUN
ma-260	108	25	and	and	CCONJ
ma-260	108	26	b	b	NOUN
ma-260	108	27	∈	∈	NOUN
ma-260	108	28	bmo(rd	bmo(rd	NUM
ma-260	108	29	)	)	PUNCT
ma-260	108	30	.	.	PUNCT
ma-260	109	1	then	then	ADV
ma-260	109	2	mb	mb	PROPN
ma-260	109	3	is	be	AUX
ma-260	109	4	bounded	bound	VERB
ma-260	109	5	on	on	ADP
ma-260	109	6	(	(	PUNCT
ma-260	109	7	lq	lq	PROPN
ma-260	109	8	,	,	PUNCT
ma-260	109	9	lp)α	lp)α	PROPN
ma-260	109	10	,	,	PUNCT
ma-260	109	11	λ(rd	λ(rd	NOUN
ma-260	109	12	)	)	PUNCT
ma-260	109	13	.	.	PUNCT
ma-260	110	1	proof	proof	NOUN
ma-260	110	2	.	.	PUNCT
ma-260	111	1	let	let	VERB
ma-260	111	2	1	1	NUM
ma-260	111	3	<	<	X
ma-260	111	4	q	q	X
ma-260	111	5	≤	≤	NUM
ma-260	111	6	α	α	NOUN
ma-260	111	7	,	,	PUNCT
ma-260	111	8	λ	λ	X
ma-260	111	9	<	<	X
ma-260	111	10	p	p	X
ma-260	111	11	<	<	X
ma-260	111	12	∞	∞	NUM
ma-260	112	1	such	such	ADJ
ma-260	112	2	that	that	SCONJ
ma-260	112	3	1q	1q	NUM
ma-260	112	4	+	+	NOUN
ma-260	112	5	2	2	NUM
ma-260	112	6	p	p	NOUN
ma-260	112	7	<	<	X
ma-260	112	8	1	1	NUM
ma-260	112	9	α	α	NOUN
ma-260	112	10	+	+	NOUN
ma-260	112	11	1	1	NUM
ma-260	112	12	λ	λ	NOUN
ma-260	112	13	,	,	PUNCT
ma-260	112	14	b	b	PROPN
ma-260	112	15	∈	∈	PROPN
ma-260	112	16	bmo(rd	bmo(rd	NUM
ma-260	112	17	)	)	PUNCT
ma-260	112	18	and	and	CCONJ
ma-260	112	19	f	f	PROPN
ma-260	112	20	∈	∈	PROPN
ma-260	112	21	(	(	PUNCT
ma-260	112	22	lq	lq	PROPN
ma-260	112	23	,	,	PUNCT
ma-260	112	24	lp)α	lp)α	PROPN
ma-260	112	25	,	,	PUNCT
ma-260	112	26	λ(rd).by	λ(rd).by	PUNCT
ma-260	112	27	taking	take	VERB
ma-260	112	28	the	the	DET
ma-260	112	29	(	(	PUNCT
ma-260	112	30	lq	lq	PROPN
ma-260	112	31	,	,	PUNCT
ma-260	112	32	lp)α	lp)α	PROPN
ma-260	112	33	,	,	PUNCT
ma-260	112	34	λ(rd)-norm	λ(rd)-norm	NOUN
ma-260	112	35	of	of	ADP
ma-260	112	36	both	both	DET
ma-260	112	37	sides	side	NOUN
ma-260	112	38	of	of	ADP
ma-260	112	39	the	the	DET
ma-260	112	40	estimate	estimate	NOUN
ma-260	112	41	in	in	ADP
ma-260	112	42	lemma	lemma	PROPN
ma-260	112	43	3.1	3.1	NUM
ma-260	112	44	,	,	PUNCT
ma-260	112	45	we	we	PRON
ma-260	112	46	obtain	obtain	VERB
ma-260	112	47	‖mbf	‖mbf	NUM
ma-260	112	48	‖(lq	‖(lq	CCONJ
ma-260	112	49	,	,	PUNCT
ma-260	112	50	lp)α	lp)α	PROPN
ma-260	112	51	,	,	PUNCT
ma-260	112	52	λ(rd	λ(rd	ADV
ma-260	112	53	)	)	PUNCT
ma-260	112	54	<	<	X
ma-260	112	55	∼	∼	X
ma-260	112	56	‖b‖bmo(rd	‖b‖bmo(rd	NOUN
ma-260	112	57	)	)	PUNCT
ma-260	113	1	‖m(mf	‖m(mf	X
ma-260	113	2	)	)	PUNCT
ma-260	113	3	‖(lq	‖(lq	NUM
ma-260	113	4	,	,	PUNCT
ma-260	113	5	lp)α	lp)α	PROPN
ma-260	113	6	,	,	PUNCT
ma-260	113	7	λ(rd	λ(rd	ADV
ma-260	113	8	)	)	PUNCT
ma-260	113	9	.according	.accorde	VERB
ma-260	113	10	to	to	ADP
ma-260	113	11	the	the	DET
ma-260	113	12	first	first	ADJ
ma-260	113	13	point	point	NOUN
ma-260	113	14	of	of	ADP
ma-260	113	15	theorem	theorem	ADJ
ma-260	113	16	2.4	2.4	NUM
ma-260	113	17	,	,	PUNCT
ma-260	113	18	we	we	PRON
ma-260	113	19	have	have	VERB
ma-260	113	20	‖m(mf	‖m(mf	NOUN
ma-260	113	21	)	)	PUNCT
ma-260	113	22	‖(lq	‖(lq	NUM
ma-260	113	23	,	,	PUNCT
ma-260	113	24	lp)α	lp)α	PROPN
ma-260	113	25	,	,	PUNCT
ma-260	113	26	λ(rd	λ(rd	ADV
ma-260	113	27	)	)	PUNCT
ma-260	114	1	<	<	X
ma-260	114	2	∼	∼	X
ma-260	114	3	‖mf	‖mf	NUM
ma-260	114	4	‖(lq	‖(lq	NUM
ma-260	114	5	,	,	PUNCT
ma-260	114	6	lp)α	lp)α	PROPN
ma-260	114	7	,	,	PUNCT
ma-260	114	8	λ(rd	λ(rd	ADV
ma-260	114	9	)	)	PUNCT
ma-260	114	10	<	<	X
ma-260	114	11	∼	∼	NOUN
ma-260	114	12	‖f	‖f	ADJ
ma-260	114	13	‖(lq	‖(lq	CCONJ
ma-260	114	14	,	,	PUNCT
ma-260	114	15	lp)α	lp)α	PROPN
ma-260	114	16	,	,	PUNCT
ma-260	114	17	λ(rd	λ(rd	PRON
ma-260	114	18	)	)	PUNCT
ma-260	114	19	.we	.we	PUNCT
ma-260	115	1	deduce	deduce	VERB
ma-260	115	2	that	that	PRON
ma-260	115	3	‖mbf	‖mbf	NOUN
ma-260	115	4	‖(lq	‖(lq	CCONJ
ma-260	115	5	,	,	PUNCT
ma-260	115	6	lp)α	lp)α	PROPN
ma-260	115	7	,	,	PUNCT
ma-260	115	8	λ(rd	λ(rd	ADV
ma-260	115	9	)	)	PUNCT
ma-260	115	10	<	<	X
ma-260	115	11	∼	∼	X
ma-260	115	12	‖b‖bmo(rd	‖b‖bmo(rd	NOUN
ma-260	115	13	)	)	PUNCT
ma-260	115	14	‖f	‖f	ADP
ma-260	115	15	‖(lq	‖(lq	ADP
ma-260	115	16	,	,	PUNCT
ma-260	115	17	lp)α	lp)α	PROPN
ma-260	115	18	,	,	PUNCT
ma-260	115	19	λ(rd	λ(rd	PRON
ma-260	115	20	)	)	PUNCT
ma-260	115	21	.	.	PUNCT
ma-260	116	1	(	(	PUNCT
ma-260	116	2	3.1	3.1	NUM
ma-260	116	3	)	)	PUNCT
ma-260	116	4	�	�	NOUN
ma-260	116	5	lemma	lemma	PROPN
ma-260	116	6	3.3	3.3	NUM
ma-260	116	7	.	.	PUNCT
ma-260	117	1	let	let	VERB
ma-260	117	2	1	1	NUM
ma-260	117	3	≤	≤	NOUN
ma-260	117	4	q	q	ADJ
ma-260	117	5	≤	≤	NUM
ma-260	117	6	λ	λ	NOUN
ma-260	117	7	≤	≤	NUM
ma-260	118	1	α	α	PRON
ma-260	118	2	<	<	X
ma-260	118	3	∞	∞	NOUN
ma-260	118	4	and	and	CCONJ
ma-260	118	5	r	r	NOUN
ma-260	118	6	>	>	X
ma-260	118	7	0	0	NUM
ma-260	118	8	.	.	PUNCT
ma-260	119	1	then	then	ADV
ma-260	119	2	r−	r−	PROPN
ma-260	119	3	d	d	PROPN
ma-260	119	4	q	q	NOUN
ma-260	120	1	[	[	X
ma-260	120	2	r	r	X
ma-260	120	3	]	]	PUNCT
ma-260	120	4	d(−	d(−	NOUN
ma-260	120	5	1	1	NUM
ma-260	120	6	α	α	NOUN
ma-260	120	7	+	+	NOUN
ma-260	120	8	1	1	NUM
ma-260	120	9	q	q	NOUN
ma-260	120	10	)	)	PUNCT
ma-260	120	11	1	1	NUM
ma-260	121	1	[	[	X
ma-260	121	2	1	1	NUM
ma-260	121	3	/	/	SYM
ma-260	121	4	r	r	NOUN
ma-260	121	5	]	]	PUNCT
ma-260	121	6	d	d	X
ma-260	121	7	(	(	PUNCT
ma-260	121	8	1	1	NUM
ma-260	121	9	λ	λ	NOUN
ma-260	121	10	−	−	PROPN
ma-260	121	11	1	1	NUM
ma-260	121	12	q	q	NOUN
ma-260	121	13	)	)	PUNCT
ma-260	121	14	1	1	NUM
ma-260	121	15	max{r	max{r	NOUN
ma-260	121	16	d	d	X
ma-260	121	17	α	α	NOUN
ma-260	121	18	,	,	PUNCT
ma-260	121	19	r	r	NOUN
ma-260	121	20	d	d	PROPN
ma-260	121	21	λ	λ	PROPN
ma-260	121	22	}	}	PUNCT
ma-260	121	23	≤	≤	NUM
ma-260	121	24	2	2	NUM
ma-260	121	25	.	.	X
ma-260	122	1	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	122	2	eur	eur	PROPN
ma-260	122	3	.	.	PUNCT
ma-260	123	1	j.	j.	PROPN
ma-260	123	2	math	math	PROPN
ma-260	123	3	.	.	PUNCT
ma-260	124	1	anal	anal	PROPN
ma-260	124	2	.	.	PUNCT
ma-260	125	1	10.28924	10.28924	NUM
ma-260	125	2	/	/	SYM
ma-260	125	3	ada	ada	PROPN
ma-260	125	4	/	/	SYM
ma-260	125	5	ma.4.22	ma.4.22	PROPN
ma-260	125	6	6	6	NUM
ma-260	125	7	proof	proof	NOUN
ma-260	125	8	.	.	PUNCT
ma-260	126	1	let	let	VERB
ma-260	126	2	1	1	NUM
ma-260	126	3	≤	≤	NOUN
ma-260	126	4	q	q	ADJ
ma-260	126	5	≤	≤	NUM
ma-260	126	6	λ	λ	NOUN
ma-260	126	7	≤	≤	NUM
ma-260	127	1	α	α	PRON
ma-260	127	2	<	<	X
ma-260	127	3	∞	∞	NOUN
ma-260	127	4	and	and	CCONJ
ma-260	127	5	r	r	NOUN
ma-260	127	6	>	>	X
ma-260	127	7	0.put	0.put	NOUN
ma-260	127	8	c(r	c(r	NOUN
ma-260	127	9	)	)	PUNCT
ma-260	128	1	=	=	SYM
ma-260	129	1	r	r	NOUN
ma-260	129	2	−dq	−dq	NOUN
ma-260	130	1	[	[	X
ma-260	130	2	r	r	X
ma-260	130	3	]	]	X
ma-260	130	4	d(−	d(−	PROPN
ma-260	130	5	1α+	1α+	NUM
ma-260	130	6	1q	1q	NUM
ma-260	130	7	)	)	PUNCT
ma-260	130	8	1	1	NUM
ma-260	131	1	[	[	SYM
ma-260	131	2	1	1	NUM
ma-260	131	3	/	/	SYM
ma-260	131	4	r	r	NOUN
ma-260	131	5	]	]	PUNCT
ma-260	131	6	d	d	X
ma-260	131	7	(	(	PUNCT
ma-260	131	8	1	1	NUM
ma-260	131	9	λ	λ	NOUN
ma-260	131	10	−	−	PROPN
ma-260	131	11	1	1	NUM
ma-260	131	12	q	q	NOUN
ma-260	131	13	)	)	PUNCT
ma-260	131	14	1	1	NUM
ma-260	131	15	max{r	max{r	NOUN
ma-260	131	16	d	d	X
ma-260	131	17	α	α	NOUN
ma-260	131	18	,	,	PUNCT
ma-260	131	19	r	r	NOUN
ma-260	131	20	d	d	X
ma-260	131	21	λ	λ	NOUN
ma-260	131	22	}	}	PUNCT
ma-260	131	23	.	.	PUNCT
ma-260	132	1	c(r	c(r	NOUN
ma-260	132	2	)	)	PUNCT
ma-260	132	3	≤	≤	NOUN
ma-260	132	4	{	{	PUNCT
ma-260	132	5	r−	r−	PROPN
ma-260	132	6	d	d	PROPN
ma-260	132	7	α	α	PROPN
ma-260	132	8	(	(	PUNCT
ma-260	132	9	r	r	NOUN
ma-260	132	10	d	d	PROPN
ma-260	132	11	α	α	NOUN
ma-260	132	12	+	+	X
ma-260	132	13	r	r	NOUN
ma-260	132	14	d	d	PROPN
ma-260	132	15	λ	λ	PROPN
ma-260	132	16	)	)	PUNCT
ma-260	132	17	,	,	PUNCT
ma-260	132	18	0	0	NUM
ma-260	132	19	<	<	X
ma-260	132	20	r	r	NOUN
ma-260	132	21	≤	≤	NUM
ma-260	132	22	1	1	NUM
ma-260	132	23	r−	r−	PROPN
ma-260	132	24	d	d	PROPN
ma-260	132	25	λ	λ	PROPN
ma-260	132	26	(	(	PUNCT
ma-260	132	27	r	r	NOUN
ma-260	132	28	d	d	PROPN
ma-260	132	29	α	α	NOUN
ma-260	132	30	+	+	X
ma-260	132	31	r	r	NOUN
ma-260	132	32	d	d	PROPN
ma-260	132	33	λ	λ	PROPN
ma-260	132	34	)	)	PUNCT
ma-260	132	35	,	,	PUNCT
ma-260	132	36	r	r	NOUN
ma-260	132	37	>	>	X
ma-260	132	38	1	1	NUM
ma-260	132	39	≤	≤	NOUN
ma-260	132	40	{	{	PUNCT
ma-260	132	41	1	1	NUM
ma-260	132	42	+	+	NUM
ma-260	132	43	rd(−	rd(−	NOUN
ma-260	132	44	1	1	NUM
ma-260	132	45	α	α	NOUN
ma-260	132	46	+	+	CCONJ
ma-260	132	47	1	1	NUM
ma-260	132	48	λ	λ	NOUN
ma-260	132	49	)	)	PUNCT
ma-260	132	50	,	,	PUNCT
ma-260	132	51	0	0	NUM
ma-260	132	52	<	<	X
ma-260	132	53	r	r	NOUN
ma-260	132	54	≤	≤	NUM
ma-260	132	55	1	1	NUM
ma-260	132	56	1	1	NUM
ma-260	132	57	+	+	NUM
ma-260	132	58	rd	rd	NOUN
ma-260	132	59	(	(	PUNCT
ma-260	132	60	1	1	NUM
ma-260	132	61	α	α	NOUN
ma-260	132	62	−	−	NUM
ma-260	132	63	1	1	NUM
ma-260	132	64	λ	λ	NOUN
ma-260	132	65	)	)	PUNCT
ma-260	132	66	,	,	PUNCT
ma-260	132	67	r	r	NOUN
ma-260	132	68	>	>	X
ma-260	132	69	1	1	NUM
ma-260	132	70	.	.	PUNCT
ma-260	133	1	thus	thus	ADV
ma-260	133	2	,	,	PUNCT
ma-260	133	3	c(r	c(r	NOUN
ma-260	133	4	)	)	PUNCT
ma-260	133	5	≤	≤	ADV
ma-260	133	6	2	2	NUM
ma-260	133	7	for	for	ADP
ma-260	133	8	all	all	DET
ma-260	133	9	r	r	NOUN
ma-260	133	10	>	>	X
ma-260	133	11	0	0	X
ma-260	133	12	.	.	PUNCT
ma-260	134	1	�	�	PROPN
ma-260	134	2	proof	proof	NOUN
ma-260	134	3	of	of	ADP
ma-260	134	4	theorem	theorem	ADJ
ma-260	134	5	1.1	1.1	NUM
ma-260	134	6	.	.	PUNCT
ma-260	135	1	let	let	VERB
ma-260	135	2	1	1	NUM
ma-260	135	3	<	<	X
ma-260	135	4	q	q	X
ma-260	135	5	≤	≤	NUM
ma-260	135	6	λ	λ	NOUN
ma-260	135	7	≤	≤	NUM
ma-260	135	8	α	α	NOUN
ma-260	135	9	<	<	X
ma-260	135	10	p	p	X
ma-260	135	11	<	<	X
ma-260	135	12	∞	∞	NUM
ma-260	135	13	such	such	ADJ
ma-260	135	14	that	that	SCONJ
ma-260	135	15	1	1	NUM
ma-260	135	16	q	q	NOUN
ma-260	135	17	+	+	NUM
ma-260	135	18	2	2	NUM
ma-260	135	19	p	p	NOUN
ma-260	135	20	<	<	X
ma-260	135	21	1	1	NUM
ma-260	135	22	α	α	NOUN
ma-260	135	23	+	+	NOUN
ma-260	135	24	1	1	NUM
ma-260	135	25	λ	λ	NOUN
ma-260	135	26	.	.	PUNCT
ma-260	136	1	(	(	PUNCT
ma-260	136	2	1	1	X
ma-260	136	3	)	)	PUNCT
ma-260	136	4	assume	assume	VERB
ma-260	136	5	that	that	SCONJ
ma-260	136	6	b	b	X
ma-260	136	7	∈	∈	PROPN
ma-260	136	8	bmo(rd	bmo(rd	NOUN
ma-260	136	9	)	)	PUNCT
ma-260	136	10	such	such	ADJ
ma-260	136	11	that	that	SCONJ
ma-260	136	12	b−	b−	PROPN
ma-260	136	13	∈	∈	PROPN
ma-260	136	14	l∞(rd	l∞(rd	NOUN
ma-260	136	15	)	)	PUNCT
ma-260	136	16	and	and	CCONJ
ma-260	136	17	f	f	PROPN
ma-260	136	18	∈	∈	PROPN
ma-260	136	19	(	(	PUNCT
ma-260	136	20	lq	lq	PROPN
ma-260	136	21	,	,	PUNCT
ma-260	136	22	lp)α	lp)α	PROPN
ma-260	136	23	,	,	PUNCT
ma-260	136	24	λ(µ).proceeding	λ(µ).proceede	VERB
ma-260	136	25	as	as	ADP
ma-260	136	26	in	in	ADP
ma-260	136	27	the	the	DET
ma-260	136	28	proof	proof	NOUN
ma-260	136	29	of	of	ADP
ma-260	136	30	theorem	theorem	NOUN
ma-260	136	31	4	4	NUM
ma-260	136	32	in	in	ADP
ma-260	136	33	[	[	PUNCT
ma-260	136	34	13	13	NUM
ma-260	136	35	]	]	PUNCT
ma-260	136	36	,	,	PUNCT
ma-260	136	37	we	we	PRON
ma-260	136	38	have	have	VERB
ma-260	136	39	‖[b	‖[b	NUM
ma-260	136	40	,	,	PUNCT
ma-260	136	41	m]f	m]f	NOUN
ma-260	136	42	‖(lq	‖(lq	NUM
ma-260	136	43	,	,	PUNCT
ma-260	136	44	lp)α	lp)α	PROPN
ma-260	136	45	,	,	PUNCT
ma-260	136	46	λ(rd	λ(rd	ADJ
ma-260	136	47	)	)	PUNCT
ma-260	136	48	≤	≤	NOUN
ma-260	136	49	∥∥mbf	∥∥mbf	NOUN
ma-260	136	50	+	+	CCONJ
ma-260	136	51	2b	2b	NUM
ma-260	136	52	−mf	−mf	X
ma-260	136	53	∥∥	∥∥	X
ma-260	136	54	(	(	PUNCT
ma-260	136	55	lq	lq	INTJ
ma-260	136	56	,	,	PUNCT
ma-260	136	57	lp)α	lp)α	PROPN
ma-260	136	58	,	,	PUNCT
ma-260	136	59	λ(rd	λ(rd	ADJ
ma-260	136	60	)	)	PUNCT
ma-260	136	61	≤	≤	NUM
ma-260	137	1	‖mbf	‖mbf	NOUN
ma-260	137	2	‖(lq	‖(lq	CCONJ
ma-260	137	3	,	,	PUNCT
ma-260	137	4	lp)α	lp)α	PROPN
ma-260	137	5	,	,	PUNCT
ma-260	137	6	λ(rd	λ(rd	PRON
ma-260	137	7	)	)	PUNCT
ma-260	138	1	+	+	CCONJ
ma-260	138	2	2	2	NUM
ma-260	138	3	∥∥b−∥∥∞	∥∥b−∥∥∞	NUM
ma-260	138	4	‖mf	‖mf	NUM
ma-260	138	5	‖(lq	‖(lq	NUM
ma-260	138	6	,	,	PUNCT
ma-260	138	7	lp)α	lp)α	PROPN
ma-260	138	8	,	,	PUNCT
ma-260	138	9	λ(rd	λ(rd	PRON
ma-260	138	10	)	)	PUNCT
ma-260	138	11	.	.	PUNCT
ma-260	139	1	from	from	ADP
ma-260	139	2	(	(	PUNCT
ma-260	139	3	3.1	3.1	NUM
ma-260	139	4	)	)	PUNCT
ma-260	139	5	and	and	CCONJ
ma-260	139	6	the	the	DET
ma-260	139	7	first	first	ADJ
ma-260	139	8	point	point	NOUN
ma-260	139	9	of	of	ADP
ma-260	139	10	theorem	theorem	ADJ
ma-260	139	11	2.4	2.4	NUM
ma-260	139	12	,	,	PUNCT
ma-260	139	13	we	we	PRON
ma-260	139	14	deduce	deduce	VERB
ma-260	139	15	that	that	DET
ma-260	139	16	‖[b	‖[b	PROPN
ma-260	139	17	,	,	PUNCT
ma-260	139	18	m]f	m]f	NOUN
ma-260	139	19	‖(lq	‖(lq	NUM
ma-260	139	20	,	,	PUNCT
ma-260	139	21	lp)α	lp)α	PROPN
ma-260	139	22	,	,	PUNCT
ma-260	139	23	λ(rd	λ(rd	ADV
ma-260	139	24	)	)	PUNCT
ma-260	139	25	<	<	X
ma-260	139	26	∼	∼	X
ma-260	139	27	(	(	PUNCT
ma-260	139	28	‖b‖bmo(rd	‖b‖bmo(rd	NOUN
ma-260	139	29	)	)	PUNCT
ma-260	139	30	+	+	CCONJ
ma-260	139	31	∥∥b−∥∥∞	∥∥b−∥∥∞	X
ma-260	139	32	)	)	PUNCT
ma-260	139	33	‖f	‖f	PRON
ma-260	139	34	‖(lq	‖(lq	CCONJ
ma-260	139	35	,	,	PUNCT
ma-260	139	36	lp)α	lp)α	PROPN
ma-260	139	37	,	,	PUNCT
ma-260	139	38	λ(rd	λ(rd	PRON
ma-260	139	39	)	)	PUNCT
ma-260	139	40	.	.	PUNCT
ma-260	140	1	(	(	PUNCT
ma-260	140	2	2	2	X
ma-260	140	3	)	)	PUNCT
ma-260	140	4	conversely	conversely	ADV
ma-260	140	5	,	,	PUNCT
ma-260	140	6	assume	assume	VERB
ma-260	140	7	that	that	SCONJ
ma-260	140	8	[	[	X
ma-260	140	9	b	b	X
ma-260	140	10	,	,	PUNCT
ma-260	140	11	m	m	VERB
ma-260	140	12	]	]	X
ma-260	140	13	is	be	AUX
ma-260	140	14	bounded	bound	VERB
ma-260	140	15	on	on	ADP
ma-260	140	16	(	(	PUNCT
ma-260	140	17	lq	lq	PROPN
ma-260	140	18	,	,	PUNCT
ma-260	140	19	lp)α	lp)α	PROPN
ma-260	140	20	,	,	PUNCT
ma-260	140	21	λ(rd).let	λ(rd).let	PROPN
ma-260	140	22	t	t	PROPN
ma-260	140	23	>	>	X
ma-260	140	24	0	0	PUNCT
ma-260	141	1	and	and	CCONJ
ma-260	141	2	x	x	PROPN
ma-260	141	3	∈	∈	PROPN
ma-260	141	4	rd	rd	PROPN
ma-260	141	5	.	.	PUNCT
ma-260	142	1	put	put	VERB
ma-260	142	2	b	b	NOUN
ma-260	142	3	=	=	PUNCT
ma-260	142	4	b(x	b(x	PROPN
ma-260	142	5	,	,	PUNCT
ma-260	142	6	t	t	PROPN
ma-260	142	7	)	)	PUNCT
ma-260	142	8	.	.	PUNCT
ma-260	143	1	denote	denote	VERB
ma-260	143	2	by	by	ADP
ma-260	143	3	mbf	mbf	PROPN
ma-260	143	4	the	the	DET
ma-260	143	5	local	local	ADJ
ma-260	143	6	maximal	maximal	ADJ
ma-260	143	7	function	function	NOUN
ma-260	143	8	of	of	ADP
ma-260	143	9	f	f	PROPN
ma-260	143	10	definedby	definedby	ADV
ma-260	143	11	:	:	PUNCT
ma-260	143	12	mbf	mbf	NOUN
ma-260	143	13	(	(	PUNCT
ma-260	143	14	x	x	NOUN
ma-260	143	15	)	)	PUNCT
ma-260	143	16	=	=	SYM
ma-260	143	17	sup	sup	NOUN
ma-260	143	18	b	b	PROPN
ma-260	143	19	′3x	′3x	PRON
ma-260	143	20	:	:	PUNCT
ma-260	143	21	b′⊂b	b′⊂b	PROPN
ma-260	143	22	|b′	|b′	PROPN
ma-260	143	23	|−1	|−1	PUNCT
ma-260	143	24	∫	∫	PROPN
ma-260	143	25	b	b	PROPN
ma-260	144	1	′	′	NUM
ma-260	144	2	|f	|f	PROPN
ma-260	145	1	(	(	PUNCT
ma-260	145	2	y)|	y)|	PROPN
ma-260	145	3	dy	dy	NOUN
ma-260	145	4	.	.	PUNCT
ma-260	146	1	since	since	SCONJ
ma-260	146	2	χb	χb	PROPN
ma-260	146	3	∈	∈	PROPN
ma-260	146	4	lα(rd	lα(rd	ADJ
ma-260	146	5	)	)	PUNCT
ma-260	146	6	∩	∩	NOUN
ma-260	146	7	lλ(rd	lλ(rd	NOUN
ma-260	146	8	)	)	PUNCT
ma-260	146	9	,	,	PUNCT
ma-260	146	10	it	it	PRON
ma-260	146	11	follows	follow	VERB
ma-260	146	12	from	from	ADP
ma-260	146	13	(	(	PUNCT
ma-260	146	14	1.2	1.2	NUM
ma-260	146	15	)	)	PUNCT
ma-260	147	1	that	that	PRON
ma-260	147	2	χb	χb	PROPN
ma-260	147	3	∈	∈	PROPN
ma-260	147	4	(	(	PUNCT
ma-260	147	5	lq	lq	PROPN
ma-260	147	6	,	,	PUNCT
ma-260	147	7	lp)α	lp)α	PROPN
ma-260	147	8	(	(	PUNCT
ma-260	147	9	rd)∩(lq	rd)∩(lq	INTJ
ma-260	147	10	,	,	PUNCT
ma-260	147	11	lp)λ	lp)λ	PROPN
ma-260	147	12	(	(	PUNCT
ma-260	147	13	rd	rd	NOUN
ma-260	147	14	)	)	PUNCT
ma-260	147	15	.	.	PUNCT
ma-260	148	1	from	from	ADP
ma-260	148	2	proposition	proposition	NOUN
ma-260	148	3	2.2	2.2	NUM
ma-260	148	4	,	,	PUNCT
ma-260	148	5	we	we	PRON
ma-260	148	6	deduce	deduce	VERB
ma-260	148	7	that	that	SCONJ
ma-260	148	8	χb	χb	PROPN
ma-260	148	9	∈	∈	PROPN
ma-260	148	10	(	(	PUNCT
ma-260	148	11	lq	lq	PROPN
ma-260	148	12	,	,	PUNCT
ma-260	148	13	lp)α	lp)α	PROPN
ma-260	148	14	,	,	PUNCT
ma-260	148	15	λ(rd).therefore	λ(rd).therefore	PROPN
ma-260	148	16	,	,	PUNCT
ma-260	148	17	there	there	PRON
ma-260	148	18	exists	exist	VERB
ma-260	148	19	a	a	DET
ma-260	148	20	constant	constant	ADJ
ma-260	148	21	c	c	NOUN
ma-260	148	22	>	>	X
ma-260	148	23	0	0	NUM
ma-260	149	1	such	such	ADJ
ma-260	149	2	that	that	DET
ma-260	149	3	‖[b	‖[b	PROPN
ma-260	149	4	,	,	PUNCT
ma-260	149	5	m]χb‖(lq	m]χb‖(lq	X
ma-260	149	6	,	,	PUNCT
ma-260	149	7	lp)α	lp)α	PROPN
ma-260	149	8	,	,	PUNCT
ma-260	149	9	λ(rd	λ(rd	ADJ
ma-260	149	10	)	)	PUNCT
ma-260	149	11	≤	≤	NUM
ma-260	149	12	c	c	X
ma-260	149	13	‖χb‖(lq	‖χb‖(lq	NUM
ma-260	149	14	,	,	PUNCT
ma-260	149	15	lp)α	lp)α	PROPN
ma-260	149	16	,	,	PUNCT
ma-260	149	17	λ(rd	λ(rd	PRON
ma-260	149	18	)	)	PUNCT
ma-260	149	19	.	.	PUNCT
ma-260	150	1	we	we	PRON
ma-260	150	2	also	also	ADV
ma-260	150	3	have	have	VERB
ma-260	150	4	|mb(b)−	|mb(b)−	NOUN
ma-260	150	5	bχb|	bχb|	NOUN
ma-260	150	6	=	=	NOUN
ma-260	150	7	|m(bχb)χb	|m(bχb)χb	NUM
ma-260	150	8	−	−	NOUN
ma-260	150	9	bm(χb)χb|	bm(χb)χb|	PUNCT
ma-260	150	10	≤	≤	NUM
ma-260	150	11	|m(bχb)−	|m(bχb)−	NUM
ma-260	150	12	bm(χb)|	bm(χb)|	PROPN
ma-260	150	13	=	=	SYM
ma-260	150	14	|[b	|[b	PROPN
ma-260	150	15	,	,	PUNCT
ma-260	150	16	m]χb|	m]χb|	NOUN
ma-260	150	17	.	.	PUNCT
ma-260	151	1	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	151	2	eur	eur	PROPN
ma-260	151	3	.	.	PUNCT
ma-260	152	1	j.	j.	PROPN
ma-260	152	2	math	math	PROPN
ma-260	152	3	.	.	PUNCT
ma-260	153	1	anal	anal	PROPN
ma-260	153	2	.	.	PUNCT
ma-260	154	1	10.28924	10.28924	NUM
ma-260	154	2	/	/	SYM
ma-260	154	3	ada	ada	PROPN
ma-260	154	4	/	/	SYM
ma-260	154	5	ma.4.22	ma.4.22	PROPN
ma-260	155	1	7applying	7applye	VERB
ma-260	155	2	hölder	hölder	NOUN
ma-260	155	3	’s	’s	PART
ma-260	155	4	inequality	inequality	NOUN
ma-260	155	5	,	,	PUNCT
ma-260	155	6	proposition	proposition	NOUN
ma-260	155	7	2.3	2.3	NUM
ma-260	155	8	and	and	CCONJ
ma-260	155	9	proposition	proposition	NOUN
ma-260	155	10	2.2	2.2	NUM
ma-260	155	11	,	,	PUNCT
ma-260	155	12	we	we	PRON
ma-260	155	13	get	get	VERB
ma-260	155	14	|b|−1	|b|−1	NUM
ma-260	155	15	∫	∫	PROPN
ma-260	155	16	b	b	PROPN
ma-260	155	17	|b(z)−mb(b)(z)|dz	|b(z)−mb(b)(z)|dz	PROPN
ma-260	155	18	≤	≤	NOUN
ma-260	155	19	(	(	PUNCT
ma-260	155	20	|b|−1	|b|−1	NUM
ma-260	155	21	∫	∫	PROPN
ma-260	155	22	b	b	PROPN
ma-260	155	23	|b(z)−mb(b)(z)|qdz	|b(z)−mb(b)(z)|qdz	PROPN
ma-260	155	24	)	)	PUNCT
ma-260	155	25	1	1	NUM
ma-260	155	26	q	q	PROPN
ma-260	155	27	≤	≤	X
ma-260	155	28	|b|−	|b|−	NOUN
ma-260	155	29	1	1	NUM
ma-260	155	30	q	q	NOUN
ma-260	156	1	(	(	PUNCT
ma-260	156	2	∫	∫	PROPN
ma-260	156	3	b	b	PROPN
ma-260	156	4	|[b	|[b	PROPN
ma-260	156	5	,	,	PUNCT
ma-260	156	6	m]χb(z)|qdz	m]χb(z)|qdz	PROPN
ma-260	156	7	)	)	PUNCT
ma-260	156	8	1	1	NUM
ma-260	156	9	q	q	NOUN
ma-260	156	10	<	<	X
ma-260	156	11	∼	∼	X
ma-260	156	12	t−	t−	X
ma-260	156	13	d	d	NOUN
ma-260	156	14	q	q	X
ma-260	157	1	[	[	X
ma-260	157	2	t	t	X
ma-260	157	3	]	]	X
ma-260	157	4	d(−	d(−	PROPN
ma-260	157	5	1	1	NUM
ma-260	157	6	α	α	NOUN
ma-260	157	7	+	+	NOUN
ma-260	157	8	1	1	NUM
ma-260	157	9	q	q	NOUN
ma-260	157	10	)	)	PUNCT
ma-260	157	11	1	1	NUM
ma-260	158	1	[	[	SYM
ma-260	158	2	1	1	NUM
ma-260	158	3	/	/	SYM
ma-260	158	4	t	t	NOUN
ma-260	158	5	]	]	X
ma-260	158	6	d	d	X
ma-260	158	7	(	(	PUNCT
ma-260	158	8	1	1	NUM
ma-260	158	9	λ	λ	NOUN
ma-260	158	10	−	−	PROPN
ma-260	158	11	1	1	NUM
ma-260	158	12	q	q	NOUN
ma-260	158	13	)	)	PUNCT
ma-260	158	14	1	1	NUM
ma-260	158	15	‖[b	‖[b	NUM
ma-260	158	16	,	,	PUNCT
ma-260	158	17	m]χb‖(lq	m]χb‖(lq	PROPN
ma-260	158	18	,	,	PUNCT
ma-260	158	19	l∞)α	l∞)α	INTJ
ma-260	158	20	,	,	PUNCT
ma-260	158	21	λ(rd	λ(rd	PRON
ma-260	158	22	)	)	PUNCT
ma-260	159	1	<	<	X
ma-260	159	2	∼	∼	X
ma-260	159	3	t−	t−	PROPN
ma-260	159	4	d	d	NOUN
ma-260	159	5	q	q	X
ma-260	160	1	[	[	X
ma-260	160	2	t	t	X
ma-260	160	3	]	]	X
ma-260	160	4	d(−	d(−	PROPN
ma-260	160	5	1	1	NUM
ma-260	160	6	α	α	NOUN
ma-260	160	7	+	+	NOUN
ma-260	160	8	1	1	NUM
ma-260	160	9	q	q	NOUN
ma-260	160	10	)	)	PUNCT
ma-260	160	11	1	1	NUM
ma-260	161	1	[	[	SYM
ma-260	161	2	1	1	NUM
ma-260	161	3	/	/	SYM
ma-260	161	4	t	t	NOUN
ma-260	161	5	]	]	X
ma-260	161	6	d	d	X
ma-260	161	7	(	(	PUNCT
ma-260	161	8	1	1	NUM
ma-260	161	9	λ	λ	NOUN
ma-260	161	10	−	−	PROPN
ma-260	161	11	1	1	NUM
ma-260	161	12	q	q	NOUN
ma-260	161	13	)	)	PUNCT
ma-260	161	14	1	1	NUM
ma-260	161	15	‖[b	‖[b	NUM
ma-260	161	16	,	,	PUNCT
ma-260	161	17	m]χb‖(lq	m]χb‖(lq	X
ma-260	161	18	,	,	PUNCT
ma-260	161	19	lp)α	lp)α	PROPN
ma-260	161	20	,	,	PUNCT
ma-260	161	21	λ(rd	λ(rd	ADV
ma-260	161	22	)	)	PUNCT
ma-260	162	1	<	<	X
ma-260	162	2	∼	∼	X
ma-260	162	3	t−	t−	PROPN
ma-260	162	4	d	d	NOUN
ma-260	162	5	q	q	X
ma-260	163	1	[	[	X
ma-260	163	2	t	t	X
ma-260	163	3	]	]	X
ma-260	163	4	d(−	d(−	PROPN
ma-260	163	5	1	1	NUM
ma-260	163	6	α	α	NOUN
ma-260	163	7	+	+	NOUN
ma-260	163	8	1	1	NUM
ma-260	163	9	q	q	NOUN
ma-260	163	10	)	)	PUNCT
ma-260	163	11	1	1	NUM
ma-260	164	1	[	[	SYM
ma-260	164	2	1	1	NUM
ma-260	164	3	/	/	SYM
ma-260	164	4	t	t	NOUN
ma-260	164	5	]	]	X
ma-260	164	6	d	d	X
ma-260	164	7	(	(	PUNCT
ma-260	164	8	1	1	NUM
ma-260	164	9	λ	λ	NOUN
ma-260	164	10	−	−	PROPN
ma-260	164	11	1	1	NUM
ma-260	164	12	q	q	NOUN
ma-260	164	13	)	)	PUNCT
ma-260	164	14	1	1	NUM
ma-260	164	15	‖χb‖(lq	‖χb‖(lq	NUM
ma-260	164	16	,	,	PUNCT
ma-260	164	17	lp)α	lp)α	PROPN
ma-260	164	18	,	,	PUNCT
ma-260	164	19	λ(rd	λ(rd	ADV
ma-260	164	20	)	)	PUNCT
ma-260	164	21	<	<	X
ma-260	164	22	∼	∼	X
ma-260	164	23	t−	t−	PROPN
ma-260	164	24	d	d	NOUN
ma-260	164	25	q	q	X
ma-260	165	1	[	[	X
ma-260	165	2	t	t	X
ma-260	165	3	]	]	X
ma-260	165	4	d(−	d(−	PROPN
ma-260	165	5	1	1	NUM
ma-260	165	6	α	α	NOUN
ma-260	165	7	+	+	NOUN
ma-260	165	8	1	1	NUM
ma-260	165	9	q	q	NOUN
ma-260	165	10	)	)	PUNCT
ma-260	165	11	1	1	NUM
ma-260	166	1	[	[	SYM
ma-260	166	2	1	1	NUM
ma-260	166	3	/	/	SYM
ma-260	166	4	t	t	NOUN
ma-260	166	5	]	]	X
ma-260	166	6	d	d	X
ma-260	166	7	(	(	PUNCT
ma-260	166	8	1	1	NUM
ma-260	166	9	λ	λ	NOUN
ma-260	166	10	−	−	PROPN
ma-260	166	11	1	1	NUM
ma-260	166	12	q	q	NOUN
ma-260	166	13	)	)	PUNCT
ma-260	166	14	1	1	NUM
ma-260	166	15	max{‖χb‖q	max{‖χb‖q	ADJ
ma-260	166	16	,	,	PUNCT
ma-260	166	17	p	p	X
ma-260	166	18	,	,	PUNCT
ma-260	166	19	α	α	PROPN
ma-260	166	20	,	,	PUNCT
ma-260	166	21	‖χb‖q	‖χb‖q	PROPN
ma-260	166	22	,	,	PUNCT
ma-260	166	23	p	p	NOUN
ma-260	166	24	,	,	PUNCT
ma-260	166	25	λ	λ	NOUN
ma-260	166	26	}	}	PUNCT
ma-260	166	27	.	.	PUNCT
ma-260	167	1	it	it	PRON
ma-260	167	2	follows	follow	VERB
ma-260	167	3	from	from	ADP
ma-260	167	4	(	(	PUNCT
ma-260	167	5	1.2	1.2	NUM
ma-260	167	6	)	)	PUNCT
ma-260	168	1	that	that	SCONJ
ma-260	168	2	|b|−1	|b|−1	NUM
ma-260	168	3	∫	∫	PROPN
ma-260	168	4	b	b	PROPN
ma-260	168	5	|b(z)−mb(b)(z)|dz	|b(z)−mb(b)(z)|dz	PROPN
ma-260	168	6	<	<	X
ma-260	168	7	∼	∼	NOUN
ma-260	168	8	t	t	NOUN
ma-260	168	9	−	−	NOUN
ma-260	169	1	d	d	NOUN
ma-260	169	2	q	q	X
ma-260	170	1	[	[	X
ma-260	170	2	t	t	X
ma-260	170	3	]	]	X
ma-260	170	4	d(−	d(−	PROPN
ma-260	170	5	1	1	NUM
ma-260	170	6	α	α	NOUN
ma-260	170	7	+	+	NOUN
ma-260	170	8	1	1	NUM
ma-260	170	9	q	q	NOUN
ma-260	170	10	)	)	PUNCT
ma-260	170	11	1	1	NUM
ma-260	171	1	[	[	SYM
ma-260	171	2	1	1	NUM
ma-260	171	3	/	/	SYM
ma-260	171	4	t	t	NOUN
ma-260	171	5	]	]	X
ma-260	171	6	d	d	X
ma-260	171	7	(	(	PUNCT
ma-260	171	8	1	1	NUM
ma-260	171	9	λ	λ	NOUN
ma-260	171	10	−	−	PROPN
ma-260	171	11	1	1	NUM
ma-260	171	12	q	q	NOUN
ma-260	171	13	)	)	PUNCT
ma-260	171	14	1	1	NUM
ma-260	171	15	max{t	max{t	NOUN
ma-260	171	16	d	d	PROPN
ma-260	171	17	α	α	PROPN
ma-260	171	18	,	,	PUNCT
ma-260	171	19	t	t	PROPN
ma-260	171	20	d	d	X
ma-260	171	21	λ	λ	PROPN
ma-260	171	22	}	}	PUNCT
ma-260	171	23	.	.	PUNCT
ma-260	172	1	so	so	ADV
ma-260	172	2	,	,	PUNCT
ma-260	172	3	by	by	ADP
ma-260	172	4	lemma	lemma	PROPN
ma-260	172	5	3.3	3.3	NUM
ma-260	172	6	,	,	PUNCT
ma-260	172	7	we	we	PRON
ma-260	172	8	obtain	obtain	VERB
ma-260	172	9	|b|−1	|b|−1	NUM
ma-260	172	10	∫	∫	PROPN
ma-260	172	11	b	b	PROPN
ma-260	172	12	|b(z)−mb(b)(z)|dz	|b(z)−mb(b)(z)|dz	PROPN
ma-260	172	13	<	<	X
ma-260	172	14	∼	∼	X
ma-260	172	15	2.denote	2.denote	NUM
ma-260	172	16	by	by	ADP
ma-260	172	17	e	e	NOUN
ma-260	172	18	:	:	PUNCT
ma-260	172	19	=	=	SYM
ma-260	172	20	{	{	PUNCT
ma-260	172	21	y	y	PROPN
ma-260	172	22	∈	∈	PROPN
ma-260	172	23	b	b	PROPN
ma-260	172	24	:	:	PUNCT
ma-260	172	25	b(y	b(y	NUM
ma-260	172	26	)	)	PUNCT
ma-260	172	27	≤	≤	NUM
ma-260	172	28	bb	bb	NUM
ma-260	172	29	}	}	PUNCT
ma-260	172	30	,	,	PUNCT
ma-260	172	31	f	f	X
ma-260	172	32	:	:	PUNCT
ma-260	172	33	=	=	SYM
ma-260	172	34	{	{	PUNCT
ma-260	172	35	y	y	PROPN
ma-260	172	36	∈	∈	PROPN
ma-260	172	37	b	b	PROPN
ma-260	172	38	:	:	PUNCT
ma-260	172	39	b(y	b(y	NUM
ma-260	172	40	)	)	PUNCT
ma-260	172	41	>	>	X
ma-260	173	1	bb}.since	bb}.since	PROPN
ma-260	173	2	∫	∫	PROPN
ma-260	173	3	e	e	X
ma-260	173	4	|b(z)−	|b(z)−	X
ma-260	173	5	bb|dz	bb|dz	PROPN
ma-260	173	6	=	=	SYM
ma-260	173	7	∫	∫	PROPN
ma-260	173	8	f	f	PROPN
ma-260	173	9	|b(z)−	|b(z)−	PROPN
ma-260	173	10	bb|dz	bb|dz	PROPN
ma-260	173	11	,	,	PUNCT
ma-260	173	12	in	in	ADP
ma-260	173	13	view	view	NOUN
ma-260	173	14	of	of	ADP
ma-260	173	15	the	the	DET
ma-260	173	16	inequality	inequality	NOUN
ma-260	173	17	b(x	b(x	NOUN
ma-260	173	18	)	)	PUNCT
ma-260	173	19	≤	≤	NUM
ma-260	173	20	bb	bb	NUM
ma-260	173	21	≤	≤	NOUN
ma-260	173	22	mb(b	mb(b	NOUN
ma-260	173	23	)	)	PUNCT
ma-260	173	24	,	,	PUNCT
ma-260	173	25	for	for	ADP
ma-260	173	26	x	x	PROPN
ma-260	173	27	∈	∈	PROPN
ma-260	173	28	e	e	NOUN
ma-260	173	29	,	,	PUNCT
ma-260	173	30	we	we	PRON
ma-260	173	31	get	get	VERB
ma-260	173	32	|b|−1	|b|−1	NUM
ma-260	173	33	∫	∫	PROPN
ma-260	173	34	b	b	PROPN
ma-260	173	35	|b(z)−	|b(z)−	PROPN
ma-260	173	36	bb|dz	bb|dz	PROPN
ma-260	173	37	=	=	SYM
ma-260	173	38	2|b|−1	2|b|−1	PROPN
ma-260	173	39	∫	∫	X
ma-260	173	40	e	e	X
ma-260	173	41	|b(z)−	|b(z)−	X
ma-260	173	42	bb|dz	bb|dz	ADP
ma-260	173	43	≤	≤	ADJ
ma-260	173	44	2|b|−1	2|b|−1	PROPN
ma-260	173	45	∫	∫	NOUN
ma-260	173	46	e	e	PROPN
ma-260	173	47	|b(z)−mb(b)(z)|dz	|b(z)−mb(b)(z)|dz	PROPN
ma-260	173	48	≤	≤	ADV
ma-260	173	49	2|b|−1	2|b|−1	NUM
ma-260	173	50	∫	∫	PROPN
ma-260	173	51	b	b	PROPN
ma-260	173	52	|b(z)−mb(b)(z)|dz	|b(z)−mb(b)(z)|dz	PROPN
ma-260	173	53	<	<	X
ma-260	173	54	∼	∼	NOUN
ma-260	173	55	4	4	NUM
ma-260	173	56	.	.	PUNCT
ma-260	173	57	by	by	ADP
ma-260	173	58	taking	take	VERB
ma-260	173	59	in	in	ADP
ma-260	173	60	the	the	DET
ma-260	173	61	left	left	ADJ
ma-260	173	62	hand	hand	NOUN
ma-260	173	63	side	side	NOUN
ma-260	173	64	the	the	DET
ma-260	173	65	supremum	supremum	ADJ
ma-260	173	66	over	over	ADP
ma-260	173	67	all	all	DET
ma-260	173	68	t	t	NOUN
ma-260	173	69	>	>	X
ma-260	173	70	0	0	PUNCT
ma-260	174	1	and	and	CCONJ
ma-260	174	2	x	x	PROPN
ma-260	174	3	∈	∈	PROPN
ma-260	174	4	rd	rd	NOUN
ma-260	174	5	,	,	PUNCT
ma-260	174	6	we	we	PRON
ma-260	174	7	obtain	obtain	VERB
ma-260	174	8	‖b‖bmo(rd	‖b‖bmo(rd	NOUN
ma-260	174	9	)	)	PUNCT
ma-260	175	1	<	<	X
ma-260	175	2	∞.in	∞.in	NOUN
ma-260	175	3	order	order	NOUN
ma-260	175	4	to	to	PART
ma-260	175	5	show	show	VERB
ma-260	175	6	that	that	SCONJ
ma-260	175	7	b−	b−	PROPN
ma-260	175	8	∈	∈	PROPN
ma-260	175	9	l∞(rd	l∞(rd	NOUN
ma-260	175	10	)	)	PUNCT
ma-260	175	11	,	,	PUNCT
ma-260	175	12	note	note	VERB
ma-260	175	13	that	that	SCONJ
ma-260	175	14	mb(b	mb(b	NOUN
ma-260	175	15	)	)	PUNCT
ma-260	175	16	≥	≥	NUM
ma-260	175	17	|b|	|b|	PROPN
ma-260	175	18	.	.	PUNCT
ma-260	176	1	hence	hence	ADV
ma-260	176	2	0	0	NUM
ma-260	176	3	≤	≤	NUM
ma-260	176	4	b−	b−	NOUN
ma-260	176	5	=	=	PRON
ma-260	176	6	|b|	|b|	PROPN
ma-260	176	7	−	−	PROPN
ma-260	176	8	b+	b+	VERB
ma-260	176	9	≤	≤	X
ma-260	176	10	mb(b)−	mb(b)−	NOUN
ma-260	176	11	b+	b+	VERB
ma-260	176	12	≤	≤	X
ma-260	176	13	mb(b)−	mb(b)−	NOUN
ma-260	176	14	b+	b+	ADV
ma-260	176	15	+	+	CCONJ
ma-260	176	16	b−	b−	PROPN
ma-260	176	17	=	=	SYM
ma-260	176	18	mb(b)−	mb(b)−	PROPN
ma-260	176	19	b.	b.	PROPN
ma-260	176	20	thus	thus	ADV
ma-260	176	21	(	(	PUNCT
ma-260	176	22	b−)b	b−)b	ADP
ma-260	176	23	<	<	X
ma-260	176	24	∼	∼	NOUN
ma-260	176	25	2	2	NUM
ma-260	176	26	,	,	PUNCT
ma-260	176	27	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	176	28	eur	eur	PROPN
ma-260	176	29	.	.	PUNCT
ma-260	177	1	j.	j.	PROPN
ma-260	177	2	math	math	PROPN
ma-260	177	3	.	.	PUNCT
ma-260	178	1	anal	anal	PROPN
ma-260	178	2	.	.	PUNCT
ma-260	179	1	10.28924	10.28924	NUM
ma-260	179	2	/	/	SYM
ma-260	179	3	ada	ada	PROPN
ma-260	179	4	/	/	SYM
ma-260	179	5	ma.4.22	ma.4.22	PROPN
ma-260	179	6	8and	8and	NUM
ma-260	179	7	by	by	ADP
ma-260	179	8	the	the	DET
ma-260	179	9	lebesgue	lebesgue	PROPN
ma-260	179	10	differentiation	differentiation	NOUN
ma-260	179	11	theorem	theorem	VERB
ma-260	179	12	we	we	PRON
ma-260	179	13	get	get	VERB
ma-260	179	14	b−(x	b−(x	NOUN
ma-260	179	15	)	)	PUNCT
ma-260	179	16	<	<	X
ma-260	179	17	∼	∼	NOUN
ma-260	179	18	2for	2for	ADP
ma-260	179	19	almost	almost	ADV
ma-260	179	20	every	every	PRON
ma-260	179	21	x	x	SYM
ma-260	179	22	∈	∈	PROPN
ma-260	179	23	rd	rd	PROPN
ma-260	179	24	.	.	PUNCT
ma-260	180	1	�	�	PROPN
ma-260	180	2	4	4	NUM
ma-260	180	3	.	.	PUNCT
ma-260	180	4	proof	proof	NOUN
ma-260	180	5	of	of	ADP
ma-260	180	6	theorem	theorem	ADJ
ma-260	180	7	1.2	1.2	NUM
ma-260	180	8	and	and	CCONJ
ma-260	180	9	theorem	theorem	VERB
ma-260	180	10	1.3	1.3	NUM
ma-260	180	11	we	we	PRON
ma-260	180	12	recall	recall	VERB
ma-260	180	13	that	that	SCONJ
ma-260	180	14	the	the	DET
ma-260	180	15	proofs	proof	NOUN
ma-260	180	16	of	of	ADP
ma-260	180	17	theorem	theorem	ADJ
ma-260	180	18	1.2	1.2	NUM
ma-260	180	19	and	and	CCONJ
ma-260	180	20	theorem	theorem	VERB
ma-260	180	21	1.3	1.3	NUM
ma-260	180	22	are	be	AUX
ma-260	180	23	simply	simply	ADV
ma-260	180	24	an	an	DET
ma-260	180	25	adaptation	adaptation	NOUN
ma-260	180	26	of	of	ADP
ma-260	180	27	thosegiven	thosegiven	VERB
ma-260	180	28	in	in	ADP
ma-260	180	29	[	[	X
ma-260	180	30	5	5	NUM
ma-260	180	31	]	]	PUNCT
ma-260	180	32	(	(	PUNCT
ma-260	180	33	see	see	VERB
ma-260	180	34	also	also	ADV
ma-260	180	35	[	[	X
ma-260	180	36	6	6	NUM
ma-260	180	37	]	]	NUM
ma-260	180	38	)	)	PUNCT
ma-260	180	39	.	.	PUNCT
ma-260	181	1	proof	proof	NOUN
ma-260	181	2	of	of	ADP
ma-260	181	3	theorem	theorem	ADJ
ma-260	181	4	1.2	1.2	NUM
ma-260	181	5	.	.	PUNCT
ma-260	182	1	let	let	VERB
ma-260	182	2	1	1	NUM
ma-260	182	3	<	<	X
ma-260	182	4	q	q	X
ma-260	182	5	≤	≤	PROPN
ma-260	182	6	λ	λ	PROPN
ma-260	182	7	,	,	PUNCT
ma-260	182	8	α	α	X
ma-260	182	9	<	<	X
ma-260	182	10	p	p	X
ma-260	182	11	<	<	X
ma-260	182	12	∞	∞	NUM
ma-260	182	13	such	such	ADJ
ma-260	182	14	that	that	DET
ma-260	182	15	1q+	1q+	NUM
ma-260	182	16	2p	2p	NOUN
ma-260	182	17	<	<	X
ma-260	182	18	1	1	NUM
ma-260	182	19	α+	α+	SYM
ma-260	182	20	1	1	NUM
ma-260	182	21	λ	λ	NOUN
ma-260	182	22	and	and	CCONJ
ma-260	182	23	f	f	PROPN
ma-260	182	24	∈	∈	PROPN
ma-260	182	25	(	(	PUNCT
ma-260	182	26	lq	lq	PROPN
ma-260	182	27	,	,	PUNCT
ma-260	182	28	lp)α	lp)α	PROPN
ma-260	182	29	,	,	PUNCT
ma-260	182	30	λ(rd).fix	λ(rd).fix	NOUN
ma-260	182	31	y	y	PROPN
ma-260	182	32	∈	∈	PROPN
ma-260	182	33	rd	rd	PROPN
ma-260	182	34	and	and	CCONJ
ma-260	182	35	r	r	NOUN
ma-260	182	36	>	>	X
ma-260	182	37	0	0	NUM
ma-260	183	1	we	we	PRON
ma-260	183	2	have	have	VERB
ma-260	183	3	f	f	NOUN
ma-260	183	4	=	=	SYM
ma-260	183	5	f	f	PROPN
ma-260	183	6	χb(y,2r	χb(y,2r	PROPN
ma-260	183	7	)	)	PUNCT
ma-260	183	8	+	+	NUM
ma-260	183	9	∞∑	∞∑	NUM
ma-260	183	10	i=1	i=1	X
ma-260	183	11	f	f	PROPN
ma-260	183	12	χb(y,2i+1r)\b(y,2i	χb(y,2i+1r)\b(y,2i	ADP
ma-260	183	13	r	r	PROPN
ma-260	183	14	)	)	PUNCT
ma-260	183	15	.	.	PUNCT
ma-260	184	1	by	by	ADP
ma-260	184	2	the	the	DET
ma-260	184	3	sublinearity	sublinearity	NOUN
ma-260	184	4	of	of	ADP
ma-260	184	5	t	t	PROPN
ma-260	184	6	and	and	CCONJ
ma-260	184	7	the	the	DET
ma-260	184	8	condition	condition	NOUN
ma-260	184	9	(	(	PUNCT
ma-260	184	10	1.3	1.3	NUM
ma-260	184	11	)	)	PUNCT
ma-260	184	12	we	we	PRON
ma-260	184	13	obtain	obtain	VERB
ma-260	184	14	|t	|t	PROPN
ma-260	185	1	f	f	PROPN
ma-260	186	1	|	|	ADV
ma-260	186	2	<	<	X
ma-260	186	3	∼	∼	X
ma-260	186	4	|t	|t	X
ma-260	187	1	(	(	PUNCT
ma-260	187	2	f	f	PROPN
ma-260	187	3	χb(y,2r))|+	χb(y,2r))|+	PROPN
ma-260	188	1	∞∑	∞∑	PROPN
ma-260	188	2	i=1	i=1	PROPN
ma-260	189	1	|b(y	|b(y	ADJ
ma-260	189	2	,	,	PUNCT
ma-260	189	3	2i+1r)|−1	2i+1r)|−1	NUM
ma-260	189	4	∫	∫	PROPN
ma-260	189	5	b(y,2i+1r	b(y,2i+1r	PROPN
ma-260	189	6	)	)	PUNCT
ma-260	189	7	|f	|f	PROPN
ma-260	190	1	(	(	PUNCT
ma-260	190	2	x)|dx	x)|dx	PROPN
ma-260	190	3	and	and	CCONJ
ma-260	190	4	therefore	therefore	ADV
ma-260	190	5	,	,	PUNCT
ma-260	190	6	an	an	DET
ma-260	190	7	application	application	NOUN
ma-260	190	8	of	of	ADP
ma-260	190	9	hölder	hölder	NOUN
ma-260	190	10	inequality	inequality	NOUN
ma-260	190	11	leads	lead	VERB
ma-260	190	12	to	to	ADP
ma-260	190	13	|t	|t	PROPN
ma-260	190	14	f	f	PROPN
ma-260	191	1	|	|	ADV
ma-260	191	2	<	<	X
ma-260	191	3	∼	∼	X
ma-260	191	4	|t	|t	X
ma-260	192	1	(	(	PUNCT
ma-260	192	2	f	f	PROPN
ma-260	192	3	χb(y,2r))|+	χb(y,2r))|+	PROPN
ma-260	193	1	∞∑	∞∑	PROPN
ma-260	193	2	i=1	i=1	PROPN
ma-260	194	1	|b(y	|b(y	PROPN
ma-260	194	2	,	,	PUNCT
ma-260	194	3	2i+1r)|−	2i+1r)|−	NUM
ma-260	194	4	1	1	NUM
ma-260	194	5	q	q	NOUN
ma-260	194	6	‖f	‖f	ADJ
ma-260	194	7	χb(y,2i+1r)‖q	χb(y,2i+1r)‖q	PROPN
ma-260	194	8	.	.	PUNCT
ma-260	195	1	taking	take	VERB
ma-260	195	2	the	the	DET
ma-260	195	3	lq	lq	NOUN
ma-260	195	4	-	-	NOUN
ma-260	195	5	norm	norm	NOUN
ma-260	195	6	of	of	ADP
ma-260	195	7	both	both	DET
ma-260	195	8	sides	side	NOUN
ma-260	195	9	on	on	ADP
ma-260	195	10	the	the	DET
ma-260	195	11	ball	ball	NOUN
ma-260	195	12	b(y	b(y	PROPN
ma-260	195	13	,	,	PUNCT
ma-260	195	14	r	r	NOUN
ma-260	195	15	)	)	PUNCT
ma-260	195	16	and	and	CCONJ
ma-260	195	17	using	use	VERB
ma-260	195	18	the	the	DET
ma-260	195	19	boundedness	boundedness	NOUN
ma-260	195	20	of	of	ADP
ma-260	195	21	t	t	PROPN
ma-260	195	22	on	on	ADP
ma-260	195	23	lq	lq	INTJ
ma-260	195	24	,	,	PUNCT
ma-260	195	25	weget	weget	NOUN
ma-260	195	26	‖(t	‖(t	NUM
ma-260	195	27	f	f	PROPN
ma-260	195	28	)	)	PUNCT
ma-260	195	29	χb(y	χb(y	PUNCT
ma-260	195	30	,	,	PUNCT
ma-260	195	31	r)‖q	r)‖q	VERB
ma-260	195	32	<	<	X
ma-260	195	33	∼	∼	NOUN
ma-260	195	34	‖f	‖f	ADJ
ma-260	195	35	χb(y,2r)‖q	χb(y,2r)‖q	PUNCT
ma-260	196	1	+	+	NUM
ma-260	196	2	∞∑	∞∑	NUM
ma-260	196	3	i=1	i=1	X
ma-260	196	4	(	(	PUNCT
ma-260	196	5	2i)−	2i)−	NUM
ma-260	196	6	d	d	NOUN
ma-260	196	7	q	q	NOUN
ma-260	196	8	‖f	‖f	ADJ
ma-260	196	9	χb(y,2i+1r)‖q	χb(y,2i+1r)‖q	PROPN
ma-260	196	10	.	.	PUNCT
ma-260	197	1	taking	take	VERB
ma-260	197	2	the	the	DET
ma-260	197	3	lp	lp	NOUN
ma-260	197	4	-	-	PUNCT
ma-260	197	5	norm	norm	NOUN
ma-260	197	6	of	of	ADP
ma-260	197	7	both	both	DET
ma-260	197	8	sides	side	NOUN
ma-260	197	9	with	with	ADP
ma-260	197	10	respect	respect	NOUN
ma-260	197	11	to	to	ADP
ma-260	197	12	y	y	PROPN
ma-260	197	13	,	,	PUNCT
ma-260	197	14	it	it	PRON
ma-260	197	15	comes	come	VERB
ma-260	197	16	that	that	SCONJ
ma-260	197	17	r	r	NOUN
ma-260	197	18	‖t	‖t	NOUN
ma-260	197	19	f	f	NOUN
ma-260	197	20	‖q	‖q	PROPN
ma-260	197	21	,	,	PUNCT
ma-260	197	22	p	p	X
ma-260	197	23	<	<	X
ma-260	197	24	∼	∼	NOUN
ma-260	197	25	2r	2r	NUM
ma-260	197	26	‖f	‖f	ADP
ma-260	197	27	‖q	‖q	ADP
ma-260	197	28	,	,	PUNCT
ma-260	197	29	p	p	X
ma-260	197	30	+	+	NOUN
ma-260	198	1	∞∑	∞∑	NUM
ma-260	198	2	i=1	i=1	X
ma-260	199	1	(	(	PUNCT
ma-260	199	2	2i)−	2i)−	NUM
ma-260	199	3	d	d	NOUN
ma-260	199	4	q	q	NOUN
ma-260	199	5	2i+1r	2i+1r	NUM
ma-260	199	6	‖f	‖f	ADJ
ma-260	199	7	‖q	‖q	NOUN
ma-260	199	8	,	,	PUNCT
ma-260	199	9	p	p	X
ma-260	199	10	.	.	PUNCT
ma-260	200	1	on	on	ADP
ma-260	200	2	the	the	DET
ma-260	200	3	one	one	NUM
ma-260	200	4	hand	hand	NOUN
ma-260	200	5	,	,	PUNCT
ma-260	200	6	we	we	PRON
ma-260	200	7	have	have	VERB
ma-260	200	8	,	,	PUNCT
ma-260	200	9	2r	2r	NUM
ma-260	200	10	‖f	‖f	ADP
ma-260	200	11	‖q	‖q	NOUN
ma-260	200	12	,	,	PUNCT
ma-260	200	13	p	p	NOUN
ma-260	200	14	=	=	X
ma-260	201	1	[	[	X
ma-260	201	2	2r	2r	X
ma-260	201	3	]	]	PUNCT
ma-260	202	1	d	d	X
ma-260	202	2	(	(	PUNCT
ma-260	202	3	1	1	NUM
ma-260	202	4	α	α	NOUN
ma-260	202	5	−	−	PROPN
ma-260	202	6	1	1	NUM
ma-260	202	7	q	q	NOUN
ma-260	202	8	−	−	PROPN
ma-260	202	9	1	1	NUM
ma-260	202	10	p	p	NOUN
ma-260	202	11	)	)	PUNCT
ma-260	202	12	1	1	NUM
ma-260	203	1	[	[	X
ma-260	203	2	1/2r	1/2r	NUM
ma-260	203	3	]	]	PUNCT
ma-260	203	4	d(−	d(−	PROPN
ma-260	203	5	1	1	NUM
ma-260	203	6	λ	λ	NOUN
ma-260	203	7	+	+	NOUN
ma-260	203	8	1	1	NUM
ma-260	203	9	q	q	NOUN
ma-260	203	10	+	+	NUM
ma-260	203	11	1	1	NUM
ma-260	203	12	p	p	NOUN
ma-260	203	13	)	)	PUNCT
ma-260	203	14	1	1	NUM
ma-260	204	1	[	[	X
ma-260	204	2	2r	2r	X
ma-260	204	3	]	]	PUNCT
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ma-260	210	2	,	,	PUNCT
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ma-260	210	16	+	+	NOUN
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ma-260	210	19	+	+	NUM
ma-260	210	20	1	1	NUM
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ma-260	212	2	(	(	PUNCT
ma-260	212	3	1	1	NUM
ma-260	212	4	λ	λ	NOUN
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ma-260	212	9	1	1	NUM
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ma-260	213	1	(	(	PUNCT
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ma-260	235	3	1	1	NUM
ma-260	235	4	λ	λ	NOUN
ma-260	235	5	−	−	PROPN
ma-260	235	6	1	1	NUM
ma-260	235	7	q	q	NOUN
ma-260	235	8	−	−	PROPN
ma-260	235	9	1	1	NUM
ma-260	235	10	p	p	NOUN
ma-260	235	11	)	)	PUNCT
ma-260	235	12	1	1	NUM
ma-260	235	13	‖f	‖f	PRON
ma-260	235	14	‖(lq	‖(lq	CCONJ
ma-260	235	15	,	,	PUNCT
ma-260	235	16	lp)α	lp)α	PROPN
ma-260	235	17	,	,	PUNCT
ma-260	235	18	λ(rd	λ(rd	PRON
ma-260	235	19	)	)	PUNCT
ma-260	235	20	.	.	PUNCT
ma-260	236	1	it	it	PRON
ma-260	236	2	follows	follow	VERB
ma-260	236	3	that	that	SCONJ
ma-260	237	1	[	[	X
ma-260	237	2	r	r	X
ma-260	237	3	]	]	X
ma-260	237	4	d	d	X
ma-260	237	5	(	(	PUNCT
ma-260	237	6	1	1	NUM
ma-260	237	7	α	α	NOUN
ma-260	237	8	−	−	PROPN
ma-260	237	9	1	1	NUM
ma-260	237	10	q	q	NOUN
ma-260	237	11	−	−	PROPN
ma-260	237	12	1	1	NUM
ma-260	237	13	p	p	NOUN
ma-260	237	14	)	)	PUNCT
ma-260	237	15	1	1	NUM
ma-260	238	1	[	[	X
ma-260	238	2	1	1	NUM
ma-260	238	3	/	/	SYM
ma-260	238	4	r	r	NOUN
ma-260	238	5	]	]	PUNCT
ma-260	238	6	d(−	d(−	PROPN
ma-260	238	7	1	1	NUM
ma-260	238	8	λ	λ	NOUN
ma-260	238	9	+	+	NOUN
ma-260	238	10	1	1	NUM
ma-260	238	11	q	q	NOUN
ma-260	238	12	+	+	NUM
ma-260	238	13	1	1	NUM
ma-260	238	14	p	p	NOUN
ma-260	238	15	)	)	PUNCT
ma-260	238	16	1	1	NUM
ma-260	238	17	r	r	NOUN
ma-260	238	18	‖t	‖t	NOUN
ma-260	238	19	f	f	NOUN
ma-260	238	20	‖q	‖q	NOUN
ma-260	238	21	,	,	PUNCT
ma-260	238	22	p	p	X
ma-260	238	23	<	<	NOUN
ma-260	238	24	∼	∼	NOUN
ma-260	238	25	‖f	‖f	ADJ
ma-260	238	26	‖(lq	‖(lq	CCONJ
ma-260	238	27	,	,	PUNCT
ma-260	238	28	lp)α	lp)α	PROPN
ma-260	238	29	,	,	PUNCT
ma-260	238	30	λ(rd	λ(rd	PRON
ma-260	238	31	)	)	PUNCT
ma-260	238	32	.	.	PUNCT
ma-260	239	1	(	(	PUNCT
ma-260	239	2	4.3	4.3	NUM
ma-260	239	3	)	)	PUNCT
ma-260	239	4	we	we	PRON
ma-260	239	5	obtain	obtain	VERB
ma-260	239	6	the	the	DET
ma-260	239	7	desired	desire	VERB
ma-260	239	8	result	result	NOUN
ma-260	239	9	by	by	ADP
ma-260	239	10	taking	take	VERB
ma-260	239	11	the	the	DET
ma-260	239	12	supremum	supremum	ADJ
ma-260	239	13	over	over	ADP
ma-260	239	14	all	all	DET
ma-260	239	15	r	r	NOUN
ma-260	239	16	>	>	X
ma-260	239	17	0	0	NUM
ma-260	239	18	in	in	ADP
ma-260	239	19	the	the	DET
ma-260	239	20	left	left	ADJ
ma-260	239	21	hand	hand	NOUN
ma-260	239	22	side	side	NOUN
ma-260	239	23	of	of	ADP
ma-260	239	24	(	(	PUNCT
ma-260	239	25	4.3	4.3	NUM
ma-260	239	26	)	)	PUNCT
ma-260	239	27	.	.	PUNCT
ma-260	240	1	�	�	PROPN
ma-260	240	2	proof	proof	NOUN
ma-260	240	3	of	of	ADP
ma-260	240	4	theorem	theorem	NOUN
ma-260	240	5	1.3	1.3	NUM
ma-260	240	6	.	.	PUNCT
ma-260	241	1	let	let	VERB
ma-260	241	2	1	1	NUM
ma-260	241	3	<	<	X
ma-260	241	4	q	q	X
ma-260	241	5	≤	≤	PROPN
ma-260	241	6	λ	λ	PROPN
ma-260	241	7	,	,	PUNCT
ma-260	241	8	α	α	X
ma-260	241	9	<	<	X
ma-260	241	10	p	p	X
ma-260	241	11	<	<	X
ma-260	241	12	∞	∞	NUM
ma-260	241	13	such	such	ADJ
ma-260	241	14	that	that	SCONJ
ma-260	241	15	1q	1q	NUM
ma-260	241	16	+	+	CCONJ
ma-260	241	17	2p	2p	NUM
ma-260	241	18	<	<	SYM
ma-260	241	19	1	1	NUM
ma-260	241	20	α	α	NOUN
ma-260	241	21	+	+	NOUN
ma-260	241	22	1	1	NUM
ma-260	241	23	λ	λ	NOUN
ma-260	241	24	and	and	CCONJ
ma-260	241	25	b	b	NOUN
ma-260	241	26	∈	∈	PROPN
ma-260	241	27	bmo(rd).let	bmo(rd).let	NOUN
ma-260	241	28	f	f	X
ma-260	241	29	be	be	AUX
ma-260	241	30	any	any	DET
ma-260	241	31	element	element	NOUN
ma-260	241	32	of	of	ADP
ma-260	241	33	f	f	PROPN
ma-260	241	34	∈	∈	PROPN
ma-260	241	35	(	(	PUNCT
ma-260	241	36	lq	lq	PROPN
ma-260	241	37	,	,	PUNCT
ma-260	241	38	lp)α	lp)α	PROPN
ma-260	241	39	,	,	PUNCT
ma-260	241	40	λ(rd	λ(rd	NOUN
ma-260	241	41	)	)	PUNCT
ma-260	241	42	.	.	PUNCT
ma-260	242	1	we	we	PRON
ma-260	242	2	recall	recall	VERB
ma-260	242	3	that	that	PRON
ma-260	242	4	(	(	PUNCT
ma-260	242	5	lq	lq	PROPN
ma-260	242	6	,	,	PUNCT
ma-260	242	7	lp)α	lp)α	PROPN
ma-260	242	8	,	,	PUNCT
ma-260	242	9	λ(rd	λ(rd	NUM
ma-260	242	10	)	)	PUNCT
ma-260	242	11	is	be	AUX
ma-260	242	12	a	a	DET
ma-260	242	13	subspace	subspace	NOUN
ma-260	242	14	of	of	ADP
ma-260	242	15	themorrey	themorrey	NOUN
ma-260	242	16	space	space	NOUN
ma-260	242	17	lq	lq	VERB
ma-260	242	18	,	,	PUNCT
ma-260	242	19	d(1−	d(1−	X
ma-260	242	20	q	q	PROPN
ma-260	242	21	α	α	NOUN
ma-260	242	22	)	)	PUNCT
ma-260	242	23	(	(	PUNCT
ma-260	242	24	rd	rd	NOUN
ma-260	242	25	)	)	PUNCT
ma-260	242	26	.	.	PUNCT
ma-260	243	1	proceeding	proceed	VERB
ma-260	243	2	as	as	ADP
ma-260	243	3	in	in	ADP
ma-260	243	4	the	the	DET
ma-260	243	5	proof	proof	NOUN
ma-260	243	6	of	of	ADP
ma-260	243	7	[	[	X
ma-260	243	8	5	5	NUM
ma-260	243	9	,	,	PUNCT
ma-260	243	10	theorem	theorem	VERB
ma-260	243	11	2.2	2.2	NUM
ma-260	243	12	]	]	PUNCT
ma-260	243	13	,	,	PUNCT
ma-260	243	14	we	we	PRON
ma-260	243	15	have	have	VERB
ma-260	243	16	that	that	PRON
ma-260	243	17	for	for	ADP
ma-260	243	18	all	all	DET
ma-260	243	19	y	y	PROPN
ma-260	243	20	∈	∈	PROPN
ma-260	243	21	rd	rd	PROPN
ma-260	243	22	and	and	CCONJ
ma-260	243	23	r	r	NOUN
ma-260	243	24	>	>	X
ma-260	243	25	0	0	NUM
ma-260	243	26	,	,	PUNCT
ma-260	243	27	‖[b	‖[b	PROPN
ma-260	243	28	,	,	PUNCT
ma-260	243	29	t	t	X
ma-260	243	30	]	]	X
ma-260	243	31	f	f	X
ma-260	243	32	χb(y	χb(y	PROPN
ma-260	243	33	,	,	PUNCT
ma-260	243	34	r)‖q	r)‖q	VERB
ma-260	243	35	<	<	X
ma-260	243	36	∼	∼	NOUN
ma-260	243	37	‖f	‖f	ADJ
ma-260	243	38	χb(y,2r)‖q	χb(y,2r)‖q	PUNCT
ma-260	244	1	+	+	NUM
ma-260	244	2	∞∑	∞∑	NUM
ma-260	244	3	i=1	i=1	X
ma-260	244	4	(	(	PUNCT
ma-260	244	5	2i	2i	NUM
ma-260	244	6	r)−d	r)−d	PROPN
ma-260	245	1	[	[	X
ma-260	245	2	∫	∫	X
ma-260	245	3	b(y	b(y	PROPN
ma-260	245	4	,	,	PUNCT
ma-260	245	5	r	r	NOUN
ma-260	245	6	)	)	PUNCT
ma-260	245	7	(	(	PUNCT
ma-260	245	8	∫	∫	PROPN
ma-260	245	9	b(y,2i+1r	b(y,2i+1r	PROPN
ma-260	245	10	)	)	PUNCT
ma-260	245	11	|b(x)−	|b(x)−	NOUN
ma-260	245	12	b(z)||f	b(z)||f	NOUN
ma-260	245	13	(	(	PUNCT
ma-260	245	14	x)|dx	x)|dx	PROPN
ma-260	245	15	)	)	PUNCT
ma-260	245	16	q	q	PROPN
ma-260	245	17	dz	dz	X
ma-260	245	18	]	]	PUNCT
ma-260	245	19	1	1	NUM
ma-260	245	20	p	p	NOUN
ma-260	245	21	.	.	PUNCT
ma-260	246	1	therefore	therefore	ADV
ma-260	246	2	,	,	PUNCT
ma-260	246	3	using	use	VERB
ma-260	246	4	the	the	DET
ma-260	246	5	john	john	PROPN
ma-260	246	6	-	-	PUNCT
ma-260	246	7	nirenberg	nirenberg	PROPN
ma-260	246	8	theorem	theorem	NOUN
ma-260	246	9	on	on	ADP
ma-260	246	10	bmo	bmo	NOUN
ma-260	246	11	-	-	PUNCT
ma-260	246	12	functions	function	NOUN
ma-260	246	13	(	(	PUNCT
ma-260	246	14	see	see	VERB
ma-260	246	15	[	[	X
ma-260	246	16	12	12	NUM
ma-260	246	17	,	,	PUNCT
ma-260	246	18	corollary	corollary	ADJ
ma-260	246	19	7.1.8	7.1.8	PROPN
ma-260	246	20	]	]	PUNCT
ma-260	246	21	)	)	PUNCT
ma-260	246	22	,	,	PUNCT
ma-260	246	23	weobtain	weobtain	NOUN
ma-260	246	24	‖[b	‖[b	PROPN
ma-260	246	25	,	,	PUNCT
ma-260	246	26	t	t	X
ma-260	246	27	]	]	X
ma-260	246	28	f	f	X
ma-260	246	29	χb(y	χb(y	PROPN
ma-260	246	30	,	,	PUNCT
ma-260	246	31	r)‖q	r)‖q	VERB
ma-260	246	32	<	<	X
ma-260	246	33	∼	∼	NOUN
ma-260	246	34	‖f	‖f	ADJ
ma-260	246	35	χb(y,2r)‖q	χb(y,2r)‖q	PUNCT
ma-260	247	1	+	+	NUM
ma-260	247	2	‖b‖bmo(rd	‖b‖bmo(rd	NOUN
ma-260	247	3	)	)	PUNCT
ma-260	248	1	∞∑	∞∑	NUM
ma-260	248	2	i=1	i=1	X
ma-260	248	3	(	(	PUNCT
ma-260	248	4	2i)−	2i)−	NUM
ma-260	248	5	d	d	NOUN
ma-260	248	6	q	q	NOUN
ma-260	248	7	‖f	‖f	ADJ
ma-260	248	8	χb(y,2i+1r)‖q	χb(y,2i+1r)‖q	PROPN
ma-260	248	9	.	.	PUNCT
ma-260	249	1	using	use	VERB
ma-260	249	2	the	the	DET
ma-260	249	3	same	same	ADJ
ma-260	249	4	argument	argument	NOUN
ma-260	249	5	as	as	ADP
ma-260	249	6	in	in	ADP
ma-260	249	7	the	the	DET
ma-260	249	8	proof	proof	NOUN
ma-260	249	9	of	of	ADP
ma-260	249	10	theorem	theorem	ADJ
ma-260	249	11	1.2	1.2	NUM
ma-260	249	12	,	,	PUNCT
ma-260	249	13	we	we	PRON
ma-260	249	14	end	end	VERB
ma-260	249	15	the	the	DET
ma-260	249	16	proof	proof	NOUN
ma-260	249	17	.	.	PUNCT
ma-260	250	1	�	�	PROPN
ma-260	250	2	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	250	3	eur	eur	PROPN
ma-260	250	4	.	.	PUNCT
ma-260	251	1	j.	j.	PROPN
ma-260	251	2	math	math	PROPN
ma-260	251	3	.	.	PUNCT
ma-260	252	1	anal	anal	PROPN
ma-260	252	2	.	.	PUNCT
ma-260	253	1	10.28924	10.28924	NUM
ma-260	253	2	/	/	SYM
ma-260	253	3	ada	ada	PROPN
ma-260	253	4	/	/	SYM
ma-260	253	5	ma.4.22	ma.4.22	PROPN
ma-260	253	6	10references	10references	PUNCT
ma-260	254	1	[	[	X
ma-260	254	2	1	1	NUM
ma-260	254	3	]	]	PUNCT
ma-260	254	4	m.	m.	NOUN
ma-260	254	5	agcayazi	agcayazi	PROPN
ma-260	254	6	,	,	PUNCT
ma-260	254	7	a.	a.	NOUN
ma-260	254	8	gogatishvili	gogatishvili	NOUN
ma-260	254	9	,	,	PUNCT
ma-260	254	10	k.	k.	PROPN
ma-260	254	11	koca	koca	PROPN
ma-260	254	12	,	,	PUNCT
ma-260	254	13	r.	r.	PROPN
ma-260	254	14	ch	ch	PROPN
ma-260	254	15	.	.	PUNCT
ma-260	254	16	mustafayev	mustafayev	PROPN
ma-260	254	17	,	,	PUNCT
ma-260	254	18	a	a	DET
ma-260	254	19	note	note	NOUN
ma-260	254	20	on	on	ADP
ma-260	254	21	maximal	maximal	ADJ
ma-260	254	22	commutators	commutator	NOUN
ma-260	254	23	and	and	CCONJ
ma-260	254	24	commutators	commutator	VERB
ma-260	254	25	ofmaximal	ofmaximal	ADJ
ma-260	254	26	functions	function	NOUN
ma-260	254	27	,	,	PUNCT
ma-260	254	28	j.	j.	PROPN
ma-260	254	29	math	math	PROPN
ma-260	254	30	.	.	PUNCT
ma-260	255	1	soc	soc	PROPN
ma-260	255	2	.	.	PUNCT
ma-260	256	1	japan	japan	PROPN
ma-260	256	2	,	,	PUNCT
ma-260	256	3	67	67	NUM
ma-260	256	4	(	(	PUNCT
ma-260	256	5	2015	2015	NUM
ma-260	256	6	)	)	PUNCT
ma-260	256	7	,	,	PUNCT
ma-260	256	8	581	581	NUM
ma-260	256	9	-	-	SYM
ma-260	256	10	593.[2	593.[2	NUM
ma-260	256	11	]	]	PUNCT
ma-260	256	12	j.	j.	PROPN
ma-260	256	13	bastero	bastero	PROPN
ma-260	256	14	,	,	PUNCT
ma-260	256	15	m.	m.	NOUN
ma-260	256	16	milman	milman	NOUN
ma-260	256	17	,	,	PUNCT
ma-260	256	18	f.	f.	PROPN
ma-260	256	19	j.	j.	PROPN
ma-260	256	20	ruiz	ruiz	PROPN
ma-260	256	21	,	,	PUNCT
ma-260	256	22	commutators	commutator	NOUN
ma-260	256	23	for	for	ADP
ma-260	256	24	the	the	DET
ma-260	256	25	maximal	maximal	ADJ
ma-260	256	26	and	and	CCONJ
ma-260	256	27	sharp	sharp	ADJ
ma-260	256	28	functions	function	NOUN
ma-260	256	29	,	,	PUNCT
ma-260	256	30	proc	proc	NOUN
ma-260	256	31	.	.	PUNCT
ma-260	257	1	amer	amer	PROPN
ma-260	257	2	.	.	PUNCT
ma-260	257	3	math	math	PROPN
ma-260	257	4	.	.	PUNCT
ma-260	258	1	soc	soc	PROPN
ma-260	258	2	.	.	PUNCT
ma-260	258	3	,	,	PUNCT
ma-260	258	4	128(2000	128(2000	NUM
ma-260	258	5	)	)	PUNCT
ma-260	258	6	,	,	PUNCT
ma-260	258	7	3329	3329	NUM
ma-260	258	8	-	-	SYM
ma-260	258	9	3334.[3	3334.[3	NUM
ma-260	258	10	]	]	PUNCT
ma-260	258	11	s.	s.	PROPN
ma-260	258	12	chanillo	chanillo	PROPN
ma-260	258	13	,	,	PUNCT
ma-260	258	14	a	a	DET
ma-260	258	15	note	note	NOUN
ma-260	258	16	on	on	ADP
ma-260	258	17	commutators	commutator	NOUN
ma-260	258	18	,	,	PUNCT
ma-260	258	19	indiana	indiana	PROPN
ma-260	258	20	univ	univ	PROPN
ma-260	258	21	.	.	PUNCT
ma-260	259	1	math	math	PROPN
ma-260	259	2	.	.	PUNCT
ma-260	260	1	j.	j.	PROPN
ma-260	260	2	,	,	PUNCT
ma-260	260	3	31	31	NUM
ma-260	260	4	(	(	PUNCT
ma-260	260	5	1982	1982	NUM
ma-260	260	6	)	)	PUNCT
ma-260	260	7	,	,	PUNCT
ma-260	260	8	7	7	NUM
ma-260	260	9	-	-	SYM
ma-260	260	10	16.[4	16.[4	NUM
ma-260	260	11	]	]	X
ma-260	260	12	f.	f.	PROPN
ma-260	260	13	chiarenza	chiarenza	PROPN
ma-260	260	14	,	,	PUNCT
ma-260	260	15	m.	m.	NOUN
ma-260	260	16	frasca	frasca	PROPN
ma-260	260	17	,	,	PUNCT
ma-260	260	18	morrey	morrey	PROPN
ma-260	260	19	spaces	space	NOUN
ma-260	260	20	and	and	CCONJ
ma-260	260	21	hardy	hardy	ADJ
ma-260	260	22	-	-	PUNCT
ma-260	260	23	littlewood	littlewood	NOUN
ma-260	260	24	maximal	maximal	ADJ
ma-260	260	25	function	function	NOUN
ma-260	260	26	,	,	PUNCT
ma-260	260	27	rend	rend	VERB
ma-260	260	28	.	.	PUNCT
ma-260	260	29	math	math	NOUN
ma-260	260	30	.	.	PUNCT
ma-260	261	1	7	7	NUM
ma-260	261	2	(	(	PUNCT
ma-260	261	3	1987	1987	NUM
ma-260	261	4	)	)	PUNCT
ma-260	261	5	,	,	PUNCT
ma-260	261	6	273	273	NUM
ma-260	261	7	-	-	SYM
ma-260	261	8	279.[5	279.[5	NUM
ma-260	261	9	]	]	X
ma-260	261	10	d.	d.	PROPN
ma-260	261	11	fan	fan	PROPN
ma-260	261	12	,	,	PUNCT
ma-260	261	13	s.	s.	PROPN
ma-260	261	14	lu	lu	PROPN
ma-260	261	15	and	and	CCONJ
ma-260	261	16	d.	d.	PROPN
ma-260	261	17	yang	yang	PROPN
ma-260	261	18	,	,	PUNCT
ma-260	261	19	regularity	regularity	NOUN
ma-260	261	20	in	in	ADP
ma-260	261	21	morrey	morrey	PROPN
ma-260	261	22	spaces	space	NOUN
ma-260	261	23	of	of	ADP
ma-260	261	24	strong	strong	ADJ
ma-260	261	25	solutions	solution	NOUN
ma-260	261	26	to	to	ADP
ma-260	261	27	nondivergence	nondivergence	NOUN
ma-260	261	28	elliptic	elliptic	ADJ
ma-260	261	29	equations	equation	NOUN
ma-260	261	30	withvmo	withvmo	NOUN
ma-260	261	31	coefficients	coefficient	VERB
ma-260	261	32	,	,	PUNCT
ma-260	261	33	georgian	georgian	ADJ
ma-260	261	34	math	math	NOUN
ma-260	261	35	.	.	PUNCT
ma-260	262	1	j.	j.	PROPN
ma-260	262	2	5	5	NUM
ma-260	262	3	(	(	PUNCT
ma-260	262	4	1998	1998	NUM
ma-260	262	5	)	)	PUNCT
ma-260	262	6	,	,	PUNCT
ma-260	262	7	425	425	NUM
ma-260	262	8	-	-	SYM
ma-260	262	9	440.[6	440.[6	NUM
ma-260	262	10	]	]	X
ma-260	262	11	j.	j.	PROPN
ma-260	262	12	feuto	feuto	PROPN
ma-260	262	13	,	,	PUNCT
ma-260	262	14	norm	norm	NOUN
ma-260	262	15	inequalities	inequality	NOUN
ma-260	262	16	in	in	ADP
ma-260	262	17	some	some	DET
ma-260	262	18	subspaces	subspace	NOUN
ma-260	262	19	of	of	ADP
ma-260	262	20	morrey	morrey	PROPN
ma-260	262	21	space	space	NOUN
ma-260	262	22	,	,	PUNCT
ma-260	262	23	ann	ann	PROPN
ma-260	262	24	.	.	PROPN
ma-260	262	25	math	math	PROPN
ma-260	262	26	.	.	PUNCT
ma-260	263	1	blaise	blaise	PROPN
ma-260	263	2	pascal	pascal	PROPN
ma-260	263	3	21	21	NUM
ma-260	263	4	(	(	PUNCT
ma-260	263	5	2014	2014	NUM
ma-260	263	6	)	)	PUNCT
ma-260	263	7	,	,	PUNCT
ma-260	263	8	21	21	NUM
ma-260	263	9	-	-	SYM
ma-260	263	10	37.[7	37.[7	NUM
ma-260	263	11	]	]	PUNCT
ma-260	263	12	i.	i.	PROPN
ma-260	263	13	fofana	fofana	PROPN
ma-260	263	14	,	,	PUNCT
ma-260	263	15	etude	etude	NOUN
ma-260	263	16	d’une	d’une	NOUN
ma-260	263	17	classe	classe	NOUN
ma-260	263	18	d’espaces	d’espace	NOUN
ma-260	263	19	de	de	X
ma-260	263	20	fonctions	fonction	NOUN
ma-260	263	21	contenant	contenant	X
ma-260	263	22	les	les	X
ma-260	263	23	espaces	espaces	X
ma-260	263	24	de	de	X
ma-260	263	25	lorentz	lorentz	PROPN
ma-260	263	26	,	,	PUNCT
ma-260	263	27	afr	afr	PROPN
ma-260	263	28	.	.	PUNCT
ma-260	264	1	mat	mat	NOUN
ma-260	264	2	.	.	NOUN
ma-260	264	3	2	2	NUM
ma-260	264	4	(	(	PUNCT
ma-260	264	5	1988	1988	NUM
ma-260	264	6	)	)	PUNCT
ma-260	264	7	,	,	PUNCT
ma-260	264	8	29	29	NUM
ma-260	264	9	-	-	SYM
ma-260	264	10	50.[8	50.[8	NUM
ma-260	264	11	]	]	PUNCT
ma-260	264	12	i.	i.	PROPN
ma-260	264	13	fofana	fofana	PROPN
ma-260	264	14	,	,	PUNCT
ma-260	264	15	continuité	continuité	X
ma-260	264	16	de	de	X
ma-260	264	17	l’intégrale	l’intégrale	PROPN
ma-260	264	18	fractionnaire	fractionnaire	NOUN
ma-260	264	19	et	et	NOUN
ma-260	264	20	espace	espace	NOUN
ma-260	264	21	(	(	PUNCT
ma-260	264	22	lq	lq	PROPN
ma-260	264	23	,	,	PUNCT
ma-260	264	24	lp)α	lp)α	PROPN
ma-260	264	25	,	,	PUNCT
ma-260	264	26	c.	c.	PROPN
ma-260	264	27	r.	r.	PROPN
ma-260	264	28	acad	acad	PROPN
ma-260	264	29	.	.	PUNCT
ma-260	265	1	sci	sci	PROPN
ma-260	265	2	.	.	PUNCT
ma-260	265	3	paris	paris	PROPN
ma-260	265	4	308	308	NUM
ma-260	265	5	(	(	PUNCT
ma-260	265	6	1989	1989	NUM
ma-260	265	7	)	)	PUNCT
ma-260	265	8	,	,	PUNCT
ma-260	265	9	525	525	NUM
ma-260	265	10	-	-	SYM
ma-260	265	11	527.[9	527.[9	NUM
ma-260	265	12	]	]	PUNCT
ma-260	265	13	i.	i.	NOUN
ma-260	265	14	fofana	fofana	PROPN
ma-260	265	15	,	,	PUNCT
ma-260	265	16	espace	espace	X
ma-260	265	17	(	(	PUNCT
ma-260	265	18	lq	lq	PROPN
ma-260	265	19	,	,	PUNCT
ma-260	265	20	lp)α	lp)α	PROPN
ma-260	265	21	et	et	NOUN
ma-260	265	22	continuité	continuité	X
ma-260	265	23	de	de	X
ma-260	265	24	l’opérateur	l’opérateur	PROPN
ma-260	265	25	maximal	maximal	ADJ
ma-260	265	26	fractionnaire	fractionnaire	NOUN
ma-260	265	27	de	de	X
ma-260	265	28	hardy	hardy	ADJ
ma-260	265	29	-	-	PUNCT
ma-260	265	30	littlewood	littlewood	NOUN
ma-260	265	31	,	,	PUNCT
ma-260	265	32	afr	afr	PROPN
ma-260	265	33	.	.	PUNCT
ma-260	266	1	mat	mat	PROPN
ma-260	266	2	.	.	NOUN
ma-260	266	3	3(2001	3(2001	NUM
ma-260	266	4	)	)	PUNCT
ma-260	266	5	,	,	PUNCT
ma-260	266	6	23	23	NUM
ma-260	266	7	-	-	SYM
ma-260	266	8	37.[10	37.[10	NUM
ma-260	266	9	]	]	PUNCT
ma-260	266	10	j.	j.	PROPN
ma-260	266	11	garciá	garciá	PROPN
ma-260	266	12	-	-	PUNCT
ma-260	266	13	cuerva	cuerva	PROPN
ma-260	266	14	,	,	PUNCT
ma-260	266	15	e.	e.	PROPN
ma-260	266	16	harboure	harboure	PROPN
ma-260	266	17	,	,	PUNCT
ma-260	266	18	c.	c.	PROPN
ma-260	266	19	segovia	segovia	PROPN
ma-260	266	20	,	,	PUNCT
ma-260	266	21	j.	j.	PROPN
ma-260	266	22	l.	l.	PROPN
ma-260	266	23	torrea	torrea	PROPN
ma-260	266	24	,	,	PUNCT
ma-260	266	25	weighted	weight	VERB
ma-260	266	26	norm	norm	NOUN
ma-260	266	27	inequalities	inequality	NOUN
ma-260	266	28	for	for	ADP
ma-260	266	29	commutators	commutator	NOUN
ma-260	266	30	of	of	ADP
ma-260	266	31	stronglysingular	stronglysingular	ADJ
ma-260	266	32	integrals	integral	NOUN
ma-260	266	33	,	,	PUNCT
ma-260	266	34	indiana	indiana	PROPN
ma-260	266	35	univ	univ	PROPN
ma-260	266	36	.	.	PUNCT
ma-260	267	1	math	math	PROPN
ma-260	267	2	.	.	PUNCT
ma-260	268	1	j.	j.	PROPN
ma-260	268	2	,	,	PUNCT
ma-260	268	3	40	40	NUM
ma-260	268	4	(	(	PUNCT
ma-260	268	5	1991	1991	NUM
ma-260	268	6	)	)	PUNCT
ma-260	268	7	,	,	PUNCT
ma-260	268	8	1397	1397	NUM
ma-260	268	9	-	-	SYM
ma-260	268	10	1420.[11	1420.[11	NUM
ma-260	268	11	]	]	PUNCT
ma-260	268	12	a.	a.	NOUN
ma-260	268	13	gogatishvili	gogatishvili	NOUN
ma-260	268	14	,	,	PUNCT
ma-260	268	15	r.ch	r.ch	PROPN
ma-260	268	16	.	.	PROPN
ma-260	268	17	mustafayev	mustafayev	PROPN
ma-260	268	18	,	,	PUNCT
ma-260	268	19	m.	m.	NOUN
ma-260	268	20	agcayazi	agcayazi	PROPN
ma-260	268	21	,	,	PUNCT
ma-260	268	22	weak	weak	ADJ
ma-260	268	23	-	-	PUNCT
ma-260	268	24	type	type	NOUN
ma-260	268	25	estimates	estimate	NOUN
ma-260	268	26	in	in	ADP
ma-260	268	27	morrey	morrey	PROPN
ma-260	268	28	spaces	space	NOUN
ma-260	268	29	for	for	ADP
ma-260	268	30	maximal	maximal	ADJ
ma-260	268	31	commuatatorand	commuatatorand	NOUN
ma-260	268	32	commutator	commutator	NOUN
ma-260	268	33	of	of	ADP
ma-260	268	34	maximal	maximal	ADJ
ma-260	268	35	function	function	NOUN
ma-260	268	36	,	,	PUNCT
ma-260	268	37	tokyo	tokyo	PROPN
ma-260	268	38	j.	j.	PROPN
ma-260	268	39	math	math	PROPN
ma-260	268	40	.	.	PUNCT
ma-260	269	1	41	41	NUM
ma-260	269	2	(	(	PUNCT
ma-260	269	3	2018	2018	NUM
ma-260	269	4	)	)	PUNCT
ma-260	269	5	,	,	PUNCT
ma-260	269	6	193	193	NUM
ma-260	269	7	-	-	SYM
ma-260	269	8	218.[12	218.[12	NUM
ma-260	269	9	]	]	X
ma-260	269	10	l.	l.	PROPN
ma-260	269	11	grafakos	grafakos	PROPN
ma-260	269	12	,	,	PUNCT
ma-260	269	13	modern	modern	ADJ
ma-260	269	14	fourier	fourier	NOUN
ma-260	269	15	analysis	analysis	NOUN
ma-260	269	16	,	,	PUNCT
ma-260	269	17	2nd	2nd	ADJ
ma-260	269	18	ed	ed	NOUN
ma-260	269	19	.	.	PROPN
ma-260	269	20	,	,	PUNCT
ma-260	269	21	graduate	graduate	NOUN
ma-260	269	22	texts	text	NOUN
ma-260	269	23	in	in	ADP
ma-260	269	24	mathematics	mathematic	NOUN
ma-260	269	25	vol	vol	NOUN
ma-260	269	26	.	.	PROPN
ma-260	270	1	250	250	NUM
ma-260	270	2	,	,	PUNCT
ma-260	270	3	springer	springer	NOUN
ma-260	270	4	,	,	PUNCT
ma-260	270	5	new	new	PROPN
ma-260	270	6	york	york	PROPN
ma-260	270	7	,	,	PUNCT
ma-260	270	8	2009.[13	2009.[13	PROPN
ma-260	270	9	]	]	X
ma-260	270	10	v.s.	v.s.	X
ma-260	270	11	guliyev	guliyev	NOUN
ma-260	270	12	,	,	PUNCT
ma-260	270	13	maximal	maximal	ADJ
ma-260	270	14	commutator	commutator	NOUN
ma-260	270	15	and	and	CCONJ
ma-260	270	16	commutator	commutator	NOUN
ma-260	270	17	of	of	ADP
ma-260	270	18	maximal	maximal	ADJ
ma-260	270	19	function	function	NOUN
ma-260	270	20	on	on	ADP
ma-260	270	21	total	total	ADJ
ma-260	270	22	morrey	morrey	PROPN
ma-260	270	23	spaces	space	NOUN
ma-260	270	24	,	,	PUNCT
ma-260	270	25	j.	j.	PROPN
ma-260	270	26	math	math	PROPN
ma-260	270	27	.	.	PUNCT
ma-260	271	1	inequal.16	inequal.16	PROPN
ma-260	271	2	(	(	PUNCT
ma-260	271	3	2022	2022	NUM
ma-260	271	4	)	)	PUNCT
ma-260	271	5	,	,	PUNCT
ma-260	271	6	1509	1509	NUM
ma-260	271	7	-	-	SYM
ma-260	271	8	1524[14	1524[14	NUM
ma-260	271	9	]	]	PUNCT
ma-260	271	10	v.	v.	PROPN
ma-260	271	11	s.	s.	PROPN
ma-260	271	12	guliyev	guliyev	PROPN
ma-260	271	13	,	,	PUNCT
ma-260	271	14	j.	j.	PROPN
ma-260	271	15	j.	j.	PROPN
ma-260	271	16	hasanov	hasanov	PROPN
ma-260	271	17	,	,	PUNCT
ma-260	271	18	y.	y.	PROPN
ma-260	271	19	zeren	zeren	PROPN
ma-260	271	20	,	,	PUNCT
ma-260	271	21	necessary	necessary	ADJ
ma-260	271	22	and	and	CCONJ
ma-260	271	23	sufficient	sufficient	ADJ
ma-260	271	24	conditions	condition	NOUN
ma-260	271	25	for	for	ADP
ma-260	271	26	the	the	DET
ma-260	271	27	boundedness	boundedness	NOUN
ma-260	271	28	of	of	ADP
ma-260	271	29	the	the	DET
ma-260	271	30	riesz	riesz	PROPN
ma-260	271	31	potentialin	potentialin	PROPN
ma-260	271	32	modified	modify	VERB
ma-260	271	33	morrey	morrey	PROPN
ma-260	271	34	spaces	space	NOUN
ma-260	271	35	,	,	PUNCT
ma-260	271	36	j.	j.	PROPN
ma-260	271	37	math	math	PROPN
ma-260	271	38	.	.	PUNCT
ma-260	272	1	inequal	inequal	ADJ
ma-260	272	2	.	.	PUNCT
ma-260	273	1	5	5	NUM
ma-260	273	2	(	(	PUNCT
ma-260	273	3	2011	2011	NUM
ma-260	273	4	)	)	PUNCT
ma-260	273	5	,	,	PUNCT
ma-260	273	6	491	491	NUM
ma-260	273	7	-	-	SYM
ma-260	273	8	506.[15	506.[15	NUM
ma-260	273	9	]	]	PUNCT
ma-260	273	10	g.	g.	PROPN
ma-260	273	11	hu	hu	PROPN
ma-260	273	12	,	,	PUNCT
ma-260	273	13	d.	d.	PROPN
ma-260	273	14	yang	yang	PROPN
ma-260	273	15	,	,	PUNCT
ma-260	273	16	maximal	maximal	ADJ
ma-260	273	17	commutators	commutator	NOUN
ma-260	273	18	of	of	ADP
ma-260	273	19	bmo	bmo	NOUN
ma-260	273	20	functions	function	NOUN
ma-260	273	21	and	and	CCONJ
ma-260	273	22	singular	singular	ADJ
ma-260	273	23	integral	integral	ADJ
ma-260	273	24	operators	operator	NOUN
ma-260	273	25	with	with	ADP
ma-260	273	26	non	non	ADJ
ma-260	273	27	-	-	ADJ
ma-260	273	28	smooth	smooth	ADJ
ma-260	273	29	kernelson	kernelson	NOUN
ma-260	273	30	spaces	space	NOUN
ma-260	273	31	of	of	ADP
ma-260	273	32	homogeneous	homogeneous	ADJ
ma-260	273	33	type	type	NOUN
ma-260	273	34	,	,	PUNCT
ma-260	273	35	j.	j.	PROPN
ma-260	273	36	math	math	PROPN
ma-260	273	37	.	.	PUNCT
ma-260	274	1	anal	anal	PROPN
ma-260	274	2	.	.	PUNCT
ma-260	275	1	appl	appl	PROPN
ma-260	275	2	.	.	PUNCT
ma-260	276	1	354	354	NUM
ma-260	276	2	(	(	PUNCT
ma-260	276	3	2009	2009	NUM
ma-260	276	4	)	)	PUNCT
ma-260	276	5	,	,	PUNCT
ma-260	276	6	249	249	NUM
ma-260	276	7	-	-	SYM
ma-260	276	8	262.[16	262.[16	NUM
ma-260	276	9	]	]	PUNCT
ma-260	276	10	s.	s.	PROPN
ma-260	276	11	janson	janson	PROPN
ma-260	276	12	,	,	PUNCT
ma-260	276	13	mean	mean	VERB
ma-260	276	14	oscillation	oscillation	NOUN
ma-260	276	15	and	and	CCONJ
ma-260	276	16	commutators	commutator	NOUN
ma-260	276	17	of	of	ADP
ma-260	276	18	singular	singular	ADJ
ma-260	276	19	integral	integral	ADJ
ma-260	276	20	operators	operator	NOUN
ma-260	276	21	,	,	PUNCT
ma-260	276	22	ark	ark	PROPN
ma-260	276	23	.	.	PROPN
ma-260	276	24	mat	mat	PROPN
ma-260	276	25	.	.	PROPN
ma-260	276	26	,	,	PUNCT
ma-260	276	27	16	16	NUM
ma-260	276	28	(	(	PUNCT
ma-260	276	29	1978	1978	NUM
ma-260	276	30	)	)	PUNCT
ma-260	276	31	,	,	PUNCT
ma-260	276	32	263	263	NUM
ma-260	276	33	-	-	SYM
ma-260	276	34	270.[17	270.[17	NUM
ma-260	276	35	]	]	PUNCT
ma-260	276	36	p.	p.	NOUN
ma-260	276	37	nagacy	nagacy	PROPN
ma-260	276	38	,	,	PUNCT
ma-260	276	39	b.	b.	PROPN
ma-260	276	40	a.	a.	PROPN
ma-260	276	41	kpata	kpata	PROPN
ma-260	276	42	,	,	PUNCT
ma-260	276	43	norm	norm	NOUN
ma-260	276	44	inequalities	inequality	NOUN
ma-260	276	45	for	for	ADP
ma-260	276	46	fractional	fractional	ADJ
ma-260	276	47	integral	integral	ADJ
ma-260	276	48	and	and	CCONJ
ma-260	276	49	fractional	fractional	ADJ
ma-260	276	50	maximal	maximal	ADJ
ma-260	276	51	operators	operator	NOUN
ma-260	276	52	in	in	ADP
ma-260	276	53	the	the	DET
ma-260	276	54	total	total	ADJ
ma-260	276	55	fofanaspaces	fofanaspace	NOUN
ma-260	276	56	,	,	PUNCT
ma-260	276	57	preprint.[18	preprint.[18	PROPN
ma-260	276	58	]	]	PUNCT
ma-260	276	59	y.	y.	PROPN
ma-260	276	60	sawano	sawano	PROPN
ma-260	276	61	,	,	PUNCT
ma-260	276	62	g.	g.	PROPN
ma-260	276	63	di	di	PROPN
ma-260	276	64	fazio	fazio	PROPN
ma-260	276	65	,	,	PUNCT
ma-260	276	66	d.	d.	PROPN
ma-260	276	67	i.	i.	PROPN
ma-260	276	68	hakim	hakim	PROPN
ma-260	276	69	,	,	PUNCT
ma-260	276	70	morrey	morrey	PROPN
ma-260	276	71	spaces	space	NOUN
ma-260	276	72	-	-	PUNCT
ma-260	276	73	introduction	introduction	NOUN
ma-260	276	74	and	and	CCONJ
ma-260	276	75	applications	application	NOUN
ma-260	276	76	to	to	ADP
ma-260	276	77	integral	integral	ADJ
ma-260	276	78	operators	operator	NOUN
ma-260	276	79	and	and	CCONJ
ma-260	276	80	pde’s	pde’s	NOUN
ma-260	276	81	,	,	PUNCT
ma-260	276	82	vol	vol	NOUN
ma-260	276	83	.	.	PUNCT
ma-260	277	1	i	i	PRON
ma-260	277	2	,	,	PUNCT
ma-260	277	3	monographs	monograph	NOUN
ma-260	277	4	and	and	CCONJ
ma-260	277	5	research	research	NOUN
ma-260	277	6	notes	note	NOUN
ma-260	277	7	in	in	ADP
ma-260	277	8	mathematics	mathematic	NOUN
ma-260	277	9	,	,	PUNCT
ma-260	277	10	crc	crc	NOUN
ma-260	277	11	press	press	PROPN
ma-260	277	12	,	,	PUNCT
ma-260	277	13	boca	boca	PROPN
ma-260	277	14	raton	raton	PROPN
ma-260	277	15	,	,	PUNCT
ma-260	277	16	fl	fl	PROPN
ma-260	277	17	,	,	PUNCT
ma-260	277	18	409	409	NUM
ma-260	277	19	pp	pp	NOUN
ma-260	277	20	.	.	PUNCT
ma-260	278	1	(	(	PUNCT
ma-260	278	2	2020).[19	2020).[19	NUM
ma-260	278	3	]	]	X
ma-260	278	4	f.	f.	PROPN
ma-260	278	5	soria	soria	PROPN
ma-260	278	6	,	,	PUNCT
ma-260	278	7	g.	g.	PROPN
ma-260	278	8	weiss	weiss	PROPN
ma-260	278	9	and	and	CCONJ
ma-260	278	10	d.	d.	PROPN
ma-260	278	11	i.	i.	PROPN
ma-260	278	12	hakim	hakim	PROPN
ma-260	278	13	,	,	PUNCT
ma-260	278	14	a	a	DET
ma-260	278	15	remark	remark	NOUN
ma-260	278	16	on	on	ADP
ma-260	278	17	singular	singular	ADJ
ma-260	278	18	integrals	integral	NOUN
ma-260	278	19	and	and	CCONJ
ma-260	278	20	power	power	NOUN
ma-260	278	21	weights	weight	NOUN
ma-260	278	22	,	,	PUNCT
ma-260	278	23	indiana	indiana	PROPN
ma-260	278	24	univ	univ	PROPN
ma-260	278	25	.	.	PUNCT
ma-260	278	26	math	math	PROPN
ma-260	278	27	.	.	PUNCT
ma-260	279	1	j.	j.	PROPN
ma-260	279	2	43(1994	43(1994	PROPN
ma-260	279	3	)	)	PUNCT
ma-260	279	4	,	,	PUNCT
ma-260	279	5	187	187	NUM
ma-260	279	6	-	-	SYM
ma-260	279	7	204.[20	204.[20	NUM
ma-260	279	8	]	]	X
ma-260	279	9	e.m	e.m	PROPN
ma-260	279	10	.	.	PROPN
ma-260	279	11	stein	stein	PROPN
ma-260	279	12	,	,	PUNCT
ma-260	279	13	harmonic	harmonic	VERB
ma-260	279	14	analysis	analysis	NOUN
ma-260	279	15	:	:	PUNCT
ma-260	279	16	real	real	ADJ
ma-260	279	17	variable	variable	ADJ
ma-260	279	18	methods	method	NOUN
ma-260	279	19	,	,	PUNCT
ma-260	279	20	orthogonality	orthogonality	NOUN
ma-260	279	21	,	,	PUNCT
ma-260	279	22	and	and	CCONJ
ma-260	279	23	oscillatory	oscillatory	ADJ
ma-260	279	24	integrals	integral	NOUN
ma-260	279	25	princeton	princeton	PROPN
ma-260	279	26	mathe	mathe	PROPN
ma-260	279	27	-	-	PUNCT
ma-260	279	28	matical	matical	ADJ
ma-260	279	29	series	series	NOUN
ma-260	279	30	,	,	PUNCT
ma-260	279	31	vol	vol	NOUN
ma-260	279	32	.	.	PROPN
ma-260	279	33	43	43	NUM
ma-260	279	34	,	,	PUNCT
ma-260	279	35	princeton	princeton	PROPN
ma-260	279	36	university	university	PROPN
ma-260	279	37	press	press	PROPN
ma-260	279	38	,	,	PUNCT
ma-260	279	39	princeton	princeton	PROPN
ma-260	279	40	,	,	PUNCT
ma-260	279	41	new	new	PROPN
ma-260	279	42	jersey	jersey	PROPN
ma-260	279	43	(	(	PUNCT
ma-260	279	44	1993	1993	NUM
ma-260	279	45	)	)	PUNCT
ma-260	279	46	.	.	PUNCT
ma-260	280	1	https://doi.org/10.28924/ada/ma.4.22	https://doi.org/10.28924/ada/ma.4.22	PROPN
ma-260	280	2	1	1	NUM
ma-260	280	3	.	.	PUNCT
ma-260	280	4	introduction	introduction	NOUN
ma-260	280	5	and	and	CCONJ
ma-260	280	6	main	main	ADJ
ma-260	280	7	results	result	NOUN
ma-260	280	8	2	2	NUM
ma-260	280	9	.	.	PUNCT
ma-260	281	1	some	some	DET
ma-260	281	2	properties	property	NOUN
ma-260	281	3	of	of	ADP
ma-260	281	4	total	total	ADJ
ma-260	281	5	fofana	fofana	NOUN
ma-260	281	6	spaces	space	VERB
ma-260	281	7	3	3	X
ma-260	281	8	.	.	PUNCT
ma-260	281	9	proof	proof	NOUN
ma-260	281	10	of	of	ADP
ma-260	281	11	theorem	theorem	ADJ
ma-260	281	12	1.1	1.1	NUM
ma-260	281	13	4	4	NUM
ma-260	281	14	.	.	PUNCT
ma-260	281	15	proof	proof	NOUN
ma-260	281	16	of	of	ADP
ma-260	281	17	theorem	theorem	ADJ
ma-260	281	18	1.2	1.2	NUM
ma-260	281	19	and	and	CCONJ
ma-260	281	20	theorem	theorem	VERB
ma-260	281	21	1.3	1.3	NUM
ma-260	281	22	references	reference	NOUN