id	sid	tid	token	lemma	pos
ma-415	1	1	2025	2025	NUM
ma-415	1	2	ada	ada	PROPN
ma-415	1	3	academica	academica	PROPN
ma-415	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-415	1	5	.	.	PUNCT
ma-415	2	1	j.	j.	PROPN
ma-415	2	2	math	math	PROPN
ma-415	2	3	.	.	PUNCT
ma-415	3	1	anal	anal	ADJ
ma-415	3	2	.	.	PUNCT
ma-415	4	1	5	5	NUM
ma-415	4	2	(	(	PUNCT
ma-415	4	3	2025	2025	NUM
ma-415	4	4	)	)	PUNCT
ma-415	4	5	22doi	22doi	NOUN
ma-415	4	6	:	:	PUNCT
ma-415	4	7	10.28924	10.28924	NUM
ma-415	4	8	/	/	SYM
ma-415	4	9	ada	ada	NOUN
ma-415	4	10	/	/	SYM
ma-415	4	11	ma.5.22	ma.5.22	NOUN
ma-415	4	12	estimates	estimate	NOUN
ma-415	4	13	of	of	ADP
ma-415	4	14	variable	variable	ADJ
ma-415	4	15	kernel	kernel	PROPN
ma-415	4	16	parameterized	parameterized	PROPN
ma-415	4	17	littlewood	littlewood	PROPN
ma-415	4	18	–	–	PUNCT
ma-415	4	19	paley	paley	ADJ
ma-415	4	20	operators	operator	NOUN
ma-415	4	21	on	on	ADP
ma-415	4	22	variable	variable	ADJ
ma-415	4	23	herz	herz	PROPN
ma-415	4	24	spaces	space	NOUN
ma-415	4	25	afif	afif	PROPN
ma-415	4	26	abdalmonem1,∗	abdalmonem1,∗	PROPN
ma-415	4	27	,	,	PUNCT
ma-415	4	28	omer	omer	PROPN
ma-415	4	29	khalil2	khalil2	PROPN
ma-415	4	30	,	,	PUNCT
ma-415	4	31	omer	omer	PROPN
ma-415	4	32	abdalrhman3	abdalrhman3	PROPN
ma-415	4	33	1faculty	1faculty	NUM
ma-415	4	34	of	of	ADP
ma-415	4	35	science	science	NOUN
ma-415	4	36	,	,	PUNCT
ma-415	4	37	department	department	NOUN
ma-415	4	38	of	of	ADP
ma-415	4	39	mathematics	mathematics	PROPN
ma-415	4	40	,	,	PUNCT
ma-415	4	41	university	university	NOUN
ma-415	4	42	of	of	ADP
ma-415	4	43	dalanj	dalanj	ADJ
ma-415	4	44	,	,	PUNCT
ma-415	4	45	dalanj	dalanj	ADJ
ma-415	4	46	,	,	PUNCT
ma-415	4	47	sudan	sudan	PROPN
ma-415	4	48	afeefy86@gmail.com	afeefy86@gmail.com	PROPN
ma-415	4	49	2	2	NUM
ma-415	4	50	college	college	NOUN
ma-415	4	51	of	of	ADP
ma-415	4	52	mathematics	mathematic	NOUN
ma-415	4	53	and	and	CCONJ
ma-415	4	54	statistics	statistic	NOUN
ma-415	4	55	,	,	PUNCT
ma-415	4	56	northwest	northwest	PROPN
ma-415	4	57	normal	normal	ADJ
ma-415	4	58	university	university	NOUN
ma-415	4	59	,	,	PUNCT
ma-415	4	60	china	china	PROPN
ma-415	4	61	us.omer2008@yahoo.com	us.omer2008@yahoo.com	X
ma-415	5	1	3college	3college	NUM
ma-415	5	2	of	of	ADP
ma-415	5	3	education	education	NOUN
ma-415	5	4	,	,	PUNCT
ma-415	5	5	shendi	shendi	ADJ
ma-415	5	6	university	university	NOUN
ma-415	5	7	,	,	PUNCT
ma-415	5	8	sudan	sudan	PROPN
ma-415	5	9	humoora@gmail.com	humoora@gmail.com	PROPN
ma-415	6	1	∗correspondence	∗correspondence	NOUN
ma-415	6	2	:	:	PUNCT
ma-415	7	1	afeefy86@gmail.com	afeefy86@gmail.com	X
ma-415	7	2	abstract	abstract	NOUN
ma-415	7	3	.	.	PUNCT
ma-415	8	1	in	in	ADP
ma-415	8	2	this	this	DET
ma-415	8	3	article	article	NOUN
ma-415	8	4	,	,	PUNCT
ma-415	8	5	we	we	PRON
ma-415	8	6	prove	prove	VERB
ma-415	8	7	some	some	DET
ma-415	8	8	boundedness	boundedness	NOUN
ma-415	8	9	results	result	NOUN
ma-415	8	10	for	for	ADP
ma-415	8	11	variable	variable	ADJ
ma-415	8	12	kernel	kernel	NOUN
ma-415	8	13	parameterizedlittlewood−paley	parameterizedlittlewood−paley	NOUN
ma-415	8	14	operators	operator	NOUN
ma-415	8	15	on	on	ADP
ma-415	8	16	the	the	DET
ma-415	8	17	homogeneous	homogeneous	ADJ
ma-415	8	18	herz	herz	PROPN
ma-415	8	19	spaces	space	VERB
ma-415	8	20	k̇α(·),q	k̇α(·),q	PROPN
ma-415	8	21	(	(	PUNCT
ma-415	8	22	·	·	PUNCT
ma-415	8	23	)	)	PUNCT
ma-415	9	1	p	p	X
ma-415	9	2	(	(	PUNCT
ma-415	9	3	·	·	PUNCT
ma-415	9	4	)	)	PUNCT
ma-415	9	5	(	(	PUNCT
ma-415	9	6	rn	rn	NOUN
ma-415	9	7	)	)	PUNCT
ma-415	9	8	.	.	PUNCT
ma-415	10	1	several	several	ADJ
ma-415	10	2	known	know	VERB
ma-415	10	3	resultsare	resultsare	NOUN
ma-415	10	4	extended	extend	VERB
ma-415	10	5	.	.	PUNCT
ma-415	11	1	1	1	X
ma-415	11	2	.	.	X
ma-415	11	3	introduction	introduction	NOUN
ma-415	11	4	suppose	suppose	VERB
ma-415	11	5	that	that	SCONJ
ma-415	11	6	ψ(x1	ψ(x1	NOUN
ma-415	11	7	,	,	PUNCT
ma-415	11	8	z1	z1	ADJ
ma-415	11	9	)	)	PUNCT
ma-415	11	10	∈	∈	PROPN
ma-415	11	11	l∞(rn)×	l∞(rn)×	PROPN
ma-415	11	12	lb(sn−1	lb(sn−1	PROPN
ma-415	11	13	)	)	PUNCT
ma-415	11	14	(	(	PUNCT
ma-415	11	15	where	where	SCONJ
ma-415	11	16	b	b	X
ma-415	11	17	≥	≥	NUM
ma-415	11	18	1	1	NUM
ma-415	11	19	)	)	PUNCT
ma-415	11	20	satisfies:(1	satisfies:(1	PROPN
ma-415	11	21	)	)	PUNCT
ma-415	11	22	ψ(x1	ψ(x1	NOUN
ma-415	11	23	,	,	PUNCT
ma-415	11	24	αz1	αz1	NOUN
ma-415	11	25	)	)	PUNCT
ma-415	11	26	=	=	SYM
ma-415	11	27	ψ(x1	ψ(x1	NOUN
ma-415	11	28	,	,	PUNCT
ma-415	11	29	z1	z1	NOUN
ma-415	11	30	)	)	PUNCT
ma-415	11	31	and	and	CCONJ
ma-415	11	32	∫	∫	PROPN
ma-415	11	33	sn−1	sn−1	PROPN
ma-415	11	34	ψ(x1	ψ(x1	PROPN
ma-415	11	35	,	,	PUNCT
ma-415	11	36	z	z	NOUN
ma-415	11	37	′	′	NOUN
ma-415	11	38	1)dσ(z	1)dσ(z	NUM
ma-415	11	39	′1	′1	NOUN
ma-415	11	40	)	)	PUNCT
ma-415	11	41	=	=	SYM
ma-415	11	42	0	0	NUM
ma-415	11	43	,	,	PUNCT
ma-415	11	44	for	for	ADP
ma-415	11	45	all	all	DET
ma-415	11	46	z1	z1	VERB
ma-415	11	47	,	,	PUNCT
ma-415	11	48	x1	x1	PROPN
ma-415	11	49	∈	∈	PROPN
ma-415	11	50	rn	rn	PROPN
ma-415	11	51	,	,	PUNCT
ma-415	11	52	α	α	PROPN
ma-415	11	53	>	>	X
ma-415	11	54	0	0	NUM
ma-415	11	55	;	;	PUNCT
ma-415	11	56	(	(	PUNCT
ma-415	11	57	2	2	X
ma-415	11	58	)	)	PUNCT
ma-415	11	59	‖ψ‖l∞(rn)×lb(sn−1	‖ψ‖l∞(rn)×lb(sn−1	PROPN
ma-415	11	60	)	)	PUNCT
ma-415	11	61	:	:	PUNCT
ma-415	11	62	=	=	SYM
ma-415	11	63	sup	sup	PROPN
ma-415	11	64	x1∈rn	x1∈rn	PROPN
ma-415	11	65	(	(	PUNCT
ma-415	11	66	∫	∫	PROPN
ma-415	11	67	sn−1	sn−1	PROPN
ma-415	11	68	|ψ(x1	|ψ(x1	PROPN
ma-415	11	69	,	,	PUNCT
ma-415	11	70	z	z	NOUN
ma-415	11	71	′	′	NUM
ma-415	11	72	1)|bdz	1)|bdz	NUM
ma-415	11	73	′1	′1	NOUN
ma-415	11	74	)	)	PUNCT
ma-415	11	75	1	1	NUM
ma-415	11	76	b	b	NOUN
ma-415	11	77	<	<	X
ma-415	11	78	∞	∞	PROPN
ma-415	11	79	,	,	PUNCT
ma-415	11	80	where	where	SCONJ
ma-415	11	81	sn−1	sn−1	PROPN
ma-415	11	82	(	(	PUNCT
ma-415	11	83	for	for	ADP
ma-415	11	84	n	n	PRON
ma-415	11	85	≥	≥	NOUN
ma-415	11	86	2	2	NUM
ma-415	11	87	)	)	PUNCT
ma-415	11	88	is	be	AUX
ma-415	11	89	the	the	DET
ma-415	11	90	unit	unit	NOUN
ma-415	11	91	sphere	sphere	ADV
ma-415	11	92	in	in	ADP
ma-415	11	93	rn	rn	PROPN
ma-415	11	94	equipped	equip	VERB
ma-415	11	95	with	with	ADP
ma-415	11	96	lebesgue	lebesgue	ADJ
ma-415	11	97	measure	measure	NOUN
ma-415	11	98	dz	dz	PROPN
ma-415	11	99	′1	′1	PROPN
ma-415	11	100	.	.	PROPN
ma-415	11	101	theparameterized	theparameterize	VERB
ma-415	11	102	littlewood−paley	littlewood−paley	PROPN
ma-415	11	103	operators	operator	NOUN
ma-415	11	104	,	,	PUNCT
ma-415	11	105	denoted	denote	VERB
ma-415	11	106	by	by	ADP
ma-415	11	107	µσψ	µσψ	NOUN
ma-415	11	108	,	,	PUNCT
ma-415	11	109	s	s	PART
ma-415	11	110	and	and	CCONJ
ma-415	11	111	µ∗,σψ	µ∗,σψ	PROPN
ma-415	11	112	,	,	PUNCT
ma-415	11	113	λ	λ	PROPN
ma-415	11	114	,	,	PUNCT
ma-415	11	115	are	be	AUX
ma-415	11	116	closely	closely	ADV
ma-415	11	117	associated	associate	VERB
ma-415	11	118	withthe	withthe	PROPN
ma-415	11	119	lusin	lusin	NOUN
ma-415	11	120	area	area	NOUN
ma-415	11	121	integral	integral	ADJ
ma-415	11	122	and	and	CCONJ
ma-415	11	123	littlewood−paley	littlewood−paley	ADJ
ma-415	11	124	g∗λ	g∗λ	PUNCT
ma-415	11	125	function	function	NOUN
ma-415	11	126	.	.	PUNCT
ma-415	12	1	these	these	DET
ma-415	12	2	operators	operator	NOUN
ma-415	12	3	are	be	AUX
ma-415	12	4	defined	define	VERB
ma-415	12	5	as	as	SCONJ
ma-415	12	6	follows	follow	VERB
ma-415	12	7	µσψ	µσψ	NOUN
ma-415	12	8	,	,	PUNCT
ma-415	12	9	s(f	s(f	PROPN
ma-415	12	10	)	)	PUNCT
ma-415	12	11	(	(	PUNCT
ma-415	12	12	x	x	X
ma-415	12	13	)	)	PUNCT
ma-415	12	14	=	=	SYM
ma-415	12	15	(	(	PUNCT
ma-415	12	16	∫	∫	PROPN
ma-415	12	17	∫	∫	PROPN
ma-415	12	18	σ(x	σ(x	PROPN
ma-415	12	19	)	)	PUNCT
ma-415	12	20	∣∣∣∣	∣∣∣∣	NOUN
ma-415	12	21	1	1	NUM
ma-415	12	22	tσ	tσ	NOUN
ma-415	12	23	∫	∫	PROPN
ma-415	12	24	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	12	25	ψ(y1	ψ(y1	NOUN
ma-415	12	26	,	,	PUNCT
ma-415	12	27	y1	y1	ADJ
ma-415	12	28	−	−	PROPN
ma-415	12	29	z1	z1	PROPN
ma-415	12	30	)	)	PUNCT
ma-415	12	31	|y1	|y1	VERB
ma-415	12	32	−	−	PROPN
ma-415	12	33	z1|n−σ	z1|n−σ	X
ma-415	12	34	f	f	X
ma-415	12	35	(	(	PUNCT
ma-415	12	36	z1)dz1	z1)dz1	VERB
ma-415	12	37	∣∣∣∣2	∣∣∣∣2	NOUN
ma-415	12	38	dy1dt	dy1dt	NUM
ma-415	12	39	tn+1	tn+1	NOUN
ma-415	12	40	)	)	PUNCT
ma-415	12	41	1	1	NUM
ma-415	12	42	2	2	NUM
ma-415	12	43	and	and	CCONJ
ma-415	12	44	µ∗,σψ	µ∗,σψ	NOUN
ma-415	12	45	,	,	PUNCT
ma-415	12	46	λ(f	λ(f	PROPN
ma-415	12	47	)	)	PUNCT
ma-415	12	48	(	(	PUNCT
ma-415	12	49	x	x	X
ma-415	12	50	)	)	PUNCT
ma-415	12	51	=	=	SYM
ma-415	13	1	(	(	PUNCT
ma-415	13	2	∫	∫	PROPN
ma-415	13	3	∫	∫	PROPN
ma-415	13	4	rn+1	rn+1	PROPN
ma-415	13	5	+	+	CCONJ
ma-415	13	6	(	(	PUNCT
ma-415	13	7	t	t	PROPN
ma-415	13	8	t	t	PROPN
ma-415	13	9	+	+	CCONJ
ma-415	13	10	|x1	|x1	NUM
ma-415	13	11	−	−	PROPN
ma-415	13	12	y1|	y1|	NOUN
ma-415	13	13	)	)	PUNCT
ma-415	13	14	λn	λn	PROPN
ma-415	13	15	∣∣∣∣	∣∣∣∣	NOUN
ma-415	13	16	1	1	NUM
ma-415	13	17	tσ	tσ	NOUN
ma-415	13	18	∫	∫	PROPN
ma-415	13	19	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	13	20	ψ(y1	ψ(y1	NOUN
ma-415	13	21	,	,	PUNCT
ma-415	13	22	y1	y1	ADJ
ma-415	13	23	−	−	PROPN
ma-415	13	24	z1	z1	PROPN
ma-415	13	25	)	)	PUNCT
ma-415	13	26	|y1	|y1	VERB
ma-415	13	27	−	−	PROPN
ma-415	13	28	z1|n−σ	z1|n−σ	X
ma-415	13	29	f	f	X
ma-415	13	30	(	(	PUNCT
ma-415	13	31	z1)dz1	z1)dz1	VERB
ma-415	13	32	∣∣∣∣2	∣∣∣∣2	NOUN
ma-415	13	33	dy1dt	dy1dt	NUM
ma-415	13	34	tn+1	tn+1	NOUN
ma-415	13	35	)	)	PUNCT
ma-415	13	36	1	1	NUM
ma-415	13	37	2	2	NUM
ma-415	13	38	,	,	PUNCT
ma-415	13	39	where	where	SCONJ
ma-415	13	40	σ(x	σ(x	NOUN
ma-415	13	41	)	)	PUNCT
ma-415	13	42	=	=	PRON
ma-415	13	43	{	{	PUNCT
ma-415	13	44	(	(	PUNCT
ma-415	13	45	y1	y1	PROPN
ma-415	13	46	,	,	PUNCT
ma-415	13	47	t	t	PROPN
ma-415	13	48	)	)	PUNCT
ma-415	13	49	∈	∈	PROPN
ma-415	13	50	rn+1	rn+1	PROPN
ma-415	13	51	+	+	CCONJ
ma-415	13	52	:	:	PUNCT
ma-415	13	53	|x1	|x1	NUM
ma-415	13	54	−	−	PROPN
ma-415	13	55	y1|	y1|	ADP
ma-415	13	56	<	<	X
ma-415	13	57	t	t	PROPN
ma-415	13	58	and	and	CCONJ
ma-415	13	59	λ	λ	X
ma-415	13	60	>	>	X
ma-415	13	61	1	1	NUM
ma-415	13	62	}	}	PUNCT
ma-415	13	63	.	.	PUNCT
ma-415	14	1	received	receive	VERB
ma-415	14	2	:	:	PUNCT
ma-415	14	3	17	17	NUM
ma-415	14	4	jul	jul	PROPN
ma-415	14	5	2025	2025	NUM
ma-415	14	6	.	.	PUNCT
ma-415	15	1	key	key	ADJ
ma-415	15	2	words	word	NOUN
ma-415	15	3	and	and	CCONJ
ma-415	15	4	phrases	phrase	NOUN
ma-415	15	5	.	.	PUNCT
ma-415	16	1	littlewood−paley	littlewood−paley	ADJ
ma-415	16	2	operator	operator	NOUN
ma-415	16	3	;	;	PUNCT
ma-415	16	4	variable	variable	ADJ
ma-415	16	5	kernel	kernel	NOUN
ma-415	16	6	;	;	PUNCT
ma-415	16	7	herz	herz	ADJ
ma-415	16	8	space	space	NOUN
ma-415	16	9	;	;	PUNCT
ma-415	16	10	variable	variable	ADJ
ma-415	16	11	exponent	exponent	NOUN
ma-415	16	12	..	..	PUNCT
ma-415	16	13	1	1	NUM
ma-415	16	14	https://adac.ee	https://adac.ee	PROPN
ma-415	16	15	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	PROPN
ma-415	16	16	https://orcid.org/0000-0002-6391-4243	https://orcid.org/0000-0002-6391-4243	PROPN
ma-415	16	17	https://orcid.org/0000-0003-0663-068x	https://orcid.org/0000-0003-0663-068x	PROPN
ma-415	16	18	eur	eur	PROPN
ma-415	16	19	.	.	PUNCT
ma-415	17	1	j.	j.	PROPN
ma-415	17	2	math	math	PROPN
ma-415	17	3	.	.	PUNCT
ma-415	18	1	anal	anal	PROPN
ma-415	18	2	.	.	PUNCT
ma-415	19	1	10.28924	10.28924	NUM
ma-415	19	2	/	/	SYM
ma-415	19	3	ada	ada	PROPN
ma-415	19	4	/	/	SYM
ma-415	19	5	ma.5.22	ma.5.22	NOUN
ma-415	19	6	2the	2the	NUM
ma-415	19	7	parameterized	parameterized	ADJ
ma-415	19	8	littlewood−paley	littlewood−paley	ADJ
ma-415	19	9	operators	operator	NOUN
ma-415	19	10	µσψ	µσψ	VERB
ma-415	19	11	,	,	PUNCT
ma-415	19	12	s	s	PART
ma-415	19	13	and	and	CCONJ
ma-415	19	14	µ∗,σψ	µ∗,σψ	PROPN
ma-415	19	15	,	,	PUNCT
ma-415	19	16	λ	λ	NOUN
ma-415	19	17	were	be	AUX
ma-415	19	18	initially	initially	ADV
ma-415	19	19	investigated	investigate	VERB
ma-415	19	20	bysakamoto	bysakamoto	NOUN
ma-415	19	21	and	and	CCONJ
ma-415	19	22	yabuta	yabuta	NOUN
ma-415	19	23	in	in	ADP
ma-415	19	24	[	[	X
ma-415	19	25	1	1	NUM
ma-415	19	26	]	]	PUNCT
ma-415	19	27	.	.	PUNCT
ma-415	20	1	they	they	PRON
ma-415	20	2	proved	prove	VERB
ma-415	20	3	that	that	SCONJ
ma-415	20	4	if	if	SCONJ
ma-415	20	5	ψ	ψ	X
ma-415	20	6	∈	∈	PROPN
ma-415	20	7	libβ(sn−1	libβ(sn−1	PROPN
ma-415	20	8	)	)	PUNCT
ma-415	20	9	and	and	CCONJ
ma-415	20	10	1	1	NUM
ma-415	20	11	<	<	X
ma-415	20	12	p	p	X
ma-415	20	13	<	<	X
ma-415	20	14	∞	∞	PROPN
ma-415	20	15	,	,	PUNCT
ma-415	20	16	then	then	ADV
ma-415	20	17	µ∗,σψ	µ∗,σψ	NOUN
ma-415	20	18	,	,	PUNCT
ma-415	20	19	λ	λ	PROPN
ma-415	20	20	and	and	CCONJ
ma-415	20	21	µσψ	µσψ	NOUN
ma-415	20	22	,	,	PUNCT
ma-415	20	23	s	s	PART
ma-415	20	24	operators	operator	NOUN
ma-415	20	25	are	be	AUX
ma-415	20	26	bounded	bound	VERB
ma-415	20	27	on	on	ADP
ma-415	20	28	lp(rn	lp(rn	PROPN
ma-415	20	29	)	)	PUNCT
ma-415	20	30	space	space	NOUN
ma-415	20	31	.	.	PUNCT
ma-415	21	1	xue	xue	PROPN
ma-415	21	2	and	and	CCONJ
ma-415	21	3	ding	ding	NOUN
ma-415	22	1	[	[	X
ma-415	22	2	2	2	NUM
ma-415	22	3	]	]	PUNCT
ma-415	22	4	established	establish	VERB
ma-415	22	5	sharp	sharp	ADJ
ma-415	22	6	lp(w	lp(w	PUNCT
ma-415	22	7	)	)	PUNCT
ma-415	22	8	boundedfor	boundedfor	ADP
ma-415	22	9	these	these	DET
ma-415	22	10	operators	operator	NOUN
ma-415	22	11	(	(	PUNCT
ma-415	22	12	µ∗,σψ	µ∗,σψ	PROPN
ma-415	22	13	,	,	PUNCT
ma-415	22	14	λ	λ	INTJ
ma-415	22	15	,	,	PUNCT
ma-415	22	16	µσψ	µσψ	INTJ
ma-415	22	17	,	,	PUNCT
ma-415	22	18	s	s	PART
ma-415	22	19	)	)	PUNCT
ma-415	22	20	in	in	ADP
ma-415	22	21	terms	term	NOUN
ma-415	22	22	of	of	ADP
ma-415	22	23	the	the	DET
ma-415	22	24	aq	aq	NOUN
ma-415	22	25	characteristic	characteristic	NOUN
ma-415	22	26	of	of	ADP
ma-415	22	27	w	w	PROPN
ma-415	22	28	,	,	PUNCT
ma-415	22	29	under	under	ADP
ma-415	22	30	the	the	DET
ma-415	22	31	condition	condition	NOUN
ma-415	22	32	ψ	ψ	ADP
ma-415	22	33	∈	∈	PROPN
ma-415	22	34	lb(sn−1	lb(sn−1	PROPN
ma-415	22	35	)	)	PUNCT
ma-415	22	36	.	.	PUNCT
ma-415	23	1	deringoz	deringoz	PROPN
ma-415	23	2	,	,	PUNCT
ma-415	23	3	guliyev	guliyev	NOUN
ma-415	23	4	and	and	CCONJ
ma-415	23	5	ragusa	ragusa	NOUN
ma-415	23	6	[	[	X
ma-415	23	7	3	3	NUM
ma-415	23	8	]	]	PUNCT
ma-415	23	9	obtained	obtain	VERB
ma-415	23	10	the	the	DET
ma-415	23	11	boundedness	boundedness	NOUN
ma-415	23	12	of	of	ADP
ma-415	23	13	intrinsic	intrinsic	ADJ
ma-415	23	14	squarefunctions	squarefunction	NOUN
ma-415	23	15	and	and	CCONJ
ma-415	23	16	their	their	PRON
ma-415	23	17	commutators	commutator	NOUN
ma-415	23	18	in	in	ADP
ma-415	23	19	the	the	DET
ma-415	23	20	framework	framework	NOUN
ma-415	23	21	of	of	ADP
ma-415	23	22	morrey	morrey	NOUN
ma-415	23	23	-	-	PUNCT
ma-415	23	24	orlicz	orlicz	NOUN
ma-415	23	25	spaces	space	NOUN
ma-415	23	26	.	.	PUNCT
ma-415	24	1	the	the	DET
ma-415	24	2	boundedness	boundedness	PROPN
ma-415	24	3	ofparametric	ofparametric	PROPN
ma-415	24	4	littlewood−paley	littlewood−paley	PROPN
ma-415	24	5	operators	operator	NOUN
ma-415	24	6	on	on	ADP
ma-415	24	7	musielak−orlicz	musielak−orlicz	NUM
ma-415	24	8	hardy	hardy	ADJ
ma-415	24	9	spaces	space	NOUN
ma-415	24	10	was	be	AUX
ma-415	24	11	further	far	ADV
ma-415	24	12	studiedin	studiedin	NOUN
ma-415	25	1	[	[	X
ma-415	25	2	4].as	4].as	NOUN
ma-415	25	3	is	be	AUX
ma-415	25	4	well	well	ADV
ma-415	25	5	known	know	VERB
ma-415	25	6	,	,	PUNCT
ma-415	25	7	over	over	ADP
ma-415	25	8	the	the	DET
ma-415	25	9	past	past	ADJ
ma-415	25	10	thirty	thirty	NUM
ma-415	25	11	years	year	NOUN
ma-415	25	12	,	,	PUNCT
ma-415	25	13	variable	variable	ADJ
ma-415	25	14	kernel	kernel	PROPN
ma-415	25	15	integral	integral	ADJ
ma-415	25	16	operators	operator	NOUN
ma-415	25	17	have	have	AUX
ma-415	25	18	become	become	VERB
ma-415	25	19	anincreasingly	anincreasingly	ADV
ma-415	25	20	active	active	ADJ
ma-415	25	21	area	area	NOUN
ma-415	25	22	of	of	ADP
ma-415	25	23	research	research	NOUN
ma-415	25	24	.	.	PUNCT
ma-415	26	1	for	for	ADP
ma-415	26	2	example	example	NOUN
ma-415	26	3	,	,	PUNCT
ma-415	26	4	tao	tao	PROPN
ma-415	26	5	et	et	PROPN
ma-415	26	6	al	al	PROPN
ma-415	26	7	.	.	PUNCT
ma-415	27	1	[	[	X
ma-415	27	2	5	5	NUM
ma-415	27	3	]	]	PUNCT
ma-415	27	4	obtained	obtain	VERB
ma-415	27	5	the	the	DET
ma-415	27	6	lp(rn	lp(rn	PROPN
ma-415	27	7	)	)	PUNCT
ma-415	27	8	boundednessof	boundednessof	NOUN
ma-415	27	9	variable	variable	ADJ
ma-415	27	10	kernel	kernel	PROPN
ma-415	27	11	fractional	fractional	PROPN
ma-415	27	12	integral	integral	ADJ
ma-415	27	13	operators	operator	NOUN
ma-415	27	14	tψ	tψ	VERB
ma-415	27	15	,	,	PUNCT
ma-415	27	16	α	α	PROPN
ma-415	27	17	,	,	PUNCT
ma-415	27	18	chen	chen	PROPN
ma-415	27	19	and	and	CCONJ
ma-415	27	20	ding	de	VERB
ma-415	28	1	[	[	X
ma-415	28	2	6	6	NUM
ma-415	28	3	]	]	PUNCT
ma-415	28	4	proved	prove	VERB
ma-415	28	5	the	the	DET
ma-415	28	6	lp(rn	lp(rn	PROPN
ma-415	28	7	)	)	PUNCT
ma-415	28	8	bound	bind	VERB
ma-415	28	9	-	-	PUNCT
ma-415	28	10	edness	edness	NOUN
ma-415	28	11	of	of	ADP
ma-415	28	12	variable	variable	ADJ
ma-415	28	13	kernel	kernel	PROPN
ma-415	28	14	littlewood−paley	littlewood−paley	PROPN
ma-415	28	15	operators	operators	PROPN
ma-415	28	16	,	,	PUNCT
ma-415	28	17	shao	shao	PROPN
ma-415	29	1	[	[	X
ma-415	29	2	7	7	NUM
ma-415	29	3	]	]	PUNCT
ma-415	29	4	investigated	investigate	VERB
ma-415	29	5	the	the	DET
ma-415	29	6	weighted	weight	VERB
ma-415	29	7	estimatesfor	estimatesfor	ADP
ma-415	29	8	variable	variable	ADJ
ma-415	29	9	kernel	kernel	PROPN
ma-415	29	10	fractional	fractional	PROPN
ma-415	29	11	integrals	integral	NOUN
ma-415	29	12	and	and	CCONJ
ma-415	29	13	their	their	PRON
ma-415	29	14	commutators	commutator	NOUN
ma-415	29	15	on	on	ADP
ma-415	29	16	generalized	generalized	ADJ
ma-415	29	17	morrey	morrey	NOUN
ma-415	29	18	spaces	space	NOUN
ma-415	29	19	,	,	PUNCT
ma-415	29	20	in	in	ADP
ma-415	29	21	[	[	PUNCT
ma-415	29	22	8]the	8]the	DET
ma-415	29	23	author	author	NOUN
ma-415	29	24	proved	prove	VERB
ma-415	29	25	the	the	DET
ma-415	29	26	boundedness	boundedness	NOUN
ma-415	29	27	properties	property	NOUN
ma-415	29	28	of	of	ADP
ma-415	29	29	marcinkiewicz	marcinkiewicz	ADJ
ma-415	29	30	integral	integral	ADJ
ma-415	29	31	operator	operator	NOUN
ma-415	29	32	µψ	µψ	VERB
ma-415	29	33	with	with	ADP
ma-415	29	34	variablekernel	variablekernel	NOUN
ma-415	29	35	on	on	ADP
ma-415	29	36	the	the	DET
ma-415	29	37	hardy	hardy	ADJ
ma-415	29	38	space	space	NOUN
ma-415	29	39	hp(rn	hp(rn	PROPN
ma-415	29	40	)	)	PUNCT
ma-415	29	41	.	.	PUNCT
ma-415	30	1	recently	recently	ADV
ma-415	30	2	,	,	PUNCT
ma-415	30	3	abdalmonem	abdalmonem	PROPN
ma-415	30	4	et	et	PROPN
ma-415	30	5	.	.	PUNCT
ma-415	31	1	al	al	PROPN
ma-415	31	2	.	.	PUNCT
ma-415	32	1	[	[	X
ma-415	32	2	9	9	NUM
ma-415	32	3	]	]	PUNCT
ma-415	32	4	obtained	obtain	VERB
ma-415	32	5	the	the	DET
ma-415	32	6	boundedness	boundedness	PROPN
ma-415	32	7	oflittlewood−paley	oflittlewood−paley	PROPN
ma-415	32	8	operators	operator	NOUN
ma-415	32	9	with	with	ADP
ma-415	32	10	variable	variable	ADJ
ma-415	32	11	kernel	kernel	NOUN
ma-415	32	12	on	on	ADP
ma-415	32	13	the	the	DET
ma-415	32	14	weighted	weight	VERB
ma-415	32	15	variable	variable	ADJ
ma-415	32	16	herz	herz	PROPN
ma-415	32	17	-	-	PUNCT
ma-415	32	18	morrey	morrey	PROPN
ma-415	32	19	spaces.moreover	spaces.moreover	PROPN
ma-415	32	20	,	,	PUNCT
ma-415	32	21	variable	variable	ADJ
ma-415	32	22	exponents	exponent	NOUN
ma-415	32	23	herz	herz	PROPN
ma-415	32	24	spaces	space	NOUN
ma-415	32	25	have	have	AUX
ma-415	32	26	been	be	AUX
ma-415	32	27	extensively	extensively	ADV
ma-415	32	28	studied	study	VERB
ma-415	32	29	by	by	ADP
ma-415	32	30	many	many	ADJ
ma-415	32	31	authors	author	NOUN
ma-415	32	32	us	we	PRON
ma-415	32	33	-	-	PUNCT
ma-415	32	34	ing	ing	ADJ
ma-415	32	35	different	different	ADJ
ma-415	32	36	methods	method	NOUN
ma-415	32	37	(	(	PUNCT
ma-415	32	38	[	[	X
ma-415	32	39	14–20	14–20	NUM
ma-415	32	40	,	,	PUNCT
ma-415	32	41	24	24	NUM
ma-415	32	42	,	,	PUNCT
ma-415	32	43	25	25	NUM
ma-415	32	44	]	]	PUNCT
ma-415	32	45	)	)	PUNCT
ma-415	32	46	.	.	PUNCT
ma-415	33	1	izuki	izuki	PROPN
ma-415	34	1	[	[	X
ma-415	34	2	23	23	NUM
ma-415	34	3	]	]	PUNCT
ma-415	34	4	defined	define	VERB
ma-415	34	5	the	the	DET
ma-415	34	6	variable	variable	ADJ
ma-415	34	7	exponent	exponent	NOUN
ma-415	34	8	homogeneous	homogeneous	PROPN
ma-415	34	9	herzspace	herzspace	PROPN
ma-415	34	10	k̇α	k̇α	PROPN
ma-415	34	11	,	,	PUNCT
ma-415	34	12	q	q	NOUN
ma-415	34	13	p(·)(rn	p(·)(rn	NOUN
ma-415	34	14	)	)	PUNCT
ma-415	34	15	and	and	CCONJ
ma-415	34	16	investigated	investigate	VERB
ma-415	34	17	the	the	DET
ma-415	34	18	boundedness	boundedness	NOUN
ma-415	34	19	of	of	ADP
ma-415	34	20	some	some	DET
ma-415	34	21	integral	integral	ADJ
ma-415	34	22	operators	operator	NOUN
ma-415	34	23	on	on	ADP
ma-415	34	24	these	these	DET
ma-415	34	25	spaces.wang	spaces.wang	PROPN
ma-415	35	1	[	[	X
ma-415	35	2	20	20	NUM
ma-415	35	3	]	]	PUNCT
ma-415	35	4	considered	consider	VERB
ma-415	35	5	the	the	DET
ma-415	35	6	boundedness	boundedness	NOUN
ma-415	35	7	results	result	NOUN
ma-415	35	8	for	for	ADP
ma-415	35	9	certain	certain	ADJ
ma-415	35	10	rough	rough	ADJ
ma-415	35	11	kernel	kernel	NOUN
ma-415	35	12	littlewood−paley	littlewood−paley	PROPN
ma-415	35	13	opera	opera	NOUN
ma-415	35	14	-	-	PUNCT
ma-415	35	15	tors	tor	NOUN
ma-415	35	16	in	in	ADP
ma-415	35	17	homogeneous	homogeneous	ADJ
ma-415	35	18	and	and	CCONJ
ma-415	35	19	homogeneous	homogeneous	ADJ
ma-415	35	20	herz	herz	PROPN
ma-415	35	21	spaces	space	NOUN
ma-415	35	22	k̇α	k̇α	PROPN
ma-415	35	23	,	,	PUNCT
ma-415	35	24	q	q	X
ma-415	35	25	(	(	PUNCT
ma-415	35	26	·	·	PUNCT
ma-415	35	27	)	)	PUNCT
ma-415	36	1	p	p	X
ma-415	36	2	(	(	PUNCT
ma-415	36	3	·	·	PUNCT
ma-415	36	4	)	)	PUNCT
ma-415	36	5	(	(	PUNCT
ma-415	36	6	rn	rn	NOUN
ma-415	36	7	)	)	PUNCT
ma-415	36	8	.	.	PUNCT
ma-415	37	1	in	in	ADP
ma-415	37	2	[	[	X
ma-415	37	3	21	21	NUM
ma-415	37	4	]	]	PUNCT
ma-415	37	5	the	the	DET
ma-415	37	6	authors	author	NOUN
ma-415	37	7	studied	study	VERB
ma-415	37	8	theboundedness	theboundedness	NOUN
ma-415	37	9	of	of	ADP
ma-415	37	10	the	the	DET
ma-415	37	11	vector	vector	NOUN
ma-415	37	12	-	-	PUNCT
ma-415	37	13	valued	value	VERB
ma-415	37	14	inequality	inequality	NOUN
ma-415	37	15	for	for	ADP
ma-415	37	16	the	the	DET
ma-415	37	17	intrinsic	intrinsic	ADJ
ma-415	37	18	square	square	ADJ
ma-415	37	19	function	function	NOUN
ma-415	37	20	in	in	ADP
ma-415	37	21	variable	variable	ADJ
ma-415	37	22	exponentshomogeneous	exponentshomogeneous	ADJ
ma-415	37	23	herz	herz	PROPN
ma-415	37	24	spaces	space	VERB
ma-415	37	25	k̇α(·),q	k̇α(·),q	PROPN
ma-415	37	26	p	p	X
ma-415	37	27	(	(	PUNCT
ma-415	37	28	·	·	PUNCT
ma-415	37	29	)	)	PUNCT
ma-415	37	30	(	(	PUNCT
ma-415	37	31	rn	rn	NOUN
ma-415	37	32	)	)	PUNCT
ma-415	37	33	.	.	PUNCT
ma-415	38	1	izuki	izuki	PROPN
ma-415	38	2	and	and	CCONJ
ma-415	38	3	noi	noi	PROPN
ma-415	39	1	[	[	X
ma-415	39	2	12	12	NUM
ma-415	39	3	]	]	PUNCT
ma-415	39	4	considered	consider	VERB
ma-415	39	5	the	the	DET
ma-415	39	6	generalized	generalize	VERB
ma-415	39	7	herz	herz	PROPN
ma-415	39	8	spaces	space	VERB
ma-415	39	9	k̇	k̇	PROPN
ma-415	39	10	α	α	PROPN
ma-415	39	11	(	(	PUNCT
ma-415	39	12	·	·	PUNCT
ma-415	39	13	)	)	PUNCT
ma-415	39	14	q(·),p(·)(rn	q(·),p(·)(rn	NOUN
ma-415	39	15	)	)	PUNCT
ma-415	39	16	and	and	CCONJ
ma-415	39	17	obtained	obtain	VERB
ma-415	39	18	some	some	DET
ma-415	39	19	boundedness	boundedness	NOUN
ma-415	39	20	results	result	NOUN
ma-415	39	21	for	for	ADP
ma-415	39	22	integral	integral	ADJ
ma-415	39	23	operators	operator	NOUN
ma-415	39	24	and	and	CCONJ
ma-415	39	25	their	their	PRON
ma-415	39	26	commutatorson	commutatorson	NOUN
ma-415	39	27	those	those	DET
ma-415	39	28	spaces	space	NOUN
ma-415	39	29	.	.	PUNCT
ma-415	40	1	in	in	ADP
ma-415	40	2	[	[	X
ma-415	40	3	13	13	NUM
ma-415	40	4	]	]	PUNCT
ma-415	40	5	the	the	DET
ma-415	40	6	author	author	NOUN
ma-415	40	7	established	establish	VERB
ma-415	40	8	the	the	DET
ma-415	40	9	boundedness	boundedness	NOUN
ma-415	40	10	properties	property	NOUN
ma-415	40	11	of	of	ADP
ma-415	40	12	the	the	DET
ma-415	40	13	rough	rough	ADJ
ma-415	40	14	kernelfractional	kernelfractional	ADJ
ma-415	40	15	integral	integral	ADJ
ma-415	40	16	operators	operator	NOUN
ma-415	40	17	in	in	ADP
ma-415	40	18	k̇α	k̇α	PROPN
ma-415	40	19	(	(	PUNCT
ma-415	40	20	·	·	PUNCT
ma-415	40	21	)	)	PUNCT
ma-415	40	22	q(·),p(·)(rn	q(·),p(·)(rn	NOUN
ma-415	40	23	)	)	PUNCT
ma-415	40	24	spaces.motivated	spaces.motivate	VERB
ma-415	40	25	by	by	ADP
ma-415	40	26	the	the	DET
ma-415	40	27	work	work	NOUN
ma-415	40	28	of	of	ADP
ma-415	40	29	[	[	X
ma-415	40	30	9	9	NUM
ma-415	40	31	,	,	PUNCT
ma-415	40	32	13	13	NUM
ma-415	40	33	,	,	PUNCT
ma-415	40	34	19],this	19],this	NUM
ma-415	40	35	paper	paper	NOUN
ma-415	40	36	discusses	discuss	VERB
ma-415	40	37	the	the	DET
ma-415	40	38	boundedness	boundedness	NOUN
ma-415	40	39	of	of	ADP
ma-415	40	40	variable	variable	NOUN
ma-415	40	41	kernelparameterized	kernelparameterize	VERB
ma-415	40	42	littlewood	littlewood	PROPN
ma-415	40	43	-	-	PUNCT
ma-415	40	44	paley	paley	PROPN
ma-415	40	45	operators	operator	NOUN
ma-415	40	46	on	on	ADP
ma-415	40	47	homogeneous	homogeneous	ADJ
ma-415	40	48	herz	herz	PROPN
ma-415	40	49	spaces	space	NOUN
ma-415	40	50	k̇α	k̇α	PROPN
ma-415	40	51	(	(	PUNCT
ma-415	40	52	·	·	PUNCT
ma-415	40	53	)	)	PUNCT
ma-415	40	54	q(·),p(·)(rn	q(·),p(·)(rn	NOUN
ma-415	40	55	)	)	PUNCT
ma-415	40	56	with	with	ADP
ma-415	40	57	threevariable	threevariable	ADJ
ma-415	40	58	exponents	exponent	NOUN
ma-415	40	59	.	.	PUNCT
ma-415	41	1	the	the	DET
ma-415	41	2	results	result	NOUN
ma-415	41	3	are	be	AUX
ma-415	41	4	also	also	ADV
ma-415	41	5	new	new	ADJ
ma-415	41	6	for	for	ADP
ma-415	41	7	the	the	DET
ma-415	41	8	case	case	NOUN
ma-415	41	9	when	when	SCONJ
ma-415	41	10	α	α	X
ma-415	41	11	(	(	PUNCT
ma-415	41	12	·	·	PUNCT
ma-415	41	13	)	)	PUNCT
ma-415	41	14	is	be	AUX
ma-415	41	15	constant	constant	ADJ
ma-415	41	16	.	.	PUNCT
ma-415	42	1	2	2	X
ma-415	42	2	.	.	X
ma-415	42	3	mathematical	mathematical	ADJ
ma-415	42	4	background	background	NOUN
ma-415	42	5	consider	consider	VERB
ma-415	42	6	a	a	DET
ma-415	42	7	lebesgue	lebesgue	ADJ
ma-415	42	8	measurable	measurable	NOUN
ma-415	42	9	set	set	NOUN
ma-415	42	10	e	e	PROPN
ma-415	42	11	⊂	⊂	PROPN
ma-415	42	12	rn	rn	PROPN
ma-415	42	13	with	with	ADP
ma-415	42	14	positive	positive	ADJ
ma-415	42	15	measure	measure	NOUN
ma-415	42	16	|e|	|e|	ADP
ma-415	42	17	>	>	X
ma-415	42	18	0	0	X
ma-415	42	19	.	.	PUNCT
ma-415	43	1	denote	denote	VERB
ma-415	43	2	by	by	ADP
ma-415	43	3	χe	χe	PROPN
ma-415	43	4	thecharacteristic	thecharacteristic	ADJ
ma-415	43	5	function	function	NOUN
ma-415	43	6	of	of	ADP
ma-415	43	7	e.	e.	PROPN
ma-415	43	8	in	in	ADP
ma-415	43	9	this	this	DET
ma-415	43	10	paper	paper	NOUN
ma-415	43	11	,	,	PUNCT
ma-415	43	12	c	c	PROPN
ma-415	43	13	represents	represent	VERB
ma-415	43	14	a	a	DET
ma-415	43	15	positive	positive	ADJ
ma-415	43	16	constant	constant	NOUN
ma-415	43	17	that	that	PRON
ma-415	43	18	may	may	AUX
ma-415	43	19	vary	vary	VERB
ma-415	43	20	betweenoccurrences	betweenoccurrence	NOUN
ma-415	43	21	.	.	PUNCT
ma-415	44	1	we	we	PRON
ma-415	44	2	write	write	VERB
ma-415	44	3	g	g	PROPN
ma-415	44	4	.	.	PUNCT
ma-415	45	1	f	f	PROPN
ma-415	45	2	means	mean	VERB
ma-415	45	3	g	g	PROPN
ma-415	45	4	≤	≤	PROPN
ma-415	45	5	cf	cf	NOUN
ma-415	45	6	,	,	PUNCT
ma-415	45	7	for	for	ADP
ma-415	45	8	some	some	DET
ma-415	45	9	constant	constant	ADJ
ma-415	45	10	c	c	NOUN
ma-415	45	11	>	>	X
ma-415	45	12	0	0	X
ma-415	45	13	.	.	PUNCT
ma-415	46	1	definition	definition	NOUN
ma-415	46	2	2.1	2.1	NUM
ma-415	46	3	(	(	PUNCT
ma-415	46	4	[	[	X
ma-415	46	5	22	22	NUM
ma-415	46	6	]	]	PUNCT
ma-415	46	7	)	)	PUNCT
ma-415	46	8	.	.	PUNCT
ma-415	47	1	(	(	PUNCT
ma-415	47	2	variable	variable	ADJ
ma-415	47	3	lebesgue	lebesgue	NOUN
ma-415	47	4	space	space	NOUN
ma-415	47	5	)	)	PUNCT
ma-415	47	6	suppose	suppose	VERB
ma-415	47	7	that	that	SCONJ
ma-415	47	8	p	p	X
ma-415	47	9	(	(	PUNCT
ma-415	47	10	·	·	PUNCT
ma-415	47	11	)	)	PUNCT
ma-415	47	12	:	:	PUNCT
ma-415	47	13	γ→	γ→	PROPN
ma-415	48	1	[	[	X
ma-415	48	2	1,∞	1,∞	NUM
ma-415	48	3	)	)	PUNCT
ma-415	48	4	is	be	AUX
ma-415	48	5	a	a	DET
ma-415	48	6	measurablefunction	measurablefunction	NOUN
ma-415	48	7	.	.	PUNCT
ma-415	49	1	the	the	DET
ma-415	49	2	lp(·)(γ	lp(·)(γ	NOUN
ma-415	49	3	)	)	PUNCT
ma-415	49	4	space	space	NOUN
ma-415	49	5	is	be	AUX
ma-415	49	6	defined	define	VERB
ma-415	49	7	by	by	ADP
ma-415	49	8	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	PROPN
ma-415	49	9	eur	eur	PROPN
ma-415	49	10	.	.	PUNCT
ma-415	50	1	j.	j.	PROPN
ma-415	50	2	math	math	PROPN
ma-415	50	3	.	.	PUNCT
ma-415	51	1	anal	anal	PROPN
ma-415	51	2	.	.	PUNCT
ma-415	52	1	10.28924	10.28924	NUM
ma-415	52	2	/	/	SYM
ma-415	52	3	ada	ada	PROPN
ma-415	52	4	/	/	SYM
ma-415	52	5	ma.5.22	ma.5.22	NOUN
ma-415	52	6	3	3	NUM
ma-415	52	7	lp(·)(γ	lp(·)(γ	NOUN
ma-415	52	8	)	)	PUNCT
ma-415	53	1	=	=	PRON
ma-415	53	2	{	{	PUNCT
ma-415	53	3	g	g	NOUN
ma-415	53	4	is	be	AUX
ma-415	53	5	measurable	measurable	ADJ
ma-415	53	6	:	:	PUNCT
ma-415	53	7	∫	∫	PROPN
ma-415	53	8	γ	γ	X
ma-415	53	9	(	(	PUNCT
ma-415	53	10	|g(x)|	|g(x)|	PROPN
ma-415	53	11	β	β	X
ma-415	53	12	)	)	PUNCT
ma-415	53	13	p(x	p(x	PROPN
ma-415	53	14	)	)	PUNCT
ma-415	53	15	dx	dx	PROPN
ma-415	53	16	<	<	X
ma-415	53	17	∞	∞	PROPN
ma-415	53	18	for	for	ADP
ma-415	53	19	some	some	DET
ma-415	53	20	constant	constant	ADJ
ma-415	53	21	β	β	X
ma-415	53	22	>	>	X
ma-415	53	23	0	0	NUM
ma-415	53	24	}	}	PUNCT
ma-415	53	25	.	.	PUNCT
ma-415	54	1	the	the	DET
ma-415	54	2	local	local	ADJ
ma-415	54	3	lp	lp	NOUN
ma-415	54	4	(	(	PUNCT
ma-415	54	5	·	·	PUNCT
ma-415	54	6	)	)	PUNCT
ma-415	54	7	loc	loc	PROPN
ma-415	54	8	(	(	PUNCT
ma-415	54	9	γ	γ	NOUN
ma-415	54	10	)	)	PUNCT
ma-415	54	11	space	space	NOUN
ma-415	54	12	is	be	AUX
ma-415	54	13	defined	define	VERB
ma-415	54	14	as	as	ADP
ma-415	54	15	l	l	NOUN
ma-415	54	16	p	p	X
ma-415	54	17	(	(	PUNCT
ma-415	54	18	·	·	PUNCT
ma-415	54	19	)	)	PUNCT
ma-415	54	20	loc	loc	NOUN
ma-415	54	21	(	(	PUNCT
ma-415	54	22	γ	γ	NOUN
ma-415	54	23	)	)	PUNCT
ma-415	54	24	=	=	NOUN
ma-415	54	25	{	{	PUNCT
ma-415	54	26	g	g	NOUN
ma-415	54	27	is	be	AUX
ma-415	54	28	measurable	measurable	ADJ
ma-415	54	29	:	:	PUNCT
ma-415	54	30	g	g	PROPN
ma-415	54	31	∈	∈	PROPN
ma-415	54	32	lp(·)(k	lp(·)(k	PROPN
ma-415	54	33	)	)	PUNCT
ma-415	54	34	for	for	ADP
ma-415	54	35	any	any	DET
ma-415	54	36	compact	compact	ADJ
ma-415	54	37	set	set	NOUN
ma-415	54	38	k	k	PROPN
ma-415	54	39	⊂	⊂	PROPN
ma-415	54	40	γ	γ	X
ma-415	54	41	}	}	PUNCT
ma-415	54	42	.	.	PUNCT
ma-415	55	1	with	with	ADP
ma-415	55	2	the	the	DET
ma-415	55	3	given	give	VERB
ma-415	55	4	norm	norm	NOUN
ma-415	55	5	,	,	PUNCT
ma-415	55	6	the	the	DET
ma-415	55	7	lebesgue	lebesgue	NOUN
ma-415	55	8	space	space	NOUN
ma-415	55	9	lp	lp	PROPN
ma-415	55	10	(	(	PUNCT
ma-415	55	11	·	·	PUNCT
ma-415	55	12	)	)	PUNCT
ma-415	55	13	loc	loc	NOUN
ma-415	55	14	(	(	PUNCT
ma-415	55	15	γ	γ	PROPN
ma-415	55	16	)	)	PUNCT
ma-415	55	17	is	be	AUX
ma-415	55	18	a	a	DET
ma-415	55	19	banach	banach	NOUN
ma-415	55	20	space	space	NOUN
ma-415	55	21	‖f	‖f	ADP
ma-415	55	22	‖lp(·)(γ	‖lp(·)(γ	NOUN
ma-415	55	23	)	)	PUNCT
ma-415	55	24	=	=	SYM
ma-415	55	25	inf	inf	PROPN
ma-415	55	26	{	{	PUNCT
ma-415	55	27	η	η	PROPN
ma-415	55	28	>	>	X
ma-415	55	29	0	0	NUM
ma-415	55	30	:	:	PUNCT
ma-415	56	1	∫	∫	PROPN
ma-415	56	2	e	e	X
ma-415	56	3	(	(	PUNCT
ma-415	56	4	|g(x)|	|g(x)|	PROPN
ma-415	56	5	β	β	X
ma-415	56	6	)	)	PUNCT
ma-415	56	7	p(x	p(x	PROPN
ma-415	56	8	)	)	PUNCT
ma-415	56	9	dx	dx	PROPN
ma-415	56	10	≤	≤	NUM
ma-415	56	11	1	1	NUM
ma-415	56	12	}	}	PUNCT
ma-415	56	13	.	.	PUNCT
ma-415	57	1	let	let	VERB
ma-415	57	2	p−	p−	NOUN
ma-415	57	3	=	=	PUNCT
ma-415	57	4	ess	ess	PROPN
ma-415	57	5	inf{p(x	inf{p(x	PROPN
ma-415	57	6	)	)	PUNCT
ma-415	57	7	:	:	PUNCT
ma-415	58	1	x	x	X
ma-415	58	2	∈	∈	PROPN
ma-415	58	3	γ	γ	X
ma-415	58	4	}	}	PUNCT
ma-415	58	5	,	,	PUNCT
ma-415	58	6	p+	p+	NOUN
ma-415	58	7	=	=	SYM
ma-415	58	8	ess	ess	PROPN
ma-415	58	9	sup{p(x	sup{p(x	PROPN
ma-415	58	10	)	)	PUNCT
ma-415	58	11	:	:	PUNCT
ma-415	58	12	x	x	X
ma-415	58	13	∈	∈	PROPN
ma-415	58	14	γ	γ	X
ma-415	58	15	}	}	PUNCT
ma-415	58	16	denote	denote	VERB
ma-415	58	17	the	the	DET
ma-415	58	18	essential	essential	ADJ
ma-415	58	19	infimum	infimum	ADJ
ma-415	58	20	andsupremum	andsupremum	NOUN
ma-415	58	21	of	of	ADP
ma-415	58	22	p(γ	p(γ	NOUN
ma-415	58	23	)	)	PUNCT
ma-415	58	24	,	,	PUNCT
ma-415	58	25	respectively	respectively	ADV
ma-415	58	26	.	.	PUNCT
ma-415	59	1	p(γ	p(γ	NOUN
ma-415	59	2	)	)	PUNCT
ma-415	59	3	represents	represent	VERB
ma-415	59	4	the	the	DET
ma-415	59	5	collection	collection	NOUN
ma-415	59	6	of	of	ADP
ma-415	59	7	all	all	DET
ma-415	59	8	measurable	measurable	ADJ
ma-415	59	9	functions	function	NOUN
ma-415	59	10	p(·)with	p(·)with	ADP
ma-415	59	11	p−	p−	NOUN
ma-415	59	12	>	>	X
ma-415	59	13	1	1	NUM
ma-415	59	14	.	.	PUNCT
ma-415	60	1	p+	p+	VERB
ma-415	60	2	<	<	X
ma-415	60	3	+	+	PROPN
ma-415	60	4	∞.	∞.	PROPN
ma-415	60	5	p0(γ	p0(γ	NOUN
ma-415	60	6	)	)	PUNCT
ma-415	60	7	consists	consist	VERB
ma-415	60	8	of	of	ADP
ma-415	60	9	all	all	DET
ma-415	60	10	measurable	measurable	ADJ
ma-415	60	11	functions	function	NOUN
ma-415	60	12	p	p	X
ma-415	60	13	(	(	PUNCT
ma-415	60	14	·	·	PUNCT
ma-415	60	15	)	)	PUNCT
ma-415	60	16	such	such	ADJ
ma-415	60	17	that	that	SCONJ
ma-415	60	18	p−	p−	NOUN
ma-415	60	19	>	>	X
ma-415	60	20	0and	0and	PROPN
ma-415	60	21	p+	p+	NOUN
ma-415	60	22	<	<	X
ma-415	60	23	+	+	PROPN
ma-415	60	24	∞.	∞.	PROPN
ma-415	60	25	furthermore	furthermore	ADV
ma-415	60	26	,	,	PUNCT
ma-415	60	27	b(rn	b(rn	PROPN
ma-415	60	28	)	)	PUNCT
ma-415	60	29	is	be	AUX
ma-415	60	30	defined	define	VERB
ma-415	60	31	as	as	ADP
ma-415	60	32	the	the	DET
ma-415	60	33	subset	subset	NOUN
ma-415	60	34	of	of	ADP
ma-415	60	35	p	p	X
ma-415	60	36	(	(	PUNCT
ma-415	60	37	·	·	PUNCT
ma-415	60	38	)	)	PUNCT
ma-415	60	39	∈	∈	PROPN
ma-415	60	40	p(rn	p(rn	PROPN
ma-415	60	41	)	)	PUNCT
ma-415	60	42	for	for	ADP
ma-415	60	43	which	which	PRON
ma-415	60	44	thehardy−littlewood	thehardy−littlewood	NOUN
ma-415	60	45	maximal	maximal	ADJ
ma-415	60	46	operator	operator	NOUN
ma-415	60	47	m∗	m∗	NOUN
ma-415	60	48	is	be	AUX
ma-415	60	49	bounded	bound	VERB
ma-415	60	50	in	in	ADP
ma-415	60	51	variable	variable	ADJ
ma-415	60	52	lp	lp	PROPN
ma-415	60	53	(	(	PUNCT
ma-415	60	54	·	·	PUNCT
ma-415	60	55	)	)	PUNCT
ma-415	60	56	space.we	space.we	PRON
ma-415	61	1	know	know	VERB
ma-415	61	2	that	that	SCONJ
ma-415	61	3	,	,	PUNCT
ma-415	61	4	if	if	SCONJ
ma-415	61	5	p	p	X
ma-415	61	6	(	(	PUNCT
ma-415	61	7	·	·	PUNCT
ma-415	61	8	)	)	PUNCT
ma-415	61	9	∈	∈	PROPN
ma-415	61	10	p(rn	p(rn	PROPN
ma-415	61	11	)	)	PUNCT
ma-415	61	12	,	,	PUNCT
ma-415	61	13	then	then	ADV
ma-415	61	14	the	the	DET
ma-415	61	15	operator	operator	NOUN
ma-415	61	16	m∗	m∗	VERB
ma-415	61	17	,	,	PUNCT
ma-415	61	18	m∗g(x	m∗g(x	ADJ
ma-415	61	19	)	)	PUNCT
ma-415	61	20	=	=	SYM
ma-415	61	21	sup	sup	NOUN
ma-415	61	22	b⊆rn	b⊆rn	NOUN
ma-415	61	23	,	,	PUNCT
ma-415	61	24	b3x	b3x	VERB
ma-415	61	25	1	1	NUM
ma-415	61	26	|b|	|b|	PROPN
ma-415	61	27	∫	∫	PROPN
ma-415	61	28	b	b	X
ma-415	61	29	|g(y)|dy	|g(y)|dy	PROPN
ma-415	61	30	,	,	PUNCT
ma-415	61	31	is	be	AUX
ma-415	61	32	bounded	bound	VERB
ma-415	61	33	in	in	ADP
ma-415	61	34	variable	variable	ADJ
ma-415	61	35	lp	lp	PROPN
ma-415	61	36	(	(	PUNCT
ma-415	61	37	·	·	PUNCT
ma-415	61	38	)	)	PUNCT
ma-415	61	39	space	space	NOUN
ma-415	62	1	[	[	X
ma-415	62	2	24	24	NUM
ma-415	62	3	]	]	PUNCT
ma-415	62	4	,	,	PUNCT
ma-415	62	5	where	where	SCONJ
ma-415	62	6	m∗	m∗	PROPN
ma-415	62	7	denotes	denote	VERB
ma-415	62	8	the	the	DET
ma-415	62	9	hardy−littlewood	hardy−littlewood	NUM
ma-415	62	10	maximal	maximal	ADJ
ma-415	62	11	operator.let	operator.let	X
ma-415	62	12	us	we	PRON
ma-415	62	13	now	now	ADV
ma-415	62	14	recall	recall	VERB
ma-415	62	15	the	the	DET
ma-415	62	16	definition	definition	NOUN
ma-415	62	17	of	of	ADP
ma-415	62	18	herz	herz	PROPN
ma-415	62	19	space	space	PROPN
ma-415	62	20	k̇α(·),q	k̇α(·),q	PROPN
ma-415	62	21	(	(	PUNCT
ma-415	62	22	·	·	PUNCT
ma-415	62	23	)	)	PUNCT
ma-415	63	1	p	p	X
ma-415	63	2	(	(	PUNCT
ma-415	63	3	·	·	PUNCT
ma-415	63	4	)	)	PUNCT
ma-415	63	5	(	(	PUNCT
ma-415	63	6	rn	rn	NOUN
ma-415	63	7	)	)	PUNCT
ma-415	63	8	.	.	PUNCT
ma-415	64	1	let	let	VERB
ma-415	64	2	bk	bk	VERB
ma-415	64	3	=	=	PUNCT
ma-415	64	4	{	{	PUNCT
ma-415	64	5	y	y	PROPN
ma-415	64	6	∈	∈	PROPN
ma-415	64	7	rn	rn	PROPN
ma-415	64	8	:	:	PUNCT
ma-415	64	9	|y	|y	NOUN
ma-415	64	10	|	|	ADV
ma-415	64	11	≤	≤	VERB
ma-415	64	12	2k	2k	NUM
ma-415	64	13	}	}	PUNCT
ma-415	64	14	,	,	PUNCT
ma-415	65	1	k	k	PROPN
ma-415	65	2	∈	∈	PROPN
ma-415	65	3	z	z	PROPN
ma-415	65	4	,	,	PUNCT
ma-415	65	5	ck	ck	INTJ
ma-415	65	6	=	=	SYM
ma-415	65	7	bk\bk−1	bk\bk−1	NOUN
ma-415	65	8	,	,	PUNCT
ma-415	65	9	χck	χck	NOUN
ma-415	65	10	=	=	SYM
ma-415	65	11	χk	χk	PROPN
ma-415	65	12	.	.	PUNCT
ma-415	66	1	definition	definition	NOUN
ma-415	66	2	2.2	2.2	NUM
ma-415	66	3	(	(	PUNCT
ma-415	66	4	[	[	X
ma-415	66	5	12	12	NUM
ma-415	66	6	]	]	PUNCT
ma-415	66	7	)	)	PUNCT
ma-415	66	8	.	.	PUNCT
ma-415	67	1	let	let	VERB
ma-415	67	2	α	α	PRON
ma-415	67	3	(	(	PUNCT
ma-415	67	4	·	·	PUNCT
ma-415	67	5	)	)	PUNCT
ma-415	67	6	:	:	PUNCT
ma-415	68	1	rn	rn	VERB
ma-415	68	2	−→	−→	NOUN
ma-415	68	3	r	r	NOUN
ma-415	68	4	,	,	PUNCT
ma-415	68	5	−∞	−∞	X
ma-415	68	6	<	<	X
ma-415	68	7	α−	α−	ADP
ma-415	68	8	≤	≤	NOUN
ma-415	68	9	α+	α+	PRON
ma-415	68	10	<	<	X
ma-415	68	11	∞	∞	PROPN
ma-415	68	12	and	and	CCONJ
ma-415	68	13	q	q	NOUN
ma-415	68	14	(	(	PUNCT
ma-415	68	15	·	·	PUNCT
ma-415	68	16	)	)	PUNCT
ma-415	68	17	,	,	PUNCT
ma-415	68	18	p	p	X
ma-415	68	19	(	(	PUNCT
ma-415	68	20	·	·	PUNCT
ma-415	68	21	)	)	PUNCT
ma-415	68	22	∈	∈	PROPN
ma-415	68	23	p(rn	p(rn	PROPN
ma-415	68	24	)	)	PUNCT
ma-415	68	25	.	.	PUNCT
ma-415	69	1	thehomogeneous	thehomogeneous	ADJ
ma-415	69	2	variable	variable	ADJ
ma-415	69	3	exponents	exponent	NOUN
ma-415	69	4	herz	herz	PROPN
ma-415	69	5	k̇α(·),q	k̇α(·),q	PROPN
ma-415	69	6	(	(	PUNCT
ma-415	69	7	·	·	PUNCT
ma-415	69	8	)	)	PUNCT
ma-415	69	9	p	p	X
ma-415	69	10	(	(	PUNCT
ma-415	69	11	·	·	PUNCT
ma-415	69	12	)	)	PUNCT
ma-415	69	13	(	(	PUNCT
ma-415	69	14	rn	rn	NOUN
ma-415	69	15	)	)	PUNCT
ma-415	69	16	space	space	NOUN
ma-415	69	17	is	be	AUX
ma-415	69	18	defined	define	VERB
ma-415	69	19	by	by	ADP
ma-415	69	20	k̇	k̇	PROPN
ma-415	69	21	α(·),q	α(·),q	PROPN
ma-415	69	22	(	(	PUNCT
ma-415	69	23	·	·	PUNCT
ma-415	69	24	)	)	PUNCT
ma-415	70	1	p	p	X
ma-415	70	2	(	(	PUNCT
ma-415	70	3	·	·	PUNCT
ma-415	70	4	)	)	PUNCT
ma-415	70	5	(	(	PUNCT
ma-415	70	6	rn	rn	NOUN
ma-415	70	7	)	)	PUNCT
ma-415	70	8	=	=	PRON
ma-415	71	1	{	{	PUNCT
ma-415	71	2	f	f	PROPN
ma-415	71	3	∈	∈	PROPN
ma-415	71	4	lp	lp	PROPN
ma-415	71	5	(	(	PUNCT
ma-415	71	6	·	·	PUNCT
ma-415	71	7	)	)	PUNCT
ma-415	71	8	loc	loc	NOUN
ma-415	71	9	(	(	PUNCT
ma-415	71	10	rn\{0	rn\{0	PROPN
ma-415	71	11	}	}	PUNCT
ma-415	71	12	)	)	PUNCT
ma-415	71	13	:	:	PUNCT
ma-415	72	1	‖f	‖f	ADP
ma-415	72	2	‖	‖	PROPN
ma-415	72	3	k̇	k̇	PROPN
ma-415	72	4	α(·),q	α(·),q	NUM
ma-415	72	5	(	(	PUNCT
ma-415	72	6	·	·	PUNCT
ma-415	72	7	)	)	PUNCT
ma-415	72	8	p	p	X
ma-415	72	9	(	(	PUNCT
ma-415	72	10	·	·	PUNCT
ma-415	72	11	)	)	PUNCT
ma-415	72	12	(	(	PUNCT
ma-415	72	13	rn	rn	NOUN
ma-415	72	14	)	)	PUNCT
ma-415	72	15	<	<	X
ma-415	72	16	∞	∞	NUM
ma-415	72	17	}	}	PUNCT
ma-415	72	18	,	,	PUNCT
ma-415	72	19	where	where	SCONJ
ma-415	72	20	‖f	‖f	ADP
ma-415	72	21	‖	‖	PROPN
ma-415	72	22	k̇	k̇	PROPN
ma-415	72	23	α(·),q	α(·),q	PROPN
ma-415	72	24	(	(	PUNCT
ma-415	72	25	·	·	PUNCT
ma-415	72	26	)	)	PUNCT
ma-415	72	27	p	p	X
ma-415	72	28	(	(	PUNCT
ma-415	72	29	·	·	PUNCT
ma-415	72	30	)	)	PUNCT
ma-415	72	31	(	(	PUNCT
ma-415	72	32	rn	rn	NOUN
ma-415	72	33	)	)	PUNCT
ma-415	72	34	:	:	PUNCT
ma-415	72	35	=	=	NOUN
ma-415	72	36	∥∥∥{2kα(·)|f	∥∥∥{2kα(·)|f	ADP
ma-415	72	37	χk	χk	NOUN
ma-415	72	38	|}∞k=−∞	|}∞k=−∞	PROPN
ma-415	72	39	∥∥∥	∥∥∥	PROPN
ma-415	72	40	lq(·)(lp	lq(·)(lp	PROPN
ma-415	72	41	(	(	PUNCT
ma-415	72	42	·	·	PUNCT
ma-415	72	43	)	)	PUNCT
ma-415	72	44	)	)	PUNCT
ma-415	73	1	=	=	X
ma-415	73	2	inf	inf	NOUN
ma-415	73	3	{	{	PUNCT
ma-415	73	4	β	β	X
ma-415	73	5	>	>	X
ma-415	73	6	0	0	NUM
ma-415	73	7	:	:	PUNCT
ma-415	73	8	∞∑	∞∑	NUM
ma-415	73	9	k=−∞	k=−∞	NOUN
ma-415	73	10	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	73	11	(	(	PUNCT
ma-415	73	12	2kα(·)|f	2kα(·)|f	NUM
ma-415	73	13	χk	χk	NOUN
ma-415	73	14	|	|	ADV
ma-415	73	15	β	β	NOUN
ma-415	73	16	)	)	PUNCT
ma-415	73	17	q(·)∥∥∥∥∥	q(·)∥∥∥∥∥	NOUN
ma-415	74	1	l	l	NOUN
ma-415	74	2	p	p	X
ma-415	74	3	(	(	PUNCT
ma-415	74	4	·	·	PUNCT
ma-415	74	5	)	)	PUNCT
ma-415	74	6	q	q	PROPN
ma-415	74	7	(	(	PUNCT
ma-415	74	8	·	·	PUNCT
ma-415	74	9	)	)	PUNCT
ma-415	74	10	≤	≤	NUM
ma-415	74	11	1	1	NUM
ma-415	74	12	}	}	PUNCT
ma-415	74	13	.	.	PUNCT
ma-415	75	1	the	the	DET
ma-415	75	2	nonhomogeneous	nonhomogeneous	ADJ
ma-415	75	3	variable	variable	ADJ
ma-415	75	4	exponents	exponent	NOUN
ma-415	75	5	herz	herz	PROPN
ma-415	75	6	k̇α(·),q	k̇α(·),q	PROPN
ma-415	75	7	(	(	PUNCT
ma-415	75	8	·	·	PUNCT
ma-415	75	9	)	)	PUNCT
ma-415	75	10	p	p	X
ma-415	75	11	(	(	PUNCT
ma-415	75	12	·	·	PUNCT
ma-415	75	13	)	)	PUNCT
ma-415	75	14	(	(	PUNCT
ma-415	75	15	rn	rn	NOUN
ma-415	75	16	)	)	PUNCT
ma-415	75	17	space	space	NOUN
ma-415	75	18	is	be	AUX
ma-415	75	19	defined	define	VERB
ma-415	75	20	by	by	ADP
ma-415	75	21	k	k	PROPN
ma-415	75	22	α(·),q	α(·),q	PROPN
ma-415	75	23	(	(	PUNCT
ma-415	75	24	·	·	PUNCT
ma-415	75	25	)	)	PUNCT
ma-415	76	1	p	p	X
ma-415	76	2	(	(	PUNCT
ma-415	76	3	·	·	PUNCT
ma-415	76	4	)	)	PUNCT
ma-415	76	5	(	(	PUNCT
ma-415	76	6	rn	rn	NOUN
ma-415	76	7	)	)	PUNCT
ma-415	76	8	=	=	PRON
ma-415	77	1	{	{	PUNCT
ma-415	77	2	f	f	PROPN
ma-415	77	3	∈	∈	PROPN
ma-415	77	4	lp	lp	PROPN
ma-415	77	5	(	(	PUNCT
ma-415	77	6	·	·	PUNCT
ma-415	77	7	)	)	PUNCT
ma-415	77	8	loc	loc	NOUN
ma-415	77	9	(	(	PUNCT
ma-415	77	10	rn\{0	rn\{0	PROPN
ma-415	77	11	}	}	PUNCT
ma-415	77	12	)	)	PUNCT
ma-415	77	13	:	:	PUNCT
ma-415	78	1	‖f	‖f	ADP
ma-415	78	2	‖	‖	PROPN
ma-415	78	3	k	k	PROPN
ma-415	78	4	α(·),q	α(·),q	PROPN
ma-415	78	5	(	(	PUNCT
ma-415	78	6	·	·	PUNCT
ma-415	78	7	)	)	PUNCT
ma-415	78	8	p	p	X
ma-415	78	9	(	(	PUNCT
ma-415	78	10	·	·	PUNCT
ma-415	78	11	)	)	PUNCT
ma-415	78	12	(	(	PUNCT
ma-415	78	13	rn	rn	NOUN
ma-415	78	14	)	)	PUNCT
ma-415	78	15	<	<	X
ma-415	78	16	∞	∞	NUM
ma-415	78	17	}	}	PUNCT
ma-415	78	18	,	,	PUNCT
ma-415	78	19	where	where	SCONJ
ma-415	78	20	‖f	‖f	ADP
ma-415	78	21	‖	‖	PROPN
ma-415	78	22	k	k	PROPN
ma-415	78	23	α(·),q	α(·),q	PROPN
ma-415	78	24	(	(	PUNCT
ma-415	78	25	·	·	PUNCT
ma-415	78	26	)	)	PUNCT
ma-415	78	27	p	p	X
ma-415	78	28	(	(	PUNCT
ma-415	78	29	·	·	PUNCT
ma-415	78	30	)	)	PUNCT
ma-415	78	31	(	(	PUNCT
ma-415	78	32	rn	rn	NOUN
ma-415	78	33	)	)	PUNCT
ma-415	78	34	:	:	PUNCT
ma-415	79	1	=	=	NOUN
ma-415	79	2	∥∥∥{2kα(·)|f	∥∥∥{2kα(·)|f	PART
ma-415	79	3	χk	χk	PROPN
ma-415	79	4	|}∞k=0	|}∞k=0	ADP
ma-415	79	5	∥∥∥	∥∥∥	PROPN
ma-415	79	6	lq(·)(lp	lq(·)(lp	PROPN
ma-415	79	7	(	(	PUNCT
ma-415	79	8	·	·	PUNCT
ma-415	79	9	)	)	PUNCT
ma-415	79	10	)	)	PUNCT
ma-415	80	1	=	=	SYM
ma-415	80	2	inf	inf	PROPN
ma-415	80	3	β	β	PROPN
ma-415	80	4	>	>	X
ma-415	80	5	0	0	PUNCT
ma-415	81	1	:	:	PUNCT
ma-415	81	2	∞∑	∞∑	NUM
ma-415	81	3	k=0	k=0	PROPN
ma-415	81	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	82	1	(	(	PUNCT
ma-415	82	2	2kα(·)|f	2kα(·)|f	NUM
ma-415	82	3	χk	χk	NOUN
ma-415	82	4	|	|	ADV
ma-415	82	5	β	β	X
ma-415	82	6	)	)	PUNCT
ma-415	82	7	q	q	NOUN
ma-415	82	8	(	(	PUNCT
ma-415	82	9	·	·	PUNCT
ma-415	82	10	)	)	PUNCT
ma-415	82	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	83	1	l	l	NOUN
ma-415	83	2	p	p	X
ma-415	83	3	(	(	PUNCT
ma-415	83	4	·	·	PUNCT
ma-415	83	5	)	)	PUNCT
ma-415	83	6	q	q	PROPN
ma-415	83	7	(	(	PUNCT
ma-415	83	8	·	·	PUNCT
ma-415	83	9	)	)	PUNCT
ma-415	83	10	≤	≤	NOUN
ma-415	83	11	1	1	NUM
ma-415	83	12			NOUN
ma-415	83	13	.	.	PUNCT
ma-415	84	1	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	VERB
ma-415	84	2	eur	eur	PROPN
ma-415	84	3	.	.	PUNCT
ma-415	85	1	j.	j.	PROPN
ma-415	85	2	math	math	PROPN
ma-415	85	3	.	.	PUNCT
ma-415	86	1	anal	anal	PROPN
ma-415	86	2	.	.	PUNCT
ma-415	87	1	10.28924	10.28924	NUM
ma-415	87	2	/	/	SYM
ma-415	87	3	ada	ada	PROPN
ma-415	87	4	/	/	SYM
ma-415	87	5	ma.5.22	ma.5.22	NOUN
ma-415	87	6	4	4	NUM
ma-415	87	7	remark	remark	NOUN
ma-415	87	8	.	.	PUNCT
ma-415	88	1	(	(	PUNCT
ma-415	88	2	1	1	X
ma-415	88	3	)	)	PUNCT
ma-415	88	4	if	if	SCONJ
ma-415	88	5	k̇	k̇	PROPN
ma-415	88	6	α(·),q	α(·),q	PROPN
ma-415	88	7	(	(	PUNCT
ma-415	88	8	·	·	PUNCT
ma-415	88	9	)	)	PUNCT
ma-415	88	10	p	p	X
ma-415	88	11	(	(	PUNCT
ma-415	88	12	·	·	PUNCT
ma-415	88	13	)	)	PUNCT
ma-415	88	14	(	(	PUNCT
ma-415	88	15	rn	rn	NOUN
ma-415	88	16	)	)	PUNCT
ma-415	88	17	=	=	PUNCT
ma-415	89	1	k̇	k̇	PROPN
ma-415	89	2	α(·),q	α(·),q	NUM
ma-415	89	3	p	p	X
ma-415	89	4	(	(	PUNCT
ma-415	89	5	·	·	PUNCT
ma-415	89	6	)	)	PUNCT
ma-415	89	7	(	(	PUNCT
ma-415	89	8	rn	rn	NOUN
ma-415	89	9	)	)	PUNCT
ma-415	89	10	,	,	PUNCT
ma-415	89	11	then	then	ADV
ma-415	89	12	,	,	PUNCT
ma-415	89	13	q	q	X
ma-415	89	14	(	(	PUNCT
ma-415	89	15	·	·	PUNCT
ma-415	89	16	)	)	PUNCT
ma-415	89	17	is	be	AUX
ma-415	89	18	a	a	DET
ma-415	89	19	constant.(2	constant.(2	NOUN
ma-415	89	20	)	)	PUNCT
ma-415	89	21	if	if	SCONJ
ma-415	89	22	k̇	k̇	PROPN
ma-415	89	23	α(·),q	α(·),q	PROPN
ma-415	89	24	(	(	PUNCT
ma-415	89	25	·	·	PUNCT
ma-415	89	26	)	)	PUNCT
ma-415	89	27	p	p	X
ma-415	89	28	(	(	PUNCT
ma-415	89	29	·	·	PUNCT
ma-415	89	30	)	)	PUNCT
ma-415	89	31	(	(	PUNCT
ma-415	89	32	rn	rn	NOUN
ma-415	89	33	)	)	PUNCT
ma-415	89	34	=	=	SYM
ma-415	89	35	k̇α	k̇α	ADJ
ma-415	89	36	,	,	PUNCT
ma-415	89	37	q	q	NOUN
ma-415	89	38	p(·)(rn	p(·)(rn	PROPN
ma-415	89	39	)	)	PUNCT
ma-415	89	40	,	,	PUNCT
ma-415	89	41	then	then	ADV
ma-415	89	42	,	,	PUNCT
ma-415	89	43	both	both	PRON
ma-415	89	44	α	α	PROPN
ma-415	89	45	(	(	PUNCT
ma-415	89	46	·	·	PUNCT
ma-415	89	47	)	)	PUNCT
ma-415	89	48	,	,	PUNCT
ma-415	89	49	q	q	X
ma-415	89	50	(	(	PUNCT
ma-415	89	51	·	·	PUNCT
ma-415	89	52	)	)	PUNCT
ma-415	89	53	are	be	AUX
ma-415	89	54	constants.(3	constants.(3	PROPN
ma-415	89	55	)	)	PUNCT
ma-415	89	56	if	if	SCONJ
ma-415	89	57	k̇	k̇	PROPN
ma-415	89	58	α(·),q	α(·),q	PROPN
ma-415	89	59	(	(	PUNCT
ma-415	89	60	·	·	PUNCT
ma-415	89	61	)	)	PUNCT
ma-415	89	62	p	p	X
ma-415	89	63	(	(	PUNCT
ma-415	89	64	·	·	PUNCT
ma-415	89	65	)	)	PUNCT
ma-415	89	66	(	(	PUNCT
ma-415	89	67	rn	rn	NOUN
ma-415	89	68	)	)	PUNCT
ma-415	89	69	=	=	SYM
ma-415	89	70	k̇α	k̇α	ADJ
ma-415	89	71	,	,	PUNCT
ma-415	89	72	qp	qp	PROPN
ma-415	89	73	(	(	PUNCT
ma-415	89	74	rn	rn	NOUN
ma-415	89	75	)	)	PUNCT
ma-415	89	76	,	,	PUNCT
ma-415	89	77	then	then	ADV
ma-415	89	78	,	,	PUNCT
ma-415	89	79	α	α	X
ma-415	89	80	(	(	PUNCT
ma-415	89	81	·	·	PUNCT
ma-415	89	82	)	)	PUNCT
ma-415	89	83	,	,	PUNCT
ma-415	89	84	p	p	X
ma-415	89	85	(	(	PUNCT
ma-415	89	86	·	·	PUNCT
ma-415	89	87	)	)	PUNCT
ma-415	89	88	,	,	PUNCT
ma-415	89	89	q	q	X
ma-415	89	90	(	(	PUNCT
ma-415	89	91	·	·	PUNCT
ma-415	89	92	)	)	PUNCT
ma-415	89	93	are	be	AUX
ma-415	89	94	all	all	PRON
ma-415	89	95	constants.(4	constants.(4	PROPN
ma-415	89	96	)	)	PUNCT
ma-415	89	97	moreover	moreover	ADV
ma-415	89	98	,	,	PUNCT
ma-415	89	99	if	if	SCONJ
ma-415	89	100	p	p	X
ma-415	89	101	(	(	PUNCT
ma-415	89	102	·	·	PUNCT
ma-415	89	103	)	)	PUNCT
ma-415	89	104	=	=	SYM
ma-415	90	1	q	q	X
ma-415	90	2	(	(	PUNCT
ma-415	90	3	·	·	PUNCT
ma-415	90	4	)	)	PUNCT
ma-415	90	5	and	and	CCONJ
ma-415	90	6	α	α	X
ma-415	90	7	(	(	PUNCT
ma-415	90	8	·	·	PUNCT
ma-415	90	9	)	)	PUNCT
ma-415	90	10	=	=	SYM
ma-415	90	11	0	0	NUM
ma-415	90	12	,	,	PUNCT
ma-415	90	13	then	then	ADV
ma-415	90	14	k̇	k̇	PROPN
ma-415	90	15	α(·),q	α(·),q	PROPN
ma-415	90	16	(	(	PUNCT
ma-415	90	17	·	·	PUNCT
ma-415	90	18	)	)	PUNCT
ma-415	91	1	p	p	X
ma-415	91	2	(	(	PUNCT
ma-415	91	3	·	·	PUNCT
ma-415	91	4	)	)	PUNCT
ma-415	91	5	(	(	PUNCT
ma-415	91	6	rn	rn	NOUN
ma-415	91	7	)	)	PUNCT
ma-415	91	8	=	=	SYM
ma-415	91	9	lp(·)(rn	lp(·)(rn	PROPN
ma-415	91	10	)	)	PUNCT
ma-415	91	11	.	.	PUNCT
ma-415	92	1	next	next	ADV
ma-415	92	2	,	,	PUNCT
ma-415	92	3	we	we	PRON
ma-415	92	4	present	present	VERB
ma-415	92	5	some	some	DET
ma-415	92	6	key	key	ADJ
ma-415	92	7	lemmas	lemma	NOUN
ma-415	92	8	needed	need	VERB
ma-415	92	9	to	to	PART
ma-415	92	10	prove	prove	VERB
ma-415	92	11	our	our	PRON
ma-415	92	12	main	main	ADJ
ma-415	92	13	theorems	theorem	NOUN
ma-415	92	14	.	.	PUNCT
ma-415	93	1	lemma	lemma	PROPN
ma-415	93	2	2.3	2.3	NUM
ma-415	93	3	(	(	PUNCT
ma-415	93	4	[	[	X
ma-415	93	5	22	22	NUM
ma-415	93	6	]	]	PUNCT
ma-415	93	7	)	)	PUNCT
ma-415	93	8	.	.	PUNCT
ma-415	94	1	(	(	PUNCT
ma-415	94	2	generalized	generalize	VERB
ma-415	94	3	hölder	hölder	NOUN
ma-415	94	4	’s	’s	PART
ma-415	94	5	inequality	inequality	NOUN
ma-415	94	6	)	)	PUNCT
ma-415	94	7	let	let	VERB
ma-415	94	8	f	f	PROPN
ma-415	94	9	∈	∈	PROPN
ma-415	94	10	lp1(·)(rn	lp1(·)(rn	PROPN
ma-415	94	11	)	)	PUNCT
ma-415	94	12	,	,	PUNCT
ma-415	94	13	g	g	PROPN
ma-415	94	14	∈	∈	PROPN
ma-415	94	15	lp	lp	NOUN
ma-415	94	16	′	′	NUM
ma-415	94	17	1(·)(rn	1(·)(rn	NUM
ma-415	94	18	)	)	PUNCT
ma-415	94	19	,	,	PUNCT
ma-415	94	20	and	and	CCONJ
ma-415	94	21	p	p	X
ma-415	94	22	(	(	PUNCT
ma-415	94	23	·	·	PUNCT
ma-415	94	24	)	)	PUNCT
ma-415	94	25	∈	∈	PROPN
ma-415	94	26	p(rn	p(rn	PROPN
ma-415	94	27	)	)	PUNCT
ma-415	94	28	.	.	PUNCT
ma-415	95	1	then	then	ADV
ma-415	95	2	,	,	PUNCT
ma-415	95	3	the	the	DET
ma-415	95	4	following	follow	VERB
ma-415	95	5	inequality	inequality	NOUN
ma-415	95	6	is	be	AUX
ma-415	95	7	satisfied:∫	satisfied:∫	ADJ
ma-415	95	8	rn	rn	PROPN
ma-415	95	9	|g(x)f	|g(x)f	PROPN
ma-415	95	10	(	(	PUNCT
ma-415	95	11	x)|dx	x)|dx	PROPN
ma-415	95	12	≤	≤	ADJ
ma-415	95	13	c‖g‖	c‖g‖	NOUN
ma-415	95	14	lp	lp	NOUN
ma-415	95	15	′	′	NUM
ma-415	95	16	1(·)(rn	1(·)(rn	NUM
ma-415	95	17	)	)	PUNCT
ma-415	95	18	‖f	‖f	PUNCT
ma-415	95	19	‖lp1(·)(rn	‖lp1(·)(rn	NOUN
ma-415	95	20	)	)	PUNCT
ma-415	95	21	,	,	PUNCT
ma-415	95	22	here	here	ADV
ma-415	95	23	c	c	AUX
ma-415	95	24	=	=	SYM
ma-415	95	25	1−	1−	NUM
ma-415	95	26	1	1	NUM
ma-415	95	27	p+	p+	VERB
ma-415	95	28	+	+	NOUN
ma-415	95	29	1	1	NUM
ma-415	95	30	p−	p−	NOUN
ma-415	95	31	.	.	PUNCT
ma-415	96	1	lemma	lemma	PROPN
ma-415	96	2	2.4	2.4	NUM
ma-415	96	3	(	(	PUNCT
ma-415	96	4	[	[	X
ma-415	96	5	23	23	NUM
ma-415	96	6	]	]	PUNCT
ma-415	96	7	)	)	PUNCT
ma-415	96	8	.	.	PUNCT
ma-415	97	1	suppose	suppose	VERB
ma-415	97	2	p	p	X
ma-415	97	3	(	(	PUNCT
ma-415	97	4	·	·	PUNCT
ma-415	97	5	)	)	PUNCT
ma-415	97	6	∈	∈	PROPN
ma-415	97	7	b(rn	b(rn	PROPN
ma-415	97	8	)	)	PUNCT
ma-415	97	9	.	.	PUNCT
ma-415	98	1	for	for	ADP
ma-415	98	2	a	a	DET
ma-415	98	3	given	give	VERB
ma-415	98	4	c	c	PROPN
ma-415	98	5	>	>	PUNCT
ma-415	98	6	0	0	PROPN
ma-415	98	7	,	,	PUNCT
ma-415	98	8	the	the	DET
ma-415	98	9	following	follow	VERB
ma-415	98	10	inequality	inequality	NOUN
ma-415	98	11	is	be	AUX
ma-415	98	12	satisfied	satisfied	ADJ
ma-415	98	13	:	:	PUNCT
ma-415	98	14	c	c	NOUN
ma-415	98	15	≥	≥	NUM
ma-415	98	16	1	1	NUM
ma-415	98	17	|b|‖χb‖lp1(·)(rn)‖χb‖lp′1(·)(rn	|b|‖χb‖lp1(·)(rn)‖χb‖lp′1(·)(rn	PROPN
ma-415	98	18	)	)	PUNCT
ma-415	98	19	,	,	PUNCT
ma-415	99	1	here	here	ADV
ma-415	99	2	b	b	PROPN
ma-415	99	3	⊂	⊂	PROPN
ma-415	99	4	rn	rn	PROPN
ma-415	99	5	.	.	PROPN
ma-415	99	6	lemma	lemma	PROPN
ma-415	99	7	2.5	2.5	NUM
ma-415	99	8	(	(	PUNCT
ma-415	99	9	[	[	X
ma-415	99	10	23	23	NUM
ma-415	99	11	]	]	PUNCT
ma-415	99	12	)	)	PUNCT
ma-415	99	13	.	.	PUNCT
ma-415	100	1	suppose	suppose	VERB
ma-415	100	2	p	p	X
ma-415	100	3	(	(	PUNCT
ma-415	100	4	·	·	PUNCT
ma-415	100	5	)	)	PUNCT
ma-415	100	6	∈	∈	PROPN
ma-415	100	7	b(rn	b(rn	PROPN
ma-415	100	8	)	)	PUNCT
ma-415	100	9	.	.	PUNCT
ma-415	101	1	for	for	ADP
ma-415	101	2	n	n	NOUN
ma-415	101	3	=	=	SYM
ma-415	101	4	1	1	NUM
ma-415	101	5	,	,	PUNCT
ma-415	101	6	2	2	NUM
ma-415	101	7	,	,	PUNCT
ma-415	101	8	there	there	PRON
ma-415	101	9	are	be	VERB
ma-415	101	10	constants	constant	NOUN
ma-415	101	11	δn1	δn1	ADJ
ma-415	101	12	,	,	PUNCT
ma-415	101	13	δn2	δn2	VERB
ma-415	101	14	>	>	X
ma-415	101	15	0	0	PUNCT
ma-415	102	1	for	for	ADP
ma-415	102	2	which	which	PRON
ma-415	102	3	the	the	DET
ma-415	102	4	following	follow	VERB
ma-415	102	5	inequalities	inequality	NOUN
ma-415	102	6	hold	hold	VERB
ma-415	102	7	:	:	PUNCT
ma-415	102	8	‖χb‖lp(·)(rn	‖χb‖lp(·)(rn	PROPN
ma-415	102	9	)	)	PUNCT
ma-415	102	10	‖χs‖lp(·)(rn	‖χs‖lp(·)(rn	PROPN
ma-415	102	11	)	)	PUNCT
ma-415	102	12	.	.	PUNCT
ma-415	103	1	|b|	|b|	PROPN
ma-415	103	2	|s|	|s|	PROPN
ma-415	103	3	,	,	PUNCT
ma-415	103	4	‖χs‖lp′1(·)(rn	‖χs‖lp′1(·)(rn	NUM
ma-415	103	5	)	)	PUNCT
ma-415	103	6	‖χb‖lp′1(·)(rn	‖χb‖lp′1(·)(rn	NUM
ma-415	103	7	)	)	PUNCT
ma-415	103	8	.	.	PUNCT
ma-415	104	1	(	(	PUNCT
ma-415	104	2	|s|	|s|	NOUN
ma-415	104	3	|b|	|b|	PROPN
ma-415	104	4	)	)	PUNCT
ma-415	104	5	δn1	δn1	PROPN
ma-415	104	6	,	,	PUNCT
ma-415	104	7	‖χs‖lp1(·)(rn	‖χs‖lp1(·)(rn	PROPN
ma-415	104	8	)	)	PUNCT
ma-415	104	9	‖χb‖lp1(·)(rn	‖χb‖lp1(·)(rn	PROPN
ma-415	104	10	)	)	PUNCT
ma-415	104	11	.	.	PUNCT
ma-415	105	1	(	(	PUNCT
ma-415	105	2	|s|	|s|	NOUN
ma-415	105	3	|b|	|b|	PROPN
ma-415	105	4	)	)	PUNCT
ma-415	105	5	δn2	δn2	NOUN
ma-415	105	6	,	,	PUNCT
ma-415	105	7	here	here	ADV
ma-415	105	8	b	b	PROPN
ma-415	105	9	⊂	⊂	PROPN
ma-415	105	10	rn	rn	PROPN
ma-415	105	11	,	,	PUNCT
ma-415	105	12	s	s	PROPN
ma-415	106	1	⊂	⊂	PROPN
ma-415	106	2	b.	b.	PROPN
ma-415	106	3	lemma	lemma	PROPN
ma-415	106	4	2.6	2.6	NUM
ma-415	106	5	(	(	PUNCT
ma-415	106	6	[	[	X
ma-415	106	7	20	20	NUM
ma-415	106	8	]	]	NUM
ma-415	106	9	)	)	PUNCT
ma-415	106	10	.	.	PUNCT
ma-415	107	1	let	let	VERB
ma-415	107	2	p1	p1	PROPN
ma-415	107	3	(	(	PUNCT
ma-415	107	4	·	·	PUNCT
ma-415	107	5	)	)	PUNCT
ma-415	107	6	,	,	PUNCT
ma-415	107	7	q1	q1	PROPN
ma-415	107	8	(	(	PUNCT
ma-415	107	9	·	·	PUNCT
ma-415	107	10	)	)	PUNCT
ma-415	107	11	∈	∈	PROPN
ma-415	107	12	p0(rn	p0(rn	PROPN
ma-415	107	13	)	)	PUNCT
ma-415	107	14	,	,	PUNCT
ma-415	107	15	g	g	PROPN
ma-415	107	16	∈	∈	PROPN
ma-415	107	17	lp1(·)q1(·)(rn	lp1(·)q1(·)(rn	PROPN
ma-415	107	18	)	)	PUNCT
ma-415	107	19	,	,	PUNCT
ma-415	107	20	and	and	CCONJ
ma-415	107	21	0	0	NUM
ma-415	107	22	<	<	X
ma-415	107	23	q−	q−	PROPN
ma-415	107	24	≤	≤	PROPN
ma-415	107	25	p1	p1	PROPN
ma-415	107	26	(	(	PUNCT
ma-415	107	27	·	·	PUNCT
ma-415	107	28	)	)	PUNCT
ma-415	107	29	≤	≤	NOUN
ma-415	107	30	q+	q+	ADV
ma-415	107	31	.	.	PUNCT
ma-415	108	1	then	then	ADV
ma-415	108	2	,	,	PUNCT
ma-415	108	3	we	we	PRON
ma-415	108	4	have	have	VERB
ma-415	108	5	min(‖g‖q+	min(‖g‖q+	PROPN
ma-415	108	6	lp1(·)q1	lp1(·)q1	PROPN
ma-415	108	7	(	(	PUNCT
ma-415	108	8	·	·	PUNCT
ma-415	108	9	)	)	PUNCT
ma-415	108	10	,	,	PUNCT
ma-415	108	11	‖g‖	‖g‖	VERB
ma-415	108	12	q−	q−	PROPN
ma-415	108	13	lp1(·)q1	lp1(·)q1	PROPN
ma-415	108	14	(	(	PUNCT
ma-415	108	15	·	·	PUNCT
ma-415	108	16	)	)	PUNCT
ma-415	108	17	)	)	PUNCT
ma-415	109	1	≤	≤	NUM
ma-415	109	2	‖|g|q1(·)‖lp1	‖|g|q1(·)‖lp1	NOUN
ma-415	109	3	(	(	PUNCT
ma-415	109	4	·	·	PUNCT
ma-415	109	5	)	)	PUNCT
ma-415	109	6	≤	≤	NOUN
ma-415	110	1	max(‖g‖q+	max(‖g‖q+	PROPN
ma-415	110	2	lp1(·)q1	lp1(·)q1	PROPN
ma-415	110	3	(	(	PUNCT
ma-415	110	4	·	·	PUNCT
ma-415	110	5	)	)	PUNCT
ma-415	110	6	,	,	PUNCT
ma-415	110	7	‖g‖	‖g‖	VERB
ma-415	110	8	q−	q−	PROPN
ma-415	110	9	lp1(·)q1	lp1(·)q1	PROPN
ma-415	110	10	(	(	PUNCT
ma-415	110	11	·	·	PUNCT
ma-415	110	12	)	)	PUNCT
ma-415	110	13	)	)	PUNCT
ma-415	110	14	.	.	PUNCT
ma-415	111	1	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	VERB
ma-415	111	2	eur	eur	PROPN
ma-415	111	3	.	.	PUNCT
ma-415	112	1	j.	j.	PROPN
ma-415	112	2	math	math	PROPN
ma-415	112	3	.	.	PUNCT
ma-415	113	1	anal	anal	PROPN
ma-415	113	2	.	.	PUNCT
ma-415	114	1	10.28924	10.28924	NUM
ma-415	114	2	/	/	SYM
ma-415	114	3	ada	ada	PROPN
ma-415	114	4	/	/	SYM
ma-415	114	5	ma.5.22	ma.5.22	NOUN
ma-415	114	6	5	5	NUM
ma-415	114	7	lemma	lemma	PROPN
ma-415	114	8	2.7	2.7	NUM
ma-415	114	9	(	(	PUNCT
ma-415	114	10	[	[	X
ma-415	114	11	10	10	NUM
ma-415	114	12	]	]	NUM
ma-415	114	13	)	)	PUNCT
ma-415	114	14	.	.	PUNCT
ma-415	115	1	suppose	suppose	VERB
ma-415	115	2	that	that	SCONJ
ma-415	115	3	α	α	PROPN
ma-415	115	4	(	(	PUNCT
ma-415	115	5	·	·	PUNCT
ma-415	115	6	)	)	PUNCT
ma-415	115	7	∈	∈	PROPN
ma-415	115	8	l∞(rn	l∞(rn	PROPN
ma-415	115	9	)	)	PUNCT
ma-415	115	10	and	and	CCONJ
ma-415	115	11	r0	r0	VERB
ma-415	115	12	>	>	X
ma-415	115	13	0	0	PROPN
ma-415	115	14	.	.	PUNCT
ma-415	116	1	if	if	SCONJ
ma-415	116	2	α	α	X
ma-415	116	3	(	(	PUNCT
ma-415	116	4	·	·	PUNCT
ma-415	116	5	)	)	PUNCT
ma-415	116	6	be	be	AUX
ma-415	116	7	a	a	DET
ma-415	116	8	function	function	NOUN
ma-415	116	9	that	that	PRON
ma-415	116	10	is	be	AUX
ma-415	116	11	loghölder	loghölder	NOUN
ma-415	116	12	continuous	continuous	ADJ
ma-415	116	13	both	both	CCONJ
ma-415	116	14	both	both	PRON
ma-415	116	15	at	at	ADP
ma-415	116	16	the	the	DET
ma-415	116	17	origin	origin	NOUN
ma-415	116	18	and	and	CCONJ
ma-415	116	19	at	at	ADP
ma-415	116	20	infinity	infinity	NOUN
ma-415	116	21	,	,	PUNCT
ma-415	116	22	then	then	ADV
ma-415	116	23	for	for	ADP
ma-415	116	24	any	any	DET
ma-415	116	25	x	x	SYM
ma-415	116	26	∈	∈	PROPN
ma-415	116	27	b(0	b(0	NOUN
ma-415	116	28	,	,	PUNCT
ma-415	116	29	r0	r0	NOUN
ma-415	116	30	)	)	PUNCT
ma-415	116	31	\	\	NOUN
ma-415	116	32	b(0	b(0	PROPN
ma-415	116	33	,	,	PUNCT
ma-415	116	34	r0/2	r0/2	NUM
ma-415	116	35	)	)	PUNCT
ma-415	116	36	,	,	PUNCT
ma-415	116	37	x	x	X
ma-415	116	38	′	′	NUM
ma-415	116	39	∈	∈	PROPN
ma-415	116	40	b(0	b(0	NOUN
ma-415	116	41	,	,	PUNCT
ma-415	116	42	r1	r1	NOUN
ma-415	116	43	)	)	PUNCT
ma-415	116	44	\	\	NOUN
ma-415	116	45	b(0	b(0	PROPN
ma-415	116	46	,	,	PUNCT
ma-415	116	47	r1/2	r1/2	PROPN
ma-415	116	48	)	)	PUNCT
ma-415	116	49	,	,	PUNCT
ma-415	116	50	we	we	PRON
ma-415	116	51	have	have	VERB
ma-415	116	52	r	r	NOUN
ma-415	116	53	α(x	α(x	NOUN
ma-415	116	54	)	)	PUNCT
ma-415	116	55	0	0	NUM
ma-415	116	56	.	.	PUNCT
ma-415	117	1	rα(x	rα(x	NOUN
ma-415	118	1	′	′	NUM
ma-415	118	2	)	)	PUNCT
ma-415	118	3	1	1	NUM
ma-415	118	4	×	×	NOUN
ma-415	118	5			PROPN
ma-415	118	6	[	[	PUNCT
ma-415	118	7	r0r1	r0r1	X
ma-415	118	8	]	]	X
ma-415	118	9	α+	α+	X
ma-415	118	10	,	,	PUNCT
ma-415	118	11	0	0	NUM
ma-415	118	12	<	<	X
ma-415	118	13	r1	r1	PROPN
ma-415	118	14	≤	≤	NOUN
ma-415	118	15	r0/2	r0/2	NUM
ma-415	118	16	,	,	PUNCT
ma-415	118	17	1	1	NUM
ma-415	118	18	,	,	PUNCT
ma-415	118	19	r0/2	r0/2	NUM
ma-415	118	20	<	<	X
ma-415	118	21	r1	r1	PROPN
ma-415	118	22	≤	≤	NOUN
ma-415	118	23	2r0	2r0	NUM
ma-415	118	24	,	,	PUNCT
ma-415	118	25	[	[	PUNCT
ma-415	118	26	r0r1	r0r1	X
ma-415	118	27	]	]	PUNCT
ma-415	118	28	α−	α−	X
ma-415	118	29	,	,	PUNCT
ma-415	118	30	r1	r1	PROPN
ma-415	118	31	>	>	X
ma-415	118	32	2r0	2r0	NUM
ma-415	118	33	.	.	PUNCT
ma-415	119	1	3	3	X
ma-415	119	2	.	.	X
ma-415	119	3	boundedness	boundedness	NOUN
ma-415	119	4	of	of	ADP
ma-415	119	5	the	the	DET
ma-415	119	6	parameterized	parameterized	ADJ
ma-415	119	7	littlewood	littlewood	PROPN
ma-415	119	8	-	-	PUNCT
ma-415	119	9	paley	paley	NOUN
ma-415	119	10	operators	operator	NOUN
ma-415	119	11	in	in	ADP
ma-415	119	12	this	this	DET
ma-415	119	13	section	section	NOUN
ma-415	119	14	,	,	PUNCT
ma-415	119	15	we	we	PRON
ma-415	119	16	discuss	discuss	VERB
ma-415	119	17	the	the	DET
ma-415	119	18	boundedness	boundedness	NOUN
ma-415	119	19	of	of	ADP
ma-415	119	20	variable	variable	ADJ
ma-415	119	21	kernel	kernel	PROPN
ma-415	119	22	parameterized	parameterized	PROPN
ma-415	119	23	littlewood	littlewood	PROPN
ma-415	119	24	-	-	PUNCT
ma-415	119	25	paleyoperators	paleyoperator	NOUN
ma-415	119	26	on	on	ADP
ma-415	119	27	homogeneous	homogeneous	ADJ
ma-415	119	28	herz	herz	PROPN
ma-415	119	29	spaces	space	NOUN
ma-415	119	30	k̇α	k̇α	PROPN
ma-415	119	31	(	(	PUNCT
ma-415	119	32	·	·	PUNCT
ma-415	119	33	)	)	PUNCT
ma-415	119	34	q(·),p(·)(rn	q(·),p(·)(rn	NOUN
ma-415	119	35	)	)	PUNCT
ma-415	119	36	.	.	PUNCT
ma-415	120	1	the	the	DET
ma-415	120	2	results	result	NOUN
ma-415	120	3	are	be	AUX
ma-415	120	4	also	also	ADV
ma-415	120	5	new	new	ADJ
ma-415	120	6	for	for	ADP
ma-415	120	7	the	the	DET
ma-415	120	8	case	case	NOUN
ma-415	120	9	when	when	SCONJ
ma-415	120	10	α	α	X
ma-415	120	11	(	(	PUNCT
ma-415	120	12	·	·	PUNCT
ma-415	120	13	)	)	PUNCT
ma-415	120	14	is	be	AUX
ma-415	120	15	constant.let	constant.let	X
ma-415	120	16	1	1	NUM
ma-415	120	17	<	<	X
ma-415	120	18	q	q	X
ma-415	120	19	<	<	X
ma-415	120	20	∞	∞	PROPN
ma-415	120	21	,	,	PUNCT
ma-415	120	22	q′	q′	PUNCT
ma-415	120	23	=	=	PUNCT
ma-415	121	1	q	q	PROPN
ma-415	122	1	q−1	q−1	PROPN
ma-415	122	2	and	and	CCONJ
ma-415	122	3	w	w	PROPN
ma-415	122	4	be	be	AUX
ma-415	122	5	a	a	DET
ma-415	122	6	weight	weight	NOUN
ma-415	122	7	.	.	PUNCT
ma-415	123	1	for	for	ADP
ma-415	123	2	every	every	DET
ma-415	123	3	cube	cube	NOUN
ma-415	123	4	q	q	PROPN
ma-415	123	5	⊆	⊆	NUM
ma-415	123	6	rn	rn	NOUN
ma-415	123	7	,	,	PUNCT
ma-415	123	8	we	we	PRON
ma-415	123	9	say	say	VERB
ma-415	123	10	w	w	PROPN
ma-415	123	11	∈	∈	PROPN
ma-415	123	12	aq	aq	VERB
ma-415	123	13	if	if	SCONJ
ma-415	123	14	thereexists	thereexist	NOUN
ma-415	124	1	c	c	PROPN
ma-415	124	2	>	>	X
ma-415	124	3	0	0	PROPN
ma-415	124	4	,	,	PUNCT
ma-415	124	5	the	the	DET
ma-415	124	6	following	follow	VERB
ma-415	124	7	inequality	inequality	NOUN
ma-415	124	8	is	be	AUX
ma-415	124	9	satisfied	satisfied	ADJ
ma-415	124	10	:(	:(	PUNCT
ma-415	124	11	1	1	NUM
ma-415	124	12	|q|	|q|	VERB
ma-415	124	13	∫	∫	NOUN
ma-415	124	14	q	q	X
ma-415	124	15	w(x)dx	w(x)dx	VERB
ma-415	124	16	)	)	PUNCT
ma-415	124	17	(	(	PUNCT
ma-415	124	18	1	1	NUM
ma-415	124	19	|q|	|q|	VERB
ma-415	124	20	∫	∫	NOUN
ma-415	124	21	q	q	PROPN
ma-415	124	22	w(x)1−q′dx	w(x)1−q′dx	PROPN
ma-415	124	23	)	)	PUNCT
ma-415	125	1	q−1	q−1	PROPN
ma-415	125	2	≤	≤	NOUN
ma-415	125	3	c	c	NOUN
ma-415	125	4	<	<	X
ma-415	125	5	∞.	∞.	PROPN
ma-415	125	6	xue	xue	PROPN
ma-415	125	7	et	et	PROPN
ma-415	125	8	al	al	PROPN
ma-415	125	9	.	.	PUNCT
ma-415	126	1	[	[	X
ma-415	126	2	2	2	NUM
ma-415	126	3	]	]	PUNCT
ma-415	126	4	proved	prove	VERB
ma-415	126	5	the	the	DET
ma-415	126	6	following	following	NOUN
ma-415	126	7	lp−boundedness	lp−boundedness	ADV
ma-415	126	8	of	of	ADP
ma-415	126	9	µσψ	µσψ	NOUN
ma-415	126	10	,	,	PUNCT
ma-415	126	11	s	s	PART
ma-415	126	12	and	and	CCONJ
ma-415	126	13	µ∗,σψ	µ∗,σψ	PROPN
ma-415	126	14	,	,	PUNCT
ma-415	126	15	λ	λ	PROPN
ma-415	126	16	.	.	PUNCT
ma-415	127	1	lemma	lemma	PROPN
ma-415	127	2	3.1	3.1	NUM
ma-415	127	3	(	(	PUNCT
ma-415	127	4	[	[	X
ma-415	127	5	2	2	NUM
ma-415	127	6	]	]	PUNCT
ma-415	127	7	)	)	PUNCT
ma-415	127	8	.	.	PUNCT
ma-415	128	1	let	let	VERB
ma-415	128	2	1	1	NUM
ma-415	128	3	<	<	X
ma-415	128	4	p	p	X
ma-415	128	5	<	<	X
ma-415	128	6	∞	∞	PROPN
ma-415	128	7	and	and	CCONJ
ma-415	128	8	ψ	ψ	NOUN
ma-415	128	9	∈	∈	PROPN
ma-415	128	10	l∞(rn	l∞(rn	PROPN
ma-415	128	11	)	)	PUNCT
ma-415	128	12	×	×	PROPN
ma-415	128	13	l2(sn−1	l2(sn−1	NOUN
ma-415	128	14	)	)	PUNCT
ma-415	128	15	satisfies	satisfie	NOUN
ma-415	128	16	(	(	PUNCT
ma-415	128	17	1	1	NUM
ma-415	128	18	)	)	PUNCT
ma-415	128	19	and	and	CCONJ
ma-415	128	20	(	(	PUNCT
ma-415	128	21	2	2	NUM
ma-415	128	22	)	)	PUNCT
ma-415	128	23	.	.	PUNCT
ma-415	129	1	then	then	ADV
ma-415	129	2	,	,	PUNCT
ma-415	129	3	we	we	PRON
ma-415	129	4	have	have	VERB
ma-415	129	5	‖µσψ	‖µσψ	NOUN
ma-415	129	6	,	,	PUNCT
ma-415	129	7	s	s	PROPN
ma-415	129	8	f	f	PROPN
ma-415	129	9	‖lp(w	‖lp(w	PUNCT
ma-415	129	10	)	)	PUNCT
ma-415	129	11	.	.	PUNCT
ma-415	130	1	‖f	‖f	PRON
ma-415	130	2	‖lp(w	‖lp(w	NUM
ma-415	130	3	)	)	PUNCT
ma-415	130	4	and	and	CCONJ
ma-415	130	5	‖µ∗,σψ	‖µ∗,σψ	VERB
ma-415	130	6	,	,	PUNCT
ma-415	130	7	λf	λf	NOUN
ma-415	130	8	‖lp(w	‖lp(w	NUM
ma-415	130	9	)	)	PUNCT
ma-415	130	10	.	.	PUNCT
ma-415	131	1	‖f	‖f	PRON
ma-415	131	2	‖lp(w	‖lp(w	NUM
ma-415	131	3	)	)	PUNCT
ma-415	131	4	.	.	PUNCT
ma-415	132	1	lemma	lemma	PROPN
ma-415	132	2	3.2	3.2	NUM
ma-415	132	3	(	(	PUNCT
ma-415	132	4	[	[	X
ma-415	132	5	21	21	NUM
ma-415	132	6	]	]	PUNCT
ma-415	132	7	)	)	PUNCT
ma-415	132	8	.	.	PUNCT
ma-415	133	1	given	give	VERB
ma-415	133	2	a	a	DET
ma-415	133	3	family	family	NOUN
ma-415	133	4	of	of	ADP
ma-415	133	5	functions	function	NOUN
ma-415	133	6	f	f	X
ma-415	133	7	,	,	PUNCT
ma-415	133	8	if	if	SCONJ
ma-415	133	9	for	for	ADP
ma-415	133	10	some	some	DET
ma-415	133	11	p1	p1	NOUN
ma-415	133	12	,	,	PUNCT
ma-415	133	13	1	1	NUM
ma-415	133	14	<	<	X
ma-415	133	15	p1	p1	PROPN
ma-415	133	16	<	<	X
ma-415	133	17	∞	∞	PROPN
ma-415	133	18	,	,	PUNCT
ma-415	133	19	p1	p1	NOUN
ma-415	133	20	≤	≤	PUNCT
ma-415	133	21	p−	p−	NOUN
ma-415	133	22	and	and	CCONJ
ma-415	133	23	(	(	PUNCT
ma-415	133	24	p	p	X
ma-415	133	25	(	(	PUNCT
ma-415	133	26	·	·	PUNCT
ma-415	133	27	)	)	PUNCT
ma-415	133	28	p1	p1	NOUN
ma-415	133	29	)	)	PUNCT
ma-415	133	30	′	′	NUM
ma-415	133	31	∈	∈	PROPN
ma-415	133	32	b(e	b(e	PROPN
ma-415	133	33	)	)	PUNCT
ma-415	133	34	and	and	CCONJ
ma-415	133	35	every	every	DET
ma-415	133	36	w1	w1	NOUN
ma-415	133	37	∈	∈	PROPN
ma-415	133	38	ap1	ap1	PROPN
ma-415	133	39	,	,	PUNCT
ma-415	133	40	∫	∫	PROPN
ma-415	133	41	rn	rn	PROPN
ma-415	133	42	f1(x)p1w1(x)dx	f1(x)p1w1(x)dx	PROPN
ma-415	133	43	.	.	PUNCT
ma-415	134	1	∫	∫	PROPN
ma-415	134	2	rn	rn	PROPN
ma-415	134	3	g1(x)p1w1(x)dx	g1(x)p1w1(x)dx	PROPN
ma-415	134	4	,	,	PUNCT
ma-415	134	5	(	(	PUNCT
ma-415	134	6	f	f	X
ma-415	134	7	,	,	PUNCT
ma-415	134	8	g	g	NOUN
ma-415	134	9	)	)	PUNCT
ma-415	134	10	∈	∈	PROPN
ma-415	134	11	f	f	NOUN
ma-415	134	12	.	.	PUNCT
ma-415	135	1	if	if	SCONJ
ma-415	135	2	p	p	X
ma-415	135	3	(	(	PUNCT
ma-415	135	4	·	·	PUNCT
ma-415	135	5	)	)	PUNCT
ma-415	135	6	∈	∈	PROPN
ma-415	135	7	p(e	p(e	NOUN
ma-415	135	8	)	)	PUNCT
ma-415	135	9	and	and	CCONJ
ma-415	135	10	f1	f1	PROPN
ma-415	135	11	∈	∈	PROPN
ma-415	135	12	lp(·)(e	lp(·)(e	PROPN
ma-415	135	13	)	)	PUNCT
ma-415	135	14	,	,	PUNCT
ma-415	135	15	then	then	ADV
ma-415	135	16	for	for	ADP
ma-415	135	17	all	all	DET
ma-415	135	18	(	(	PUNCT
ma-415	135	19	f1	f1	NOUN
ma-415	135	20	,	,	PUNCT
ma-415	135	21	g1	g1	PROPN
ma-415	135	22	)	)	PUNCT
ma-415	135	23	∈	∈	PROPN
ma-415	135	24	f	f	PROPN
ma-415	135	25	,	,	PUNCT
ma-415	135	26	‖f1‖lp(·)(e	‖f1‖lp(·)(e	PROPN
ma-415	135	27	)	)	PUNCT
ma-415	135	28	.	.	PUNCT
ma-415	136	1	‖g1‖lp(·)(e	‖g1‖lp(·)(e	PROPN
ma-415	136	2	)	)	PUNCT
ma-415	136	3	.	.	PUNCT
ma-415	137	1	since	since	SCONJ
ma-415	137	2	aq	aq	ADP
ma-415	137	3	/	/	SYM
ma-415	137	4	s	s	PART
ma-415	137	5	′	′	NUM
ma-415	137	6	⊂	⊂	PROPN
ma-415	137	7	a∞	a∞	PROPN
ma-415	137	8	,	,	PUNCT
ma-415	137	9	using	use	VERB
ma-415	137	10	lemma	lemma	PROPN
ma-415	137	11	3.1	3.1	NUM
ma-415	137	12	and	and	CCONJ
ma-415	137	13	lemma	lemma	PROPN
ma-415	137	14	3.2	3.2	NUM
ma-415	137	15	,	,	PUNCT
ma-415	137	16	its	its	PRON
ma-415	137	17	simple	simple	NOUN
ma-415	137	18	to	to	PART
ma-415	137	19	obtain	obtain	VERB
ma-415	137	20	the	the	DET
ma-415	137	21	lp(·)-boundednessof	lp(·)-boundednessof	NOUN
ma-415	137	22	µσψ	µσψ	NOUN
ma-415	137	23	,	,	PUNCT
ma-415	137	24	s	s	PART
ma-415	137	25	and	and	CCONJ
ma-415	137	26	µ∗,σψ	µ∗,σψ	PROPN
ma-415	137	27	,	,	PUNCT
ma-415	137	28	λ	λ	PROPN
ma-415	137	29	.	.	PUNCT
ma-415	137	30	theorem	theorem	VERB
ma-415	137	31	3.3	3.3	NUM
ma-415	137	32	.	.	PUNCT
ma-415	137	33	assume	assume	VERB
ma-415	137	34	that	that	SCONJ
ma-415	137	35	p1	p1	PROPN
ma-415	137	36	(	(	PUNCT
ma-415	137	37	·	·	PUNCT
ma-415	137	38	)	)	PUNCT
ma-415	137	39	∈	∈	PROPN
ma-415	137	40	b(rn	b(rn	PROPN
ma-415	137	41	)	)	PUNCT
ma-415	137	42	,	,	PUNCT
ma-415	137	43	q1	q1	PROPN
ma-415	137	44	(	(	PUNCT
ma-415	137	45	·	·	PUNCT
ma-415	137	46	)	)	PUNCT
ma-415	137	47	,	,	PUNCT
ma-415	137	48	q2	q2	NOUN
ma-415	137	49	(	(	PUNCT
ma-415	137	50	·	·	PUNCT
ma-415	137	51	)	)	PUNCT
ma-415	137	52	∈	∈	PROPN
ma-415	137	53	p(rn	p(rn	PROPN
ma-415	137	54	)	)	PUNCT
ma-415	137	55	,	,	PUNCT
ma-415	137	56	λ	λ	X
ma-415	137	57	>	>	X
ma-415	137	58	2	2	NUM
ma-415	137	59	,	,	PUNCT
ma-415	137	60	2σ	2σ	NUM
ma-415	137	61	−	−	PROPN
ma-415	137	62	n	n	CCONJ
ma-415	137	63	>	>	X
ma-415	137	64	0	0	NUM
ma-415	137	65	,	,	PUNCT
ma-415	137	66	and	and	CCONJ
ma-415	137	67	ψ	ψ	X
ma-415	137	68	∈	∈	PROPN
ma-415	137	69	l∞(rn	l∞(rn	PROPN
ma-415	137	70	)	)	PUNCT
ma-415	137	71	×	×	PROPN
ma-415	137	72	l2(sn−1	l2(sn−1	NOUN
ma-415	137	73	)	)	PUNCT
ma-415	137	74	satisfies	satisfie	NOUN
ma-415	137	75	(	(	PUNCT
ma-415	137	76	1	1	NUM
ma-415	137	77	)	)	PUNCT
ma-415	137	78	and	and	CCONJ
ma-415	137	79	(	(	PUNCT
ma-415	137	80	2	2	NUM
ma-415	137	81	)	)	PUNCT
ma-415	137	82	.	.	PUNCT
ma-415	138	1	let	let	VERB
ma-415	138	2	α	α	PRON
ma-415	138	3	(	(	PUNCT
ma-415	138	4	·	·	PUNCT
ma-415	138	5	)	)	PUNCT
ma-415	138	6	∈	∈	PROPN
ma-415	138	7	l∞(rn	l∞(rn	PROPN
ma-415	138	8	)	)	PUNCT
ma-415	138	9	be	be	AUX
ma-415	138	10	a	a	DET
ma-415	138	11	function	function	NOUN
ma-415	138	12	that	that	PRON
ma-415	138	13	is	be	AUX
ma-415	138	14	log	log	NOUN
ma-415	138	15	-	-	PUNCT
ma-415	138	16	hölder	hölder	NOUN
ma-415	138	17	continuous	continuous	ADJ
ma-415	138	18	both	both	CCONJ
ma-415	138	19	at	at	ADP
ma-415	138	20	the	the	DET
ma-415	138	21	origin	origin	NOUN
ma-415	138	22	and	and	CCONJ
ma-415	138	23	at	at	ADP
ma-415	138	24	infinity	infinity	NOUN
ma-415	138	25	,	,	PUNCT
ma-415	138	26	such	such	ADJ
ma-415	138	27	that	that	SCONJ
ma-415	138	28	−nδ11	−nδ11	PROPN
ma-415	138	29	<	<	X
ma-415	138	30	α−	α−	ADP
ma-415	138	31	≤	≤	NOUN
ma-415	138	32	α+	α+	PUNCT
ma-415	138	33	<	<	X
ma-415	138	34	nδ12	nδ12	PROPN
ma-415	138	35	,	,	PUNCT
ma-415	138	36	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	PROPN
ma-415	138	37	eur	eur	PROPN
ma-415	138	38	.	.	PUNCT
ma-415	139	1	j.	j.	PROPN
ma-415	139	2	math	math	PROPN
ma-415	139	3	.	.	PUNCT
ma-415	140	1	anal	anal	PROPN
ma-415	140	2	.	.	PUNCT
ma-415	141	1	10.28924	10.28924	NUM
ma-415	141	2	/	/	SYM
ma-415	141	3	ada	ada	PROPN
ma-415	141	4	/	/	SYM
ma-415	141	5	ma.5.22	ma.5.22	NOUN
ma-415	141	6	6	6	NUM
ma-415	141	7	where	where	SCONJ
ma-415	141	8	δn1	δn1	ADJ
ma-415	141	9	,	,	PUNCT
ma-415	141	10	δn2	δn2	X
ma-415	141	11	(	(	PUNCT
ma-415	141	12	n	n	NOUN
ma-415	141	13	=	=	SYM
ma-415	141	14	1	1	NUM
ma-415	141	15	,	,	PUNCT
ma-415	141	16	2	2	NUM
ma-415	141	17	)	)	PUNCT
ma-415	141	18	are	be	AUX
ma-415	141	19	the	the	DET
ma-415	141	20	same	same	ADJ
ma-415	141	21	as	as	ADP
ma-415	141	22	in	in	ADP
ma-415	141	23	lemma	lemma	PROPN
ma-415	141	24	2.4	2.4	NUM
ma-415	141	25	.	.	PUNCT
ma-415	142	1	then	then	ADV
ma-415	142	2	,	,	PUNCT
ma-415	142	3	µσψ	µσψ	INTJ
ma-415	142	4	,	,	PUNCT
ma-415	142	5	s	s	PART
ma-415	142	6	operator	operator	NOUN
ma-415	142	7	is	be	AUX
ma-415	142	8	bounded	bound	VERB
ma-415	142	9	from	from	ADP
ma-415	142	10	k̇	k̇	PROPN
ma-415	142	11	α	α	PROPN
ma-415	142	12	(	(	PUNCT
ma-415	142	13	·	·	PUNCT
ma-415	142	14	)	)	PUNCT
ma-415	142	15	p1(·),q1(·)(rn	p1(·),q1(·)(rn	NOUN
ma-415	142	16	)	)	PUNCT
ma-415	142	17	to	to	ADP
ma-415	142	18	k̇α	k̇α	PROPN
ma-415	142	19	(	(	PUNCT
ma-415	142	20	·	·	PUNCT
ma-415	142	21	)	)	PUNCT
ma-415	142	22	p1(·),q2(·)(rn	p1(·),q2(·)(rn	PUNCT
ma-415	142	23	)	)	PUNCT
ma-415	142	24	for	for	ADP
ma-415	142	25	all	all	DET
ma-415	142	26	f	f	PROPN
ma-415	142	27	∈	∈	PROPN
ma-415	142	28	k̇α	k̇α	PROPN
ma-415	142	29	(	(	PUNCT
ma-415	142	30	·	·	PUNCT
ma-415	142	31	)	)	PUNCT
ma-415	142	32	p1(·),q1(·)(rn	p1(·),q1(·)(rn	X
ma-415	142	33	)	)	PUNCT
ma-415	142	34	.	.	PUNCT
ma-415	143	1	theorem	theorem	VERB
ma-415	143	2	3.4	3.4	NUM
ma-415	143	3	.	.	PUNCT
ma-415	144	1	assume	assume	VERB
ma-415	144	2	that	that	SCONJ
ma-415	144	3	p1	p1	PROPN
ma-415	144	4	(	(	PUNCT
ma-415	144	5	·	·	PUNCT
ma-415	144	6	)	)	PUNCT
ma-415	144	7	∈	∈	PROPN
ma-415	144	8	b(rn	b(rn	PROPN
ma-415	144	9	)	)	PUNCT
ma-415	144	10	,	,	PUNCT
ma-415	144	11	q1	q1	PROPN
ma-415	144	12	(	(	PUNCT
ma-415	144	13	·	·	PUNCT
ma-415	144	14	)	)	PUNCT
ma-415	144	15	,	,	PUNCT
ma-415	144	16	q2	q2	NOUN
ma-415	144	17	(	(	PUNCT
ma-415	144	18	·	·	PUNCT
ma-415	144	19	)	)	PUNCT
ma-415	144	20	∈	∈	PROPN
ma-415	144	21	p(rn	p(rn	PROPN
ma-415	144	22	)	)	PUNCT
ma-415	144	23	,	,	PUNCT
ma-415	144	24	λ	λ	X
ma-415	144	25	>	>	X
ma-415	144	26	2	2	NUM
ma-415	144	27	,	,	PUNCT
ma-415	144	28	2σ	2σ	NUM
ma-415	144	29	−	−	PROPN
ma-415	144	30	n	n	CCONJ
ma-415	144	31	>	>	X
ma-415	144	32	0	0	NUM
ma-415	144	33	,	,	PUNCT
ma-415	144	34	and	and	CCONJ
ma-415	144	35	ψ	ψ	X
ma-415	144	36	∈	∈	PROPN
ma-415	144	37	l∞(rn	l∞(rn	PROPN
ma-415	144	38	)	)	PUNCT
ma-415	144	39	×	×	PROPN
ma-415	144	40	l2(sn−1	l2(sn−1	NOUN
ma-415	144	41	)	)	PUNCT
ma-415	144	42	satisfies	satisfie	NOUN
ma-415	144	43	(	(	PUNCT
ma-415	144	44	1	1	NUM
ma-415	144	45	)	)	PUNCT
ma-415	144	46	and	and	CCONJ
ma-415	144	47	(	(	PUNCT
ma-415	144	48	2	2	NUM
ma-415	144	49	)	)	PUNCT
ma-415	144	50	.	.	PUNCT
ma-415	145	1	let	let	VERB
ma-415	145	2	α	α	PRON
ma-415	145	3	(	(	PUNCT
ma-415	145	4	·	·	PUNCT
ma-415	145	5	)	)	PUNCT
ma-415	145	6	∈	∈	PROPN
ma-415	145	7	l∞(rn	l∞(rn	PROPN
ma-415	145	8	)	)	PUNCT
ma-415	145	9	be	be	AUX
ma-415	145	10	a	a	DET
ma-415	145	11	function	function	NOUN
ma-415	145	12	that	that	PRON
ma-415	145	13	is	be	AUX
ma-415	145	14	log	log	NOUN
ma-415	145	15	-	-	PUNCT
ma-415	145	16	hölder	hölder	NOUN
ma-415	145	17	continuous	continuous	ADJ
ma-415	145	18	both	both	CCONJ
ma-415	145	19	at	at	ADP
ma-415	145	20	the	the	DET
ma-415	145	21	origin	origin	NOUN
ma-415	145	22	and	and	CCONJ
ma-415	145	23	at	at	ADP
ma-415	145	24	infinity	infinity	NOUN
ma-415	145	25	,	,	PUNCT
ma-415	145	26	such	such	ADJ
ma-415	145	27	that	that	SCONJ
ma-415	145	28	−nδ11	−nδ11	PROPN
ma-415	145	29	<	<	X
ma-415	145	30	α−	α−	ADP
ma-415	145	31	≤	≤	NOUN
ma-415	145	32	α+	α+	PUNCT
ma-415	145	33	<	<	X
ma-415	145	34	nδ12	nδ12	PROPN
ma-415	145	35	,	,	PUNCT
ma-415	145	36	where	where	SCONJ
ma-415	145	37	δn1	δn1	ADJ
ma-415	145	38	,	,	PUNCT
ma-415	145	39	δn2	δn2	X
ma-415	145	40	(	(	PUNCT
ma-415	145	41	n	n	NOUN
ma-415	145	42	=	=	SYM
ma-415	145	43	1	1	NUM
ma-415	145	44	,	,	PUNCT
ma-415	145	45	2	2	NUM
ma-415	145	46	)	)	PUNCT
ma-415	145	47	are	be	AUX
ma-415	145	48	the	the	DET
ma-415	145	49	same	same	ADJ
ma-415	145	50	as	as	ADP
ma-415	145	51	in	in	ADP
ma-415	145	52	lemma	lemma	PROPN
ma-415	145	53	2.4	2.4	NUM
ma-415	145	54	.	.	PUNCT
ma-415	146	1	then	then	ADV
ma-415	146	2	,	,	PUNCT
ma-415	146	3	µ∗,σψ	µ∗,σψ	PROPN
ma-415	146	4	,	,	PUNCT
ma-415	146	5	λ	λ	NOUN
ma-415	146	6	operator	operator	NOUN
ma-415	146	7	is	be	AUX
ma-415	146	8	bounded	bound	VERB
ma-415	146	9	from	from	ADP
ma-415	146	10	k̇	k̇	PROPN
ma-415	146	11	α	α	PROPN
ma-415	146	12	(	(	PUNCT
ma-415	146	13	·	·	PUNCT
ma-415	146	14	)	)	PUNCT
ma-415	146	15	p1(·),q1(·)(rn	p1(·),q1(·)(rn	NOUN
ma-415	146	16	)	)	PUNCT
ma-415	146	17	to	to	ADP
ma-415	146	18	k̇α	k̇α	PROPN
ma-415	146	19	(	(	PUNCT
ma-415	146	20	·	·	PUNCT
ma-415	146	21	)	)	PUNCT
ma-415	146	22	p1(·),q2(·)(rn	p1(·),q2(·)(rn	PUNCT
ma-415	146	23	)	)	PUNCT
ma-415	146	24	for	for	ADP
ma-415	146	25	all	all	DET
ma-415	146	26	f	f	PROPN
ma-415	146	27	∈	∈	PROPN
ma-415	146	28	k̇α	k̇α	PROPN
ma-415	146	29	(	(	PUNCT
ma-415	146	30	·	·	PUNCT
ma-415	146	31	)	)	PUNCT
ma-415	146	32	p1(·),q1(·)(rn	p1(·),q1(·)(rn	NUM
ma-415	146	33	)	)	PUNCT
ma-415	146	34	.	.	PUNCT
ma-415	147	1	before	before	ADP
ma-415	147	2	proving	prove	VERB
ma-415	147	3	theorems	theorem	NOUN
ma-415	147	4	,	,	PUNCT
ma-415	147	5	we	we	PRON
ma-415	147	6	first	first	ADV
ma-415	147	7	establish	establish	VERB
ma-415	147	8	a	a	DET
ma-415	147	9	necessary	necessary	ADJ
ma-415	147	10	inequality	inequality	NOUN
ma-415	147	11	.	.	PUNCT
ma-415	148	1	remark	remark	PROPN
ma-415	148	2	.	.	PUNCT
ma-415	149	1	let	let	VERB
ma-415	149	2	1	1	NUM
ma-415	149	3	≤	≤	NUM
ma-415	149	4	pm	pm	NOUN
ma-415	149	5	<	<	X
ma-415	149	6	∞	∞	PROPN
ma-415	149	7	,	,	PUNCT
ma-415	149	8	am	be	AUX
ma-415	149	9	≥	≥	NOUN
ma-415	149	10	0	0	NUM
ma-415	149	11	,	,	PUNCT
ma-415	149	12	m	m	PROPN
ma-415	149	13	∈	∈	NOUN
ma-415	149	14	n.	n.	NOUN
ma-415	149	15	we	we	PRON
ma-415	149	16	have	have	VERB
ma-415	149	17	∞∑	∞∑	NUM
ma-415	149	18	m=0	m=0	PROPN
ma-415	149	19	apmm	apmm	ADJ
ma-415	149	20	≤	≤	NUM
ma-415	149	21	(	(	PUNCT
ma-415	149	22	∞∑	∞∑	NUM
ma-415	149	23	m=0	m=0	PROPN
ma-415	149	24	am	be	AUX
ma-415	149	25	)	)	PUNCT
ma-415	149	26	p•	p•	NOUN
ma-415	149	27	,	,	PUNCT
ma-415	149	28	here	here	ADV
ma-415	149	29	p•	p•	NOUN
ma-415	149	30	=	=	SYM
ma-415	149	31			NUM
ma-415	149	32	min	min	PROPN
ma-415	149	33	m∈n	m∈n	PROPN
ma-415	149	34	pm	pm	NOUN
ma-415	149	35	if	if	SCONJ
ma-415	149	36	∞∑	∞∑	DET
ma-415	149	37	m=0	m=0	PROPN
ma-415	149	38	am	be	AUX
ma-415	149	39	≤	≤	NOUN
ma-415	149	40	1	1	NUM
ma-415	149	41	,	,	PUNCT
ma-415	149	42	max	max	PROPN
ma-415	149	43	m∈n	m∈n	PROPN
ma-415	149	44	pm	pm	PROPN
ma-415	149	45	if	if	SCONJ
ma-415	149	46	∞∑	∞∑	NUM
ma-415	149	47	m=0	m=0	PROPN
ma-415	149	48	am	be	AUX
ma-415	149	49	>	>	X
ma-415	149	50	1	1	NUM
ma-415	149	51	.	.	PUNCT
ma-415	149	52	remark	remark	PROPN
ma-415	149	53	.	.	PUNCT
ma-415	150	1	from	from	ADP
ma-415	150	2	(	(	PUNCT
ma-415	150	3	[	[	X
ma-415	150	4	11	11	NUM
ma-415	150	5	]	]	PUNCT
ma-415	150	6	,	,	PUNCT
ma-415	150	7	p.89	p.89	X
ma-415	150	8	]	]	PUNCT
ma-415	150	9	)	)	PUNCT
ma-415	150	10	,	,	PUNCT
ma-415	150	11	we	we	PRON
ma-415	150	12	recall	recall	VERB
ma-415	150	13	the	the	DET
ma-415	150	14	estimate	estimate	NOUN
ma-415	150	15	µσψ	µσψ	NOUN
ma-415	150	16	,	,	PUNCT
ma-415	150	17	s	s	PART
ma-415	150	18	f	f	X
ma-415	150	19	(	(	PUNCT
ma-415	150	20	x	x	NOUN
ma-415	150	21	)	)	PUNCT
ma-415	150	22	≤	≤	NOUN
ma-415	150	23	2nλµ∗,σσ	2nλµ∗,σσ	NUM
ma-415	150	24	,	,	PUNCT
ma-415	150	25	λf	λf	X
ma-415	150	26	(	(	PUNCT
ma-415	150	27	x	x	NOUN
ma-415	150	28	)	)	PUNCT
ma-415	150	29	.	.	PUNCT
ma-415	151	1	therefore	therefore	ADV
ma-415	151	2	,	,	PUNCT
ma-415	151	3	we	we	PRON
ma-415	151	4	presentonly	presentonly	ADV
ma-415	151	5	the	the	DET
ma-415	151	6	proof	proof	NOUN
ma-415	151	7	of	of	ADP
ma-415	151	8	theorem	theorem	ADJ
ma-415	151	9	3.4	3.4	NUM
ma-415	151	10	.	.	PUNCT
ma-415	152	1	proof	proof	NOUN
ma-415	152	2	.	.	PUNCT
ma-415	153	1	we	we	PRON
ma-415	153	2	present	present	VERB
ma-415	153	3	the	the	DET
ma-415	153	4	proof	proof	NOUN
ma-415	153	5	of	of	ADP
ma-415	153	6	k̇α(·),q	k̇α(·),q	PROPN
ma-415	153	7	(	(	PUNCT
ma-415	153	8	·	·	PUNCT
ma-415	153	9	)	)	PUNCT
ma-415	153	10	p	p	X
ma-415	153	11	(	(	PUNCT
ma-415	153	12	·	·	PUNCT
ma-415	153	13	)	)	PUNCT
ma-415	153	14	(	(	PUNCT
ma-415	153	15	rn	rn	NOUN
ma-415	153	16	)	)	PUNCT
ma-415	153	17	(	(	PUNCT
ma-415	153	18	homogeneous	homogeneous	ADJ
ma-415	153	19	case	case	NOUN
ma-415	153	20	)	)	PUNCT
ma-415	153	21	.	.	PUNCT
ma-415	154	1	the	the	DET
ma-415	154	2	same	same	ADJ
ma-415	154	3	argument	argument	NOUN
ma-415	154	4	holds	hold	VERB
ma-415	154	5	truefor	truefor	ADP
ma-415	154	6	kα(·),q	kα(·),q	PROPN
ma-415	154	7	(	(	PUNCT
ma-415	154	8	·	·	PUNCT
ma-415	154	9	)	)	PUNCT
ma-415	155	1	p	p	X
ma-415	155	2	(	(	PUNCT
ma-415	155	3	·	·	PUNCT
ma-415	155	4	)	)	PUNCT
ma-415	155	5	(	(	PUNCT
ma-415	155	6	rn	rn	NOUN
ma-415	155	7	)	)	PUNCT
ma-415	155	8	(	(	PUNCT
ma-415	155	9	nonhomogeneous	nonhomogeneous	ADJ
ma-415	155	10	case).let	case).let	PROPN
ma-415	155	11	f	f	PROPN
ma-415	155	12	∈	∈	PROPN
ma-415	155	13	k̇α(·),q1	k̇α(·),q1	PROPN
ma-415	155	14	(	(	PUNCT
ma-415	155	15	·	·	PUNCT
ma-415	155	16	)	)	PUNCT
ma-415	155	17	p1	p1	NOUN
ma-415	155	18	(	(	PUNCT
ma-415	155	19	·	·	PUNCT
ma-415	155	20	)	)	PUNCT
ma-415	155	21	(	(	PUNCT
ma-415	155	22	rn	rn	NOUN
ma-415	155	23	)	)	PUNCT
ma-415	155	24	.	.	PUNCT
ma-415	156	1	decomposet	decomposet	VERB
ma-415	156	2	f	f	NOUN
ma-415	156	3	as	as	ADP
ma-415	156	4	:	:	PUNCT
ma-415	156	5	f	f	PROPN
ma-415	156	6	(	(	PUNCT
ma-415	156	7	x	x	X
ma-415	156	8	)	)	PUNCT
ma-415	156	9	=	=	SYM
ma-415	157	1	∞∑	∞∑	NUM
ma-415	157	2	j=−∞	j=−∞	NOUN
ma-415	157	3	f	f	X
ma-415	157	4	(	(	PUNCT
ma-415	157	5	x)χj(x	x)χj(x	NUM
ma-415	157	6	)	)	PUNCT
ma-415	157	7	=	=	PUNCT
ma-415	158	1	∞∑	∞∑	NUM
ma-415	158	2	j=−∞	j=−∞	NUM
ma-415	158	3	fj(x	fj(x	NOUN
ma-415	158	4	)	)	PUNCT
ma-415	158	5	.	.	PUNCT
ma-415	159	1	from	from	ADP
ma-415	159	2	homogeneous	homogeneous	ADJ
ma-415	159	3	k̇α(·),q	k̇α(·),q	PROPN
ma-415	159	4	(	(	PUNCT
ma-415	159	5	·	·	PUNCT
ma-415	159	6	)	)	PUNCT
ma-415	159	7	p	p	X
ma-415	159	8	(	(	PUNCT
ma-415	159	9	·	·	PUNCT
ma-415	159	10	)	)	PUNCT
ma-415	159	11	(	(	PUNCT
ma-415	159	12	rn	rn	NOUN
ma-415	159	13	)	)	PUNCT
ma-415	159	14	(	(	PUNCT
ma-415	159	15	definition	definition	NOUN
ma-415	159	16	2.2	2.2	NUM
ma-415	159	17	)	)	PUNCT
ma-415	159	18	,	,	PUNCT
ma-415	159	19	we	we	PRON
ma-415	159	20	have	have	VERB
ma-415	159	21	‖µ∗,σψ	‖µ∗,σψ	NOUN
ma-415	159	22	,	,	PUNCT
ma-415	159	23	λ(f	λ(f	PROPN
ma-415	159	24	)	)	PUNCT
ma-415	159	25	‖	‖	PROPN
ma-415	159	26	k̇	k̇	PROPN
ma-415	159	27	α(·),q2	α(·),q2	PROPN
ma-415	159	28	(	(	PUNCT
ma-415	159	29	·	·	PUNCT
ma-415	159	30	)	)	PUNCT
ma-415	159	31	p1	p1	NOUN
ma-415	159	32	(	(	PUNCT
ma-415	159	33	·	·	PUNCT
ma-415	159	34	)	)	PUNCT
ma-415	159	35	(	(	PUNCT
ma-415	159	36	rn	rn	NOUN
ma-415	159	37	)	)	PUNCT
ma-415	159	38	=	=	VERB
ma-415	159	39	inf	inf	NOUN
ma-415	160	1	η	η	NOUN
ma-415	160	2	>	>	X
ma-415	160	3	0	0	PUNCT
ma-415	161	1	:	:	PUNCT
ma-415	161	2	∞∑	∞∑	NUM
ma-415	161	3	k=−∞	k=−∞	X
ma-415	161	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	161	5	(	(	PUNCT
ma-415	161	6	2kα(·)|µ∗,σψ	2kα(·)|µ∗,σψ	NUM
ma-415	161	7	,	,	PUNCT
ma-415	161	8	λ(f	λ(f	PROPN
ma-415	161	9	)	)	PUNCT
ma-415	161	10	χk	χk	NOUN
ma-415	161	11	|	|	ADV
ma-415	161	12	β	β	NOUN
ma-415	161	13	)	)	PUNCT
ma-415	161	14	q2	q2	NOUN
ma-415	161	15	(	(	PUNCT
ma-415	161	16	·	·	PUNCT
ma-415	161	17	)	)	PUNCT
ma-415	161	18	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	162	1	l	l	NOUN
ma-415	162	2	p1	p1	PROPN
ma-415	162	3	(	(	PUNCT
ma-415	162	4	·	·	PUNCT
ma-415	162	5	)	)	PUNCT
ma-415	162	6	q2	q2	NOUN
ma-415	162	7	(	(	PUNCT
ma-415	162	8	·	·	PUNCT
ma-415	162	9	)	)	PUNCT
ma-415	162	10	≤	≤	NOUN
ma-415	162	11	1	1	NUM
ma-415	162	12			NOUN
ma-415	162	13	.	.	PUNCT
ma-415	163	1	we	we	PRON
ma-415	163	2	have	have	VERB
ma-415	163	3	∥∥∥∥∥	∥∥∥∥∥	NUM
ma-415	163	4	(	(	PUNCT
ma-415	163	5	2kα(·)|µ∗,σψ	2kα(·)|µ∗,σψ	NUM
ma-415	163	6	,	,	PUNCT
ma-415	163	7	λ(f	λ(f	PROPN
ma-415	163	8	)	)	PUNCT
ma-415	163	9	χk	χk	NOUN
ma-415	163	10	|	|	ADV
ma-415	163	11	β	β	NOUN
ma-415	163	12	)	)	PUNCT
ma-415	163	13	q2	q2	NOUN
ma-415	163	14	(	(	PUNCT
ma-415	163	15	·	·	PUNCT
ma-415	163	16	)	)	PUNCT
ma-415	163	17	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	163	18	l	l	NOUN
ma-415	163	19	p1	p1	PROPN
ma-415	163	20	(	(	PUNCT
ma-415	163	21	·	·	PUNCT
ma-415	163	22	)	)	PUNCT
ma-415	163	23	q2	q2	NOUN
ma-415	163	24	(	(	PUNCT
ma-415	163	25	·	·	PUNCT
ma-415	163	26	)	)	PUNCT
ma-415	163	27	≤	≤	NOUN
ma-415	163	28	∥∥∥∥∥∥∥	∥∥∥∥∥∥∥	NUM
ma-415	163	29	2kα(·)|	2kα(·)|	ADP
ma-415	163	30	∞∑	∞∑	PROPN
ma-415	163	31	j=−∞	j=−∞	PROPN
ma-415	163	32	µ∗,σψ	µ∗,σψ	PROPN
ma-415	163	33	,	,	PUNCT
ma-415	163	34	λ(fj	λ(fj	NUM
ma-415	163	35	)	)	PUNCT
ma-415	163	36	χk	χk	NOUN
ma-415	163	37	|	|	ADV
ma-415	163	38	β01+β02+β03	β01+β02+β03	ADP
ma-415	163	39	q2(·)∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥	PROPN
ma-415	163	40	l	l	NOUN
ma-415	163	41	p1	p1	PROPN
ma-415	163	42	(	(	PUNCT
ma-415	163	43	·	·	PUNCT
ma-415	163	44	)	)	PUNCT
ma-415	163	45	q2	q2	NOUN
ma-415	163	46	(	(	PUNCT
ma-415	163	47	·	·	PUNCT
ma-415	163	48	)	)	PUNCT
ma-415	163	49	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	VERB
ma-415	163	50	eur	eur	PROPN
ma-415	163	51	.	.	PUNCT
ma-415	164	1	j.	j.	PROPN
ma-415	164	2	math	math	PROPN
ma-415	164	3	.	.	PUNCT
ma-415	165	1	anal	anal	PROPN
ma-415	165	2	.	.	PUNCT
ma-415	166	1	10.28924	10.28924	NUM
ma-415	166	2	/	/	SYM
ma-415	166	3	ada	ada	PROPN
ma-415	166	4	/	/	SYM
ma-415	166	5	ma.5.22	ma.5.22	NOUN
ma-415	166	6	7	7	NUM
ma-415	166	7	≤	≤	NUM
ma-415	166	8	c	c	NOUN
ma-415	166	9	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	166	10	2kα(·)|	2kα(·)|	PROPN
ma-415	166	11	k−2∑	k−2∑	PROPN
ma-415	166	12	j=−∞	j=−∞	PROPN
ma-415	166	13	µ∗,σψ	µ∗,σψ	PROPN
ma-415	166	14	,	,	PUNCT
ma-415	166	15	λ(fj	λ(fj	NUM
ma-415	166	16	)	)	PUNCT
ma-415	166	17	χk	χk	NOUN
ma-415	166	18	|	|	ADV
ma-415	166	19	β01	β01	NOUN
ma-415	166	20			PROPN
ma-415	166	21	q2	q2	NOUN
ma-415	166	22	(	(	PUNCT
ma-415	166	23	·	·	PUNCT
ma-415	166	24	)	)	PUNCT
ma-415	166	25	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	167	1	l	l	PROPN
ma-415	167	2	p1	p1	PROPN
ma-415	167	3	(	(	PUNCT
ma-415	167	4	·	·	PUNCT
ma-415	167	5	)	)	PUNCT
ma-415	167	6	q2	q2	NOUN
ma-415	167	7	(	(	PUNCT
ma-415	167	8	·	·	PUNCT
ma-415	167	9	)	)	PUNCT
ma-415	168	1	+	+	NUM
ma-415	168	2	c	c	NOUN
ma-415	168	3	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	169	1	2kα(·)|	2kα(·)|	PROPN
ma-415	169	2	k+1∑	k+1∑	PROPN
ma-415	169	3	j	j	PROPN
ma-415	170	1	=	=	PROPN
ma-415	170	2	k−1	k−1	PROPN
ma-415	170	3	µ∗,σψ	µ∗,σψ	NOUN
ma-415	170	4	,	,	PUNCT
ma-415	170	5	λ(fj	λ(fj	NUM
ma-415	170	6	)	)	PUNCT
ma-415	170	7	χk	χk	PROPN
ma-415	170	8	|	|	ADV
ma-415	170	9	β02	β02	PROPN
ma-415	170	10			PROPN
ma-415	170	11	q2	q2	PROPN
ma-415	170	12	(	(	PUNCT
ma-415	170	13	·	·	PUNCT
ma-415	170	14	)	)	PUNCT
ma-415	170	15	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	171	1	l	l	PROPN
ma-415	171	2	p1	p1	PROPN
ma-415	171	3	(	(	PUNCT
ma-415	171	4	·	·	PUNCT
ma-415	171	5	)	)	PUNCT
ma-415	171	6	q2	q2	NOUN
ma-415	171	7	(	(	PUNCT
ma-415	171	8	·	·	PUNCT
ma-415	171	9	)	)	PUNCT
ma-415	172	1	+	+	ADP
ma-415	172	2	c	c	NOUN
ma-415	172	3	∥∥∥∥∥∥∥	∥∥∥∥∥∥∥	NUM
ma-415	172	4	2kα(·)|	2kα(·)|	ADP
ma-415	172	5	∞∑	∞∑	PROPN
ma-415	172	6	j	j	PROPN
ma-415	172	7	=	=	SYM
ma-415	172	8	k+2	k+2	PROPN
ma-415	172	9	µ∗,σψ	µ∗,σψ	PROPN
ma-415	172	10	,	,	PUNCT
ma-415	172	11	λ(fj	λ(fj	NUM
ma-415	172	12	)	)	PUNCT
ma-415	172	13	χk	χk	PROPN
ma-415	173	1	|	|	ADV
ma-415	173	2	β03	β03	NUM
ma-415	174	1	q2(·)∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥	PROPN
ma-415	174	2	l	l	PROPN
ma-415	174	3	p1	p1	PROPN
ma-415	174	4	(	(	PUNCT
ma-415	174	5	·	·	PUNCT
ma-415	174	6	)	)	PUNCT
ma-415	174	7	q2	q2	NOUN
ma-415	174	8	(	(	PUNCT
ma-415	174	9	·	·	PUNCT
ma-415	174	10	)	)	PUNCT
ma-415	174	11	,	,	PUNCT
ma-415	174	12	where	where	SCONJ
ma-415	174	13	β01	β01	NOUN
ma-415	174	14	=	=	SYM
ma-415	174	15	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	174	16	{	{	PUNCT
ma-415	174	17	2kα(·)|	2kα(·)|	NUM
ma-415	174	18	k−2∑	k−2∑	PROPN
ma-415	174	19	j=−∞	j=−∞	PROPN
ma-415	174	20	µ∗,σψ	µ∗,σψ	PROPN
ma-415	174	21	,	,	PUNCT
ma-415	174	22	λ(fj)χk	λ(fj)χk	NOUN
ma-415	174	23	|	|	NOUN
ma-415	174	24	}	}	PUNCT
ma-415	174	25	∞	∞	NUM
ma-415	174	26	k=−∞	k=−∞	X
ma-415	174	27	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	174	28	lq2(·)(lp1	lq2(·)(lp1	PROPN
ma-415	174	29	(	(	PUNCT
ma-415	174	30	·	·	PUNCT
ma-415	174	31	)	)	PUNCT
ma-415	174	32	)	)	PUNCT
ma-415	174	33	,	,	PUNCT
ma-415	174	34	β02	β02	PROPN
ma-415	174	35	=	=	SYM
ma-415	174	36	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	174	37	{	{	PUNCT
ma-415	174	38	2kα(·)|	2kα(·)|	NUM
ma-415	174	39	k+1∑	k+1∑	PROPN
ma-415	174	40	j	j	PROPN
ma-415	174	41	=	=	PROPN
ma-415	174	42	k−1	k−1	PROPN
ma-415	174	43	µ∗,σψ	µ∗,σψ	NOUN
ma-415	174	44	,	,	PUNCT
ma-415	174	45	λ(fj)χk	λ(fj)χk	NOUN
ma-415	174	46	|	|	NOUN
ma-415	174	47	}	}	PUNCT
ma-415	174	48	∞	∞	NUM
ma-415	174	49	k=−∞	k=−∞	X
ma-415	174	50	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	174	51	lq2(·)(lp1	lq2(·)(lp1	PROPN
ma-415	174	52	(	(	PUNCT
ma-415	174	53	·	·	PUNCT
ma-415	174	54	)	)	PUNCT
ma-415	174	55	)	)	PUNCT
ma-415	174	56	,	,	PUNCT
ma-415	174	57	β03	β03	NUM
ma-415	174	58	=	=	SYM
ma-415	174	59	∥∥∥∥∥	∥∥∥∥∥	X
ma-415	174	60	{	{	PUNCT
ma-415	174	61	2kα(·)|	2kα(·)|	NUM
ma-415	174	62	∞∑	∞∑	PROPN
ma-415	174	63	j	j	PROPN
ma-415	174	64	=	=	SYM
ma-415	174	65	k+2	k+2	PROPN
ma-415	174	66	µ∗,σψ	µ∗,σψ	NOUN
ma-415	174	67	,	,	PUNCT
ma-415	174	68	λ(fj)χk	λ(fj)χk	NOUN
ma-415	174	69	|	|	NOUN
ma-415	174	70	}	}	PUNCT
ma-415	174	71	∞	∞	NUM
ma-415	174	72	k=−∞	k=−∞	X
ma-415	174	73	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	174	74	lq2(·)(lp1	lq2(·)(lp1	PROPN
ma-415	174	75	(	(	PUNCT
ma-415	174	76	·	·	PUNCT
ma-415	174	77	)	)	PUNCT
ma-415	174	78	)	)	PUNCT
ma-415	174	79	.	.	PUNCT
ma-415	175	1	if	if	SCONJ
ma-415	175	2	β0	β0	NOUN
ma-415	175	3	=	=	SYM
ma-415	175	4	β01	β01	PROPN
ma-415	175	5	+	+	CCONJ
ma-415	175	6	β02	β02	NUM
ma-415	175	7	+	+	CCONJ
ma-415	175	8	β03	β03	ADJ
ma-415	175	9	thus	thus	ADV
ma-415	175	10	∞∑	∞∑	NUM
ma-415	175	11	k=−∞	k=−∞	X
ma-415	175	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	176	1	(	(	PUNCT
ma-415	176	2	2kα(·)|µ∗,σψ	2kα(·)|µ∗,σψ	NOUN
ma-415	176	3	,	,	PUNCT
ma-415	176	4	λ(fj)χk	λ(fj)χk	NOUN
ma-415	176	5	|	|	NOUN
ma-415	176	6	β0	β0	ADJ
ma-415	176	7	)	)	PUNCT
ma-415	176	8	q2	q2	NOUN
ma-415	176	9	(	(	PUNCT
ma-415	176	10	·	·	PUNCT
ma-415	176	11	)	)	PUNCT
ma-415	176	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	177	1	l	l	NOUN
ma-415	177	2	p1	p1	PROPN
ma-415	177	3	(	(	PUNCT
ma-415	177	4	·	·	PUNCT
ma-415	177	5	)	)	PUNCT
ma-415	177	6	q2	q2	NOUN
ma-415	177	7	(	(	PUNCT
ma-415	177	8	·	·	PUNCT
ma-415	177	9	)	)	PUNCT
ma-415	177	10	.	.	PUNCT
ma-415	178	1	1	1	X
ma-415	178	2	.	.	X
ma-415	178	3	then	then	ADV
ma-415	178	4	‖µ∗,σψ	‖µ∗,σψ	VERB
ma-415	178	5	,	,	PUNCT
ma-415	178	6	λ(f	λ(f	PROPN
ma-415	178	7	)	)	PUNCT
ma-415	178	8	χk‖k̇α(·),q1	χk‖k̇α(·),q1	PROPN
ma-415	178	9	(	(	PUNCT
ma-415	178	10	·	·	PUNCT
ma-415	178	11	)	)	PUNCT
ma-415	178	12	p1	p1	NOUN
ma-415	178	13	(	(	PUNCT
ma-415	178	14	·	·	PUNCT
ma-415	178	15	)	)	PUNCT
ma-415	178	16	(	(	PUNCT
ma-415	178	17	rn	rn	NOUN
ma-415	178	18	)	)	PUNCT
ma-415	178	19	.	.	PUNCT
ma-415	179	1	β0	β0	ADJ
ma-415	179	2	.	.	PUNCT
ma-415	180	1	[	[	X
ma-415	180	2	β01	β01	NOUN
ma-415	180	3	+	+	CCONJ
ma-415	180	4	β02	β02	NUM
ma-415	180	5	+	+	CCONJ
ma-415	180	6	β03].therefore	β03].therefore	CCONJ
ma-415	180	7	,	,	PUNCT
ma-415	180	8	if	if	SCONJ
ma-415	180	9	we	we	PRON
ma-415	180	10	can	can	AUX
ma-415	180	11	conclude	conclude	VERB
ma-415	180	12	that	that	DET
ma-415	180	13	β01	β01	NOUN
ma-415	180	14	≤	≤	NUM
ma-415	180	15	c‖f	c‖f	NOUN
ma-415	180	16	‖k̇α(·),q1	‖k̇α(·),q1	PROPN
ma-415	180	17	(	(	PUNCT
ma-415	180	18	·	·	PUNCT
ma-415	180	19	)	)	PUNCT
ma-415	180	20	p1	p1	NOUN
ma-415	180	21	(	(	PUNCT
ma-415	180	22	·	·	PUNCT
ma-415	180	23	)	)	PUNCT
ma-415	180	24	(	(	PUNCT
ma-415	180	25	rn	rn	NOUN
ma-415	180	26	)	)	PUNCT
ma-415	180	27	,	,	PUNCT
ma-415	180	28	β02	β02	PROPN
ma-415	180	29	≤	≤	PROPN
ma-415	180	30	c‖f	c‖f	NOUN
ma-415	180	31	‖k̇α(·),q1	‖k̇α(·),q1	PROPN
ma-415	180	32	(	(	PUNCT
ma-415	180	33	·	·	PUNCT
ma-415	180	34	)	)	PUNCT
ma-415	180	35	p1	p1	NOUN
ma-415	180	36	(	(	PUNCT
ma-415	180	37	·	·	PUNCT
ma-415	180	38	)	)	PUNCT
ma-415	180	39	(	(	PUNCT
ma-415	180	40	rn	rn	NOUN
ma-415	180	41	)	)	PUNCT
ma-415	180	42	,	,	PUNCT
ma-415	180	43	β03	β03	ADJ
ma-415	180	44	≤	≤	NUM
ma-415	180	45	c‖f	c‖f	NOUN
ma-415	180	46	‖k̇α(·),q1	‖k̇α(·),q1	PROPN
ma-415	180	47	(	(	PUNCT
ma-415	180	48	·	·	PUNCT
ma-415	180	49	)	)	PUNCT
ma-415	180	50	p1	p1	NOUN
ma-415	180	51	(	(	PUNCT
ma-415	180	52	·	·	PUNCT
ma-415	180	53	)	)	PUNCT
ma-415	180	54	(	(	PUNCT
ma-415	180	55	rn	rn	NOUN
ma-415	180	56	)	)	PUNCT
ma-415	180	57	,	,	PUNCT
ma-415	180	58	we	we	PRON
ma-415	180	59	are	be	AUX
ma-415	180	60	finished	finish	VERB
ma-415	180	61	.	.	PUNCT
ma-415	181	1	let	let	VERB
ma-415	181	2	us	we	PRON
ma-415	181	3	set	set	VERB
ma-415	181	4	β0	β0	PROPN
ma-415	181	5	=	=	PUNCT
ma-415	181	6	‖f	‖f	PRON
ma-415	181	7	‖	‖	PROPN
ma-415	181	8	k̇	k̇	PROPN
ma-415	181	9	α(·),q1	α(·),q1	PROPN
ma-415	181	10	(	(	PUNCT
ma-415	181	11	·	·	PUNCT
ma-415	181	12	)	)	PUNCT
ma-415	181	13	p1	p1	NOUN
ma-415	181	14	(	(	PUNCT
ma-415	181	15	·	·	PUNCT
ma-415	181	16	)	)	PUNCT
ma-415	181	17	(	(	PUNCT
ma-415	181	18	rn	rn	NOUN
ma-415	181	19	)	)	PUNCT
ma-415	181	20	.first	.first	VERB
ma-415	181	21	,	,	PUNCT
ma-415	181	22	we	we	PRON
ma-415	181	23	estimate	estimate	VERB
ma-415	181	24	β02	β02	PROPN
ma-415	181	25	.	.	PUNCT
ma-415	182	1	from	from	ADP
ma-415	182	2	lemma	lemma	PROPN
ma-415	182	3	2.6	2.6	NUM
ma-415	182	4	and	and	CCONJ
ma-415	182	5	lemma	lemma	PROPN
ma-415	182	6	2.7	2.7	NUM
ma-415	182	7	,	,	PUNCT
ma-415	182	8	we	we	PRON
ma-415	182	9	have	have	VERB
ma-415	182	10	∞∑	∞∑	NUM
ma-415	182	11	k=−∞	k=−∞	NOUN
ma-415	182	12	∥∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥∥	NUM
ma-415	182	13			PROPN
ma-415	183	1	2kα(·)|	2kα(·)|	NUM
ma-415	183	2	k+1∑	k+1∑	PROPN
ma-415	183	3	j	j	PROPN
ma-415	183	4	=	=	PROPN
ma-415	183	5	k−1	k−1	PROPN
ma-415	183	6	µ∗,σψ	µ∗,σψ	NOUN
ma-415	183	7	,	,	PUNCT
ma-415	183	8	λ(fj)χk	λ(fj)χk	VERB
ma-415	184	1	|	|	INTJ
ma-415	184	2	β0	β0	NOUN
ma-415	184	3			PROPN
ma-415	185	1	q2(·)∥∥∥∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥∥∥∥	PROPN
ma-415	185	2	l	l	NOUN
ma-415	185	3	p1	p1	NOUN
ma-415	185	4	(	(	PUNCT
ma-415	185	5	·	·	PUNCT
ma-415	185	6	)	)	PUNCT
ma-415	185	7	q2	q2	NOUN
ma-415	185	8	(	(	PUNCT
ma-415	185	9	·	·	PUNCT
ma-415	185	10	)	)	PUNCT
ma-415	185	11	.	.	PUNCT
ma-415	186	1	∞∑	∞∑	NUM
ma-415	186	2	k=−∞	k=−∞	NOUN
ma-415	186	3	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	X
ma-415	186	4	2kα(·)|	2kα(·)|	NUM
ma-415	186	5	k+1∑	k+1∑	PROPN
ma-415	186	6	j	j	PROPN
ma-415	186	7	=	=	PROPN
ma-415	186	8	k−1	k−1	PROPN
ma-415	186	9	µ∗,σψ	µ∗,σψ	NOUN
ma-415	186	10	,	,	PUNCT
ma-415	186	11	λ(fj)χk	λ(fj)χk	NOUN
ma-415	186	12	|	|	ADV
ma-415	186	13	β0	β0	ADJ
ma-415	186	14	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	NOUN
ma-415	186	15	(	(	PUNCT
ma-415	186	16	q0	q0	PROPN
ma-415	186	17	2	2	NUM
ma-415	186	18	)	)	PUNCT
ma-415	186	19	k	k	PROPN
ma-415	186	20	lp1	lp1	PROPN
ma-415	186	21	(	(	PUNCT
ma-415	186	22	·	·	PUNCT
ma-415	186	23	)	)	PUNCT
ma-415	186	24	.	.	PUNCT
ma-415	187	1	∞∑	∞∑	NUM
ma-415	187	2	k=−∞	k=−∞	NOUN
ma-415	187	3	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	NOUN
ma-415	187	4	|	|	ADV
ma-415	187	5	k+1∑	k+1∑	PROPN
ma-415	187	6	j	j	PROPN
ma-415	188	1	=	=	PROPN
ma-415	188	2	k−1	k−1	PROPN
ma-415	188	3	µ∗,σψ	µ∗,σψ	PROPN
ma-415	188	4	,	,	PUNCT
ma-415	188	5	λ(2αj	λ(2αj	VERB
ma-415	188	6	fj)χk	fj)χk	X
ma-415	189	1	|	|	ADV
ma-415	189	2	β0	β0	PROPN
ma-415	189	3	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	PROPN
ma-415	189	4	(	(	PUNCT
ma-415	189	5	q0	q0	PROPN
ma-415	189	6	2	2	NUM
ma-415	189	7	)	)	PUNCT
ma-415	189	8	k	k	PROPN
ma-415	189	9	lp1	lp1	PROPN
ma-415	189	10	(	(	PUNCT
ma-415	189	11	·	·	PUNCT
ma-415	189	12	)	)	PUNCT
ma-415	189	13	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	VERB
ma-415	189	14	eur	eur	PROPN
ma-415	189	15	.	.	PUNCT
ma-415	190	1	j.	j.	PROPN
ma-415	190	2	math	math	PROPN
ma-415	190	3	.	.	PUNCT
ma-415	191	1	anal	anal	PROPN
ma-415	191	2	.	.	PUNCT
ma-415	192	1	10.28924	10.28924	NUM
ma-415	192	2	/	/	SYM
ma-415	192	3	ada	ada	PROPN
ma-415	192	4	/	/	SYM
ma-415	192	5	ma.5.22	ma.5.22	NOUN
ma-415	192	6	8	8	NUM
ma-415	192	7	.	.	PUNCT
ma-415	193	1	∞∑	∞∑	NUM
ma-415	193	2	k=−∞	k=−∞	NOUN
ma-415	194	1			PROPN
ma-415	194	2	k+1∑	k+1∑	PROPN
ma-415	194	3	j	j	PROPN
ma-415	194	4	=	=	PROPN
ma-415	194	5	k−1	k−1	PROPN
ma-415	194	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	194	7	|µ∗,σψ	|µ∗,σψ	PROPN
ma-415	194	8	,	,	PUNCT
ma-415	194	9	λ(2αj	λ(2αj	NOUN
ma-415	194	10	fj)χk	fj)χk	X
ma-415	195	1	|	|	ADV
ma-415	195	2	β0	β0	PROPN
ma-415	195	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	195	4	lp1	lp1	PROPN
ma-415	195	5	(	(	PUNCT
ma-415	195	6	·	·	PUNCT
ma-415	195	7	)	)	PUNCT
ma-415	195	8	(q0	(q0	NOUN
ma-415	195	9	2	2	X
ma-415	195	10	)	)	PUNCT
ma-415	195	11	k	k	NOUN
ma-415	195	12	,	,	PUNCT
ma-415	195	13	where	where	SCONJ
ma-415	195	14	(	(	PUNCT
ma-415	195	15	q0	q0	PROPN
ma-415	195	16	2)k	2)k	NOUN
ma-415	195	17	=	=	SYM
ma-415	195	18			NOUN
ma-415	195	19	(	(	PUNCT
ma-415	195	20	q2)+	q2)+	NOUN
ma-415	195	21	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	196	1	2kα(·)|	2kα(·)|	PROPN
ma-415	196	2	k+1∑	k+1∑	PROPN
ma-415	196	3	j	j	PROPN
ma-415	197	1	=	=	PROPN
ma-415	197	2	k−1	k−1	PROPN
ma-415	197	3	µ∗,σψ	µ∗,σψ	NOUN
ma-415	197	4	,	,	PUNCT
ma-415	197	5	λ(fj	λ(fj	NUM
ma-415	197	6	)	)	PUNCT
ma-415	197	7	χk	χk	NOUN
ma-415	198	1	|	|	ADV
ma-415	198	2	β0	β0	PROPN
ma-415	198	3			PROPN
ma-415	198	4	q2	q2	PROPN
ma-415	198	5	(	(	PUNCT
ma-415	198	6	·	·	PUNCT
ma-415	198	7	)	)	PUNCT
ma-415	198	8	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	198	9	l	l	PROPN
ma-415	198	10	p1	p1	PROPN
ma-415	198	11	(	(	PUNCT
ma-415	198	12	·	·	PUNCT
ma-415	198	13	)	)	PUNCT
ma-415	198	14	q2	q2	NOUN
ma-415	198	15	(	(	PUNCT
ma-415	198	16	·	·	PUNCT
ma-415	198	17	)	)	PUNCT
ma-415	198	18	≥	≥	NOUN
ma-415	198	19	1	1	NUM
ma-415	198	20	,	,	PUNCT
ma-415	198	21	(	(	PUNCT
ma-415	198	22	q2)−	q2)−	ADP
ma-415	198	23	otherwise	otherwise	ADV
ma-415	198	24	.	.	PUNCT
ma-415	199	1	by	by	ADP
ma-415	199	2	the	the	DET
ma-415	199	3	boundedness	boundedness	NOUN
ma-415	199	4	of	of	ADP
ma-415	199	5	µ∗,σψ	µ∗,σψ	PROPN
ma-415	199	6	,	,	PUNCT
ma-415	199	7	λ	λ	PROPN
ma-415	199	8	on	on	ADP
ma-415	199	9	lp	lp	PROPN
ma-415	199	10	(	(	PUNCT
ma-415	199	11	·	·	PUNCT
ma-415	199	12	)	)	PUNCT
ma-415	199	13	,	,	PUNCT
ma-415	199	14	we	we	PRON
ma-415	199	15	have	have	VERB
ma-415	199	16	∞∑	∞∑	NUM
ma-415	199	17	k=−∞	k=−∞	NOUN
ma-415	199	18	∥∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥∥	NUM
ma-415	200	1			PROPN
ma-415	201	1	2kα(·)|	2kα(·)|	NUM
ma-415	201	2	k+1∑	k+1∑	PROPN
ma-415	201	3	j	j	PROPN
ma-415	201	4	=	=	PROPN
ma-415	201	5	k−1	k−1	PROPN
ma-415	201	6	µ∗,σψ	µ∗,σψ	NOUN
ma-415	201	7	,	,	PUNCT
ma-415	201	8	λ(fj)χk	λ(fj)χk	VERB
ma-415	202	1	|	|	INTJ
ma-415	202	2	β0	β0	NOUN
ma-415	202	3			PROPN
ma-415	203	1	q2(·)∥∥∥∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥∥∥∥	PROPN
ma-415	203	2	l	l	NOUN
ma-415	203	3	p1	p1	NOUN
ma-415	203	4	(	(	PUNCT
ma-415	203	5	·	·	PUNCT
ma-415	203	6	)	)	PUNCT
ma-415	203	7	q2	q2	NOUN
ma-415	203	8	(	(	PUNCT
ma-415	203	9	·	·	PUNCT
ma-415	203	10	)	)	PUNCT
ma-415	203	11	.	.	PUNCT
ma-415	204	1	∞∑	∞∑	NUM
ma-415	204	2	k=−∞	k=−∞	NOUN
ma-415	205	1			PROPN
ma-415	205	2	k+1∑	k+1∑	PROPN
ma-415	205	3	j	j	PROPN
ma-415	206	1	=	=	VERB
ma-415	206	2	k−1	k−1	PROPN
ma-415	206	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	206	4	|(2jα(·)fj)|	|(2jα(·)fj)|	X
ma-415	206	5	β0	β0	PROPN
ma-415	206	6	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-415	206	7	lp1	lp1	PROPN
ma-415	206	8	(	(	PUNCT
ma-415	206	9	·	·	PUNCT
ma-415	206	10	)	)	PUNCT
ma-415	206	11	(q0	(q0	NOUN
ma-415	206	12	2	2	X
ma-415	206	13	)	)	PUNCT
ma-415	206	14	k	k	NOUN
ma-415	206	15	,	,	PUNCT
ma-415	206	16	.	.	PUNCT
ma-415	207	1	∞∑	∞∑	NUM
ma-415	207	2	k=−∞	k=−∞	X
ma-415	207	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	208	1	(	(	PUNCT
ma-415	208	2	2kα(·)|fk	2kα(·)|fk	NUM
ma-415	208	3	|	|	ADV
ma-415	208	4	β0	β0	PROPN
ma-415	208	5	)	)	PUNCT
ma-415	208	6	q1	q1	PROPN
ma-415	208	7	(	(	PUNCT
ma-415	208	8	·	·	PUNCT
ma-415	208	9	)	)	PUNCT
ma-415	208	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	209	1	(	(	PUNCT
ma-415	209	2	q1	q1	PROPN
ma-415	209	3	2	2	NUM
ma-415	209	4	)	)	PUNCT
ma-415	209	5	k	k	PROPN
ma-415	209	6	(	(	PUNCT
ma-415	209	7	q1)+	q1)+	PROPN
ma-415	209	8	lp1	lp1	PROPN
ma-415	209	9	(	(	PUNCT
ma-415	209	10	·	·	PUNCT
ma-415	209	11	)	)	PUNCT
ma-415	209	12	lq1	lq1	PROPN
ma-415	209	13	(	(	PUNCT
ma-415	209	14	·	·	PUNCT
ma-415	209	15	)	)	PUNCT
ma-415	209	16	.	.	PUNCT
ma-415	210	1			NOUN
ma-415	211	1	∞∑	∞∑	NUM
ma-415	211	2	k=−∞	k=−∞	X
ma-415	211	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	212	1	(	(	PUNCT
ma-415	212	2	2kα(·)|fk	2kα(·)|fk	NUM
ma-415	212	3	|	|	ADV
ma-415	212	4	β0	β0	PROPN
ma-415	212	5	)	)	PUNCT
ma-415	212	6	q1	q1	PROPN
ma-415	212	7	(	(	PUNCT
ma-415	212	8	·	·	PUNCT
ma-415	212	9	)	)	PUNCT
ma-415	212	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	213	1	lp1	lp1	PROPN
ma-415	213	2	(	(	PUNCT
ma-415	213	3	·	·	PUNCT
ma-415	213	4	)	)	PUNCT
ma-415	213	5	lq1	lq1	PROPN
ma-415	213	6	(	(	PUNCT
ma-415	213	7	·	·	PUNCT
ma-415	213	8	)	)	PUNCT
ma-415	213	9			NOUN
ma-415	213	10	q•	q•	VERB
ma-415	213	11	.	.	PUNCT
ma-415	214	1	1	1	NUM
ma-415	214	2	,	,	PUNCT
ma-415	214	3	here	here	ADV
ma-415	214	4	q•	q•	VERB
ma-415	214	5	=	=	SYM
ma-415	214	6	min	min	PROPN
ma-415	214	7	k∈n	k∈n	PROPN
ma-415	214	8	(	(	PUNCT
ma-415	214	9	q0	q0	PROPN
ma-415	214	10	2	2	NUM
ma-415	214	11	)	)	PUNCT
ma-415	214	12	k	k	NOUN
ma-415	215	1	(	(	PUNCT
ma-415	215	2	q1)+	q1)+	PROPN
ma-415	215	3	≥	≥	NUM
ma-415	215	4	1.the	1.the	DET
ma-415	215	5	previous	previous	ADJ
ma-415	215	6	calculations	calculation	NOUN
ma-415	215	7	imply	imply	VERB
ma-415	215	8	that	that	SCONJ
ma-415	215	9	β02	β02	PROPN
ma-415	215	10	.	.	PUNCT
ma-415	216	1	β0	β0	ADJ
ma-415	216	2	.	.	PUNCT
ma-415	217	1	‖f	‖f	ADP
ma-415	217	2	‖k̇α(·),q1	‖k̇α(·),q1	ADV
ma-415	217	3	(	(	PUNCT
ma-415	217	4	·	·	PUNCT
ma-415	217	5	)	)	PUNCT
ma-415	217	6	p1	p1	NOUN
ma-415	217	7	(	(	PUNCT
ma-415	217	8	·	·	PUNCT
ma-415	217	9	)	)	PUNCT
ma-415	217	10	(	(	PUNCT
ma-415	217	11	rn	rn	NOUN
ma-415	217	12	)	)	PUNCT
ma-415	217	13	.	.	PUNCT
ma-415	218	1	we	we	PRON
ma-415	218	2	must	must	AUX
ma-415	218	3	examine	examine	VERB
ma-415	218	4	µ∗,σψ	µ∗,σψ	PROPN
ma-415	218	5	,	,	PUNCT
ma-415	218	6	λfj	λfj	NOUN
ma-415	218	7	.	.	PUNCT
ma-415	219	1	by	by	ADP
ma-415	219	2	applying	apply	VERB
ma-415	219	3	the	the	DET
ma-415	219	4	minkowski	minkowski	ADJ
ma-415	219	5	inequality	inequality	NOUN
ma-415	219	6	,	,	PUNCT
ma-415	219	7	we	we	PRON
ma-415	219	8	have	have	VERB
ma-415	219	9	|µ∗,σψ	|µ∗,σψ	PROPN
ma-415	219	10	,	,	PUNCT
ma-415	219	11	λ(fj)(x)|	λ(fj)(x)|	ADV
ma-415	219	12	=	=	SYM
ma-415	219	13	(	(	PUNCT
ma-415	219	14	∫	∫	PROPN
ma-415	219	15	∞	∞	NUM
ma-415	219	16	0	0	NUM
ma-415	219	17	∫	∫	PROPN
ma-415	219	18	rn	rn	PROPN
ma-415	219	19	(	(	PUNCT
ma-415	219	20	(	(	PUNCT
ma-415	219	21	t)(t	t)(t	PROPN
ma-415	219	22	+	+	PUNCT
ma-415	219	23	|x1	|x1	NUM
ma-415	219	24	−	−	PROPN
ma-415	219	25	y1|)−1	y1|)−1	NOUN
ma-415	219	26	)	)	PUNCT
ma-415	219	27	λn	λn	PROPN
ma-415	219	28	∣∣∣∣	∣∣∣∣	NOUN
ma-415	219	29	1	1	NUM
ma-415	219	30	tσ	tσ	NOUN
ma-415	219	31	∫	∫	PROPN
ma-415	219	32	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	219	33	ψ(y1	ψ(y1	NOUN
ma-415	219	34	,	,	PUNCT
ma-415	219	35	y1	y1	ADJ
ma-415	219	36	−	−	PROPN
ma-415	219	37	z1	z1	PROPN
ma-415	219	38	)	)	PUNCT
ma-415	219	39	|y1	|y1	VERB
ma-415	219	40	−	−	PROPN
ma-415	219	41	z1|n−σ	z1|n−σ	X
ma-415	219	42	fj(z1)dz1	fj(z1)dz1	NOUN
ma-415	219	43	∣∣∣∣2	∣∣∣∣2	NOUN
ma-415	219	44	dy1dt	dy1dt	NUM
ma-415	219	45	tn+1	tn+1	NOUN
ma-415	219	46	)	)	PUNCT
ma-415	219	47	1	1	NUM
ma-415	219	48	2	2	NUM
ma-415	219	49	≤	≤	NUM
ma-415	219	50	∫	∫	PROPN
ma-415	219	51	rn	rn	PROPN
ma-415	219	52	fj(z1	fj(z1	PROPN
ma-415	219	53	)	)	PUNCT
ma-415	219	54	(	(	PUNCT
ma-415	219	55	∫	∫	PROPN
ma-415	219	56	∞	∞	NUM
ma-415	219	57	0	0	NUM
ma-415	219	58	∫	∫	PROPN
ma-415	219	59	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	219	60	(	(	PUNCT
ma-415	219	61	(	(	PUNCT
ma-415	219	62	t)(t	t)(t	X
ma-415	219	63	+	+	PUNCT
ma-415	220	1	|x1	|x1	NUM
ma-415	220	2	−	−	PROPN
ma-415	220	3	y1|)−1	y1|)−1	NOUN
ma-415	220	4	)	)	PUNCT
ma-415	220	5	λn	λn	NOUN
ma-415	220	6	|ψ(y1	|ψ(y1	ADJ
ma-415	220	7	,	,	PUNCT
ma-415	220	8	y1	y1	NOUN
ma-415	220	9	−	−	ADP
ma-415	220	10	z1)|2	z1)|2	NOUN
ma-415	220	11	|y1	|y1	VERB
ma-415	220	12	−	−	VERB
ma-415	220	13	z1|2n−2σ	z1|2n−2σ	PROPN
ma-415	220	14	dy1dt	dy1dt	NOUN
ma-415	220	15	t2σ+n+1	t2σ+n+1	NUM
ma-415	220	16	)	)	PUNCT
ma-415	220	17	1	1	NUM
ma-415	220	18	2	2	NUM
ma-415	220	19	dz1	dz1	ADJ
ma-415	220	20	≤	≤	NUM
ma-415	220	21	∫	∫	PROPN
ma-415	220	22	rn	rn	PROPN
ma-415	220	23	fj(z1	fj(z1	PROPN
ma-415	220	24	)	)	PUNCT
ma-415	220	25	(	(	PUNCT
ma-415	220	26	∫	∫	PROPN
ma-415	220	27	|x1−z1|	|x1−z1|	NOUN
ma-415	220	28	0	0	NUM
ma-415	220	29	∫	∫	PROPN
ma-415	220	30	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	220	31	(	(	PUNCT
ma-415	220	32	(	(	PUNCT
ma-415	220	33	t)(t	t)(t	X
ma-415	220	34	+	+	PUNCT
ma-415	220	35	|x1	|x1	NUM
ma-415	220	36	−	−	PROPN
ma-415	220	37	y1|)−1	y1|)−1	NOUN
ma-415	220	38	)	)	PUNCT
ma-415	220	39	λn	λn	NOUN
ma-415	220	40	|ψ(y1	|ψ(y1	ADJ
ma-415	220	41	,	,	PUNCT
ma-415	220	42	y1	y1	NOUN
ma-415	220	43	−	−	ADP
ma-415	220	44	z1)|2	z1)|2	NOUN
ma-415	220	45	|y1	|y1	VERB
ma-415	220	46	−	−	VERB
ma-415	220	47	z1|2n−2σ	z1|2n−2σ	PROPN
ma-415	220	48	dy1dt	dy1dt	NOUN
ma-415	220	49	t2σ+n+1	t2σ+n+1	NUM
ma-415	220	50	)	)	PUNCT
ma-415	220	51	1	1	NUM
ma-415	220	52	2	2	NUM
ma-415	220	53	dz1	dz1	VERB
ma-415	220	54	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	PROPN
ma-415	220	55	eur	eur	PROPN
ma-415	220	56	.	.	PUNCT
ma-415	221	1	j.	j.	PROPN
ma-415	221	2	math	math	PROPN
ma-415	221	3	.	.	PUNCT
ma-415	222	1	anal	anal	PROPN
ma-415	222	2	.	.	PUNCT
ma-415	223	1	10.28924	10.28924	NUM
ma-415	223	2	/	/	SYM
ma-415	223	3	ada	ada	PROPN
ma-415	223	4	/	/	SYM
ma-415	223	5	ma.5.22	ma.5.22	NOUN
ma-415	223	6	9	9	NUM
ma-415	223	7	+	+	CCONJ
ma-415	223	8	∫	∫	PROPN
ma-415	223	9	rn	rn	PROPN
ma-415	223	10	fj(z1	fj(z1	PROPN
ma-415	223	11	)	)	PUNCT
ma-415	223	12	(	(	PUNCT
ma-415	223	13	∫	∫	PROPN
ma-415	223	14	∞	∞	PROPN
ma-415	223	15	|x1−z1|	|x1−z1|	NOUN
ma-415	223	16	∫	∫	NOUN
ma-415	223	17	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	223	18	(	(	PUNCT
ma-415	223	19	(	(	PUNCT
ma-415	223	20	t)(t	t)(t	X
ma-415	223	21	+	+	PUNCT
ma-415	223	22	|x1	|x1	NUM
ma-415	223	23	−	−	PROPN
ma-415	223	24	y1|)−1	y1|)−1	NOUN
ma-415	223	25	)	)	PUNCT
ma-415	223	26	λn	λn	NOUN
ma-415	223	27	|ψ(y1	|ψ(y1	ADJ
ma-415	223	28	,	,	PUNCT
ma-415	223	29	y1	y1	NOUN
ma-415	223	30	−	−	ADP
ma-415	223	31	z1)|2	z1)|2	NOUN
ma-415	223	32	|y1	|y1	VERB
ma-415	223	33	−	−	VERB
ma-415	223	34	z1|2n−2σ	z1|2n−2σ	PROPN
ma-415	223	35	dy1dt	dy1dt	NOUN
ma-415	223	36	t2σ+n+1	t2σ+n+1	NUM
ma-415	223	37	)	)	PUNCT
ma-415	223	38	1	1	NUM
ma-415	223	39	2	2	NUM
ma-415	223	40	dz1	dz1	ADJ
ma-415	223	41	.	.	PUNCT
ma-415	224	1	let	let	VERB
ma-415	224	2	2ρ−	2ρ−	PROPN
ma-415	224	3	n	n	CCONJ
ma-415	224	4	>	>	X
ma-415	224	5	0	0	NUM
ma-415	225	1	and	and	CCONJ
ma-415	225	2	ψ	ψ	X
ma-415	225	3	∈	∈	PROPN
ma-415	225	4	l∞(rn)×	l∞(rn)×	PROPN
ma-415	225	5	l2(sn−1	l2(sn−1	NOUN
ma-415	225	6	)	)	PUNCT
ma-415	225	7	.	.	PUNCT
ma-415	226	1	then	then	ADV
ma-415	226	2	,	,	PUNCT
ma-415	226	3	the	the	DET
ma-415	226	4	following	follow	VERB
ma-415	226	5	inequality	inequality	NOUN
ma-415	226	6	is	be	AUX
ma-415	226	7	satisfied∫	satisfied∫	ADJ
ma-415	226	8	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	226	9	|ψ(y1	|ψ(y1	NUM
ma-415	226	10	,	,	PUNCT
ma-415	226	11	y1	y1	NOUN
ma-415	226	12	−	−	ADP
ma-415	226	13	z1)|2	z1)|2	NOUN
ma-415	226	14	|y1	|y1	VERB
ma-415	226	15	−	−	PROPN
ma-415	226	16	z1|2n−2σ	z1|2n−2σ	ADJ
ma-415	226	17	dy1	dy1	NOUN
ma-415	226	18	≤	≤	NUM
ma-415	226	19	∫	∫	PROPN
ma-415	227	1	sn−1	sn−1	PROPN
ma-415	227	2	∫	∫	PROPN
ma-415	227	3	t	t	PROPN
ma-415	227	4	0	0	PUNCT
ma-415	227	5	|ψ(sy	|ψ(sy	X
ma-415	227	6	′1	′1	X
ma-415	227	7	+	+	CCONJ
ma-415	227	8	z1	z1	PROPN
ma-415	227	9	,	,	PUNCT
ma-415	227	10	y	y	PROPN
ma-415	227	11	′	′	NOUN
ma-415	227	12	1)|2	1)|2	NUM
ma-415	227	13	s2n−2σ	s2n−2σ	PROPN
ma-415	227	14	sn−1dsdσ(y	sn−1dsdσ(y	NOUN
ma-415	227	15	′1	′1	NOUN
ma-415	227	16	)	)	PUNCT
ma-415	227	17	.	.	PUNCT
ma-415	228	1	‖ψ‖2	‖ψ‖2	PROPN
ma-415	228	2	l∞(rn)×l2(sn−1)t	l∞(rn)×l2(sn−1)t	PROPN
ma-415	228	3	2σ−n	2σ−n	PROPN
ma-415	228	4	.	.	PUNCT
ma-415	229	1	because	because	SCONJ
ma-415	229	2	|x1−	|x1−	NOUN
ma-415	229	3	z1|	z1|	ADV
ma-415	229	4	≤	≤	NUM
ma-415	229	5	|y1−	|y1−	ADJ
ma-415	229	6	z1|+	z1|+	PROPN
ma-415	229	7	|x1−	|x1−	NOUN
ma-415	229	8	y1|	y1|	VERB
ma-415	229	9	≤	≤	NUM
ma-415	229	10	|x1−	|x1−	NOUN
ma-415	229	11	y1|+	y1|+	PROPN
ma-415	229	12	t	t	PROPN
ma-415	229	13	,	,	PUNCT
ma-415	229	14	for	for	ADP
ma-415	229	15	λ	λ	PROPN
ma-415	229	16	>	>	X
ma-415	229	17	2	2	NUM
ma-415	229	18	and	and	CCONJ
ma-415	229	19	0	0	NUM
ma-415	229	20	<	<	X
ma-415	229	21	ε	ε	X
ma-415	229	22	<	<	X
ma-415	229	23	(	(	PUNCT
ma-415	229	24	λ−	λ−	PROPN
ma-415	229	25	2)n	2)n	NUM
ma-415	229	26	,	,	PUNCT
ma-415	229	27	we	we	PRON
ma-415	229	28	obtain∫	obtain∫	VERB
ma-415	229	29	|x1−z1|	|x1−z1|	PRON
ma-415	229	30	0	0	NUM
ma-415	229	31	∫	∫	PROPN
ma-415	229	32	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	229	33	(	(	PUNCT
ma-415	229	34	(	(	PUNCT
ma-415	229	35	t)(t	t)(t	X
ma-415	229	36	+	+	PUNCT
ma-415	229	37	|x1	|x1	NUM
ma-415	229	38	−	−	PROPN
ma-415	229	39	y1|)−1	y1|)−1	NOUN
ma-415	229	40	)	)	PUNCT
ma-415	229	41	λn	λn	NOUN
ma-415	229	42	|ψ(y1	|ψ(y1	ADJ
ma-415	229	43	,	,	PUNCT
ma-415	229	44	y1	y1	NOUN
ma-415	229	45	−	−	ADP
ma-415	229	46	z1)|2	z1)|2	NOUN
ma-415	229	47	|y1	|y1	VERB
ma-415	229	48	−	−	VERB
ma-415	229	49	z1|2n−2σ	z1|2n−2σ	PROPN
ma-415	229	50	dy1dt	dy1dt	NOUN
ma-415	229	51	t2σ+n+1	t2σ+n+1	NUM
ma-415	229	52	.	.	PUNCT
ma-415	230	1	∫	∫	PROPN
ma-415	230	2	|x1−z1|	|x1−z1|	PRON
ma-415	230	3	0	0	NUM
ma-415	231	1	∫	∫	PROPN
ma-415	232	1	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	232	2	(	(	PUNCT
ma-415	232	3	(	(	PUNCT
ma-415	232	4	t)(t	t)(t	X
ma-415	232	5	+	+	PUNCT
ma-415	232	6	|x1	|x1	NUM
ma-415	232	7	−	−	PROPN
ma-415	232	8	y1|)−1	y1|)−1	NUM
ma-415	232	9	)	)	PUNCT
ma-415	232	10	λn−2n−ε	λn−2n−ε	SYM
ma-415	232	11	1	1	NUM
ma-415	232	12	|x1	|x1	NUM
ma-415	232	13	−	−	PROPN
ma-415	232	14	z1|2n+ε	z1|2n+ε	PROPN
ma-415	232	15	|ψ(y1	|ψ(y1	NOUN
ma-415	232	16	,	,	PUNCT
ma-415	232	17	y1	y1	NOUN
ma-415	232	18	−	−	ADP
ma-415	232	19	z1)|2	z1)|2	NOUN
ma-415	232	20	|y1	|y1	VERB
ma-415	232	21	−	−	VERB
ma-415	232	22	z1|2n−2σ	z1|2n−2σ	NOUN
ma-415	232	23	dy1dt	dy1dt	NOUN
ma-415	232	24	t2σ−n−ε+1	t2σ−n−ε+1	NOUN
ma-415	232	25	.	.	PUNCT
ma-415	233	1	1	1	NUM
ma-415	233	2	|x1	|x1	NUM
ma-415	233	3	−	−	PROPN
ma-415	233	4	z1|2n+ε	z1|2n+ε	PROPN
ma-415	233	5	∫	∫	X
ma-415	233	6	|x1−z1|	|x1−z1|	NOUN
ma-415	233	7	0	0	NUM
ma-415	233	8	∫	∫	PROPN
ma-415	233	9	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	233	10	|ψ(y1	|ψ(y1	NUM
ma-415	233	11	,	,	PUNCT
ma-415	233	12	y1	y1	NOUN
ma-415	233	13	−	−	ADP
ma-415	233	14	z1)|2	z1)|2	NOUN
ma-415	233	15	|y1	|y1	VERB
ma-415	233	16	−	−	VERB
ma-415	233	17	z1|2n−2σ	z1|2n−2σ	NOUN
ma-415	233	18	dy1dt	dy1dt	NOUN
ma-415	233	19	t2σ−n−ε+1	t2σ−n−ε+1	NOUN
ma-415	233	20	.	.	PUNCT
ma-415	234	1	‖ψ‖2	‖ψ‖2	PROPN
ma-415	234	2	l∞(rn)×l2(sn−1	l∞(rn)×l2(sn−1	PROPN
ma-415	234	3	)	)	PUNCT
ma-415	234	4	|x1	|x1	ADP
ma-415	234	5	−	−	PROPN
ma-415	234	6	z1|2n+ε	z1|2n+ε	PROPN
ma-415	234	7	∫	∫	X
ma-415	234	8	|x1−z1|	|x1−z1|	NOUN
ma-415	234	9	0	0	NUM
ma-415	235	1	tε−1dt	tε−1dt	NUM
ma-415	235	2	.	.	PUNCT
ma-415	236	1	|x1	|x1	ADP
ma-415	236	2	−	−	PROPN
ma-415	236	3	z1|−2n	z1|−2n	X
ma-415	236	4	.	.	PUNCT
ma-415	237	1	let	let	VERB
ma-415	238	1	λ0n	λ0n	NOUN
ma-415	238	2	−	−	PROPN
ma-415	238	3	2n	2n	X
ma-415	238	4	<	<	X
ma-415	238	5	0	0	PROPN
ma-415	238	6	,	,	PUNCT
ma-415	238	7	λ0n	λ0n	PROPN
ma-415	238	8	−	−	NOUN
ma-415	238	9	n	n	NOUN
ma-415	238	10	>	>	X
ma-415	238	11	0	0	NUM
ma-415	238	12	and	and	CCONJ
ma-415	238	13	1	1	NUM
ma-415	238	14	<	<	X
ma-415	238	15	λ0	λ0	NOUN
ma-415	238	16	<	<	X
ma-415	238	17	2	2	NUM
ma-415	238	18	.	.	PUNCT
ma-415	239	1	then	then	ADV
ma-415	239	2	,	,	PUNCT
ma-415	239	3	we	we	PRON
ma-415	239	4	get∫	get∫	VERB
ma-415	239	5	∞	∞	NUM
ma-415	239	6	|x1−z1|	|x1−z1|	NOUN
ma-415	239	7	∫	∫	NOUN
ma-415	239	8	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	239	9	(	(	PUNCT
ma-415	239	10	(	(	PUNCT
ma-415	239	11	t)(t	t)(t	X
ma-415	239	12	+	+	PUNCT
ma-415	239	13	|x1	|x1	NUM
ma-415	239	14	−	−	PROPN
ma-415	239	15	y1|)−1	y1|)−1	NOUN
ma-415	239	16	)	)	PUNCT
ma-415	239	17	λn	λn	NOUN
ma-415	239	18	|ψ(y1	|ψ(y1	ADJ
ma-415	239	19	,	,	PUNCT
ma-415	239	20	y1	y1	NOUN
ma-415	239	21	−	−	ADP
ma-415	239	22	z1)|2	z1)|2	NOUN
ma-415	239	23	|y1	|y1	VERB
ma-415	239	24	−	−	VERB
ma-415	239	25	z1|2n−2σ	z1|2n−2σ	PROPN
ma-415	239	26	dy1dt	dy1dt	NOUN
ma-415	239	27	t2σ+n+1	t2σ+n+1	NUM
ma-415	239	28	.	.	PUNCT
ma-415	240	1	∫	∫	PROPN
ma-415	240	2	∞	∞	PROPN
ma-415	240	3	|x1−z1|	|x1−z1|	NOUN
ma-415	240	4	∫	∫	NOUN
ma-415	240	5	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	240	6	|x1	|x1	NUM
ma-415	240	7	−	−	PROPN
ma-415	240	8	z1|−λ0n	z1|−λ0n	PROPN
ma-415	240	9	|ψ(y1	|ψ(y1	X
ma-415	240	10	,	,	PUNCT
ma-415	240	11	y1	y1	NOUN
ma-415	240	12	−	−	ADP
ma-415	240	13	z1)|2	z1)|2	NOUN
ma-415	240	14	|y1	|y1	VERB
ma-415	240	15	−	−	VERB
ma-415	240	16	z1|2n−2σ	z1|2n−2σ	PROPN
ma-415	240	17	dy1dt	dy1dt	NOUN
ma-415	240	18	t2σ−λ0n+n+1	t2σ−λ0n+n+1	PUNCT
ma-415	240	19	.	.	PUNCT
ma-415	241	1	∫	∫	PROPN
ma-415	241	2	∞	∞	NUM
ma-415	241	3	|x1−z1|	|x1−z1|	NOUN
ma-415	241	4	|x1	|x1	ADP
ma-415	241	5	−	−	PROPN
ma-415	241	6	z1|−λ0n	z1|−λ0n	PROPN
ma-415	241	7	∫	∫	PROPN
ma-415	241	8	|y1−z1|≤t	|y1−z1|≤t	PROPN
ma-415	241	9	|ψ(y1	|ψ(y1	NUM
ma-415	241	10	,	,	PUNCT
ma-415	241	11	y1	y1	NOUN
ma-415	241	12	−	−	PROPN
ma-415	241	13	z1)|2	z1)|2	PROPN
ma-415	241	14	|y1	|y1	VERB
ma-415	241	15	−	−	PROPN
ma-415	241	16	z1|2n−λ0n	z1|2n−λ0n	PROPN
ma-415	241	17	dy1dt	dy1dt	NOUN
ma-415	241	18	tn+1	tn+1	NOUN
ma-415	241	19	.	.	PUNCT
ma-415	242	1	∫	∫	PROPN
ma-415	243	1	∞	∞	PROPN
ma-415	243	2	|x1−z1|	|x1−z1|	NOUN
ma-415	243	3	|x1	|x1	ADP
ma-415	243	4	−	−	PROPN
ma-415	243	5	z1|−λ0n	z1|−λ0n	PROPN
ma-415	243	6	∫	∫	PROPN
ma-415	244	1	sn−1	sn−1	PROPN
ma-415	244	2	∫	∫	PROPN
ma-415	244	3	t	t	PROPN
ma-415	244	4	0	0	NUM
ma-415	245	1	|ψ(y	|ψ(y	PROPN
ma-415	245	2	′1	′1	NOUN
ma-415	245	3	,	,	PUNCT
ma-415	245	4	(	(	PUNCT
ma-415	245	5	y1	y1	INTJ
ma-415	245	6	−	−	PROPN
ma-415	245	7	z1)′)|2	z1)′)|2	NOUN
ma-415	245	8	s2n−λ0n	s2n−λ0n	PROPN
ma-415	245	9	sn−1dsdσ(y	sn−1dsdσ(y	NOUN
ma-415	245	10	′1	′1	NOUN
ma-415	245	11	)	)	PUNCT
ma-415	245	12	dt	dt	PART
ma-415	245	13	tn+1	tn+1	PROPN
ma-415	245	14	.	.	PUNCT
ma-415	246	1	‖ψ‖2	‖ψ‖2	PROPN
ma-415	246	2	l∞(rn)×l2(sn−1)|x1	l∞(rn)×l2(sn−1)|x1	PROPN
ma-415	246	3	−	−	PROPN
ma-415	247	1	z1|−λ0n	z1|−λ0n	PROPN
ma-415	247	2	∫	∫	PROPN
ma-415	247	3	∞	∞	PROPN
ma-415	247	4	|x1−z1|	|x1−z1|	NOUN
ma-415	247	5	tλ0n−2n−1dt	tλ0n−2n−1dt	NOUN
ma-415	247	6	.	.	PUNCT
ma-415	248	1	|x1	|x1	CCONJ
ma-415	248	2	−	−	PROPN
ma-415	248	3	z1|−2n	z1|−2n	NUM
ma-415	248	4	.	.	PUNCT
ma-415	249	1	by	by	ADP
ma-415	249	2	combining	combine	VERB
ma-415	249	3	these	these	DET
ma-415	249	4	estimates	estimate	NOUN
ma-415	249	5	,	,	PUNCT
ma-415	249	6	we	we	PRON
ma-415	249	7	find	find	VERB
ma-415	249	8	µ∗,σψ	µ∗,σψ	NOUN
ma-415	249	9	,	,	PUNCT
ma-415	249	10	λ(f	λ(f	PROPN
ma-415	249	11	)	)	PUNCT
ma-415	249	12	(	(	PUNCT
ma-415	249	13	x	x	NOUN
ma-415	249	14	)	)	PUNCT
ma-415	249	15	.	.	PUNCT
ma-415	250	1	∫	∫	PROPN
ma-415	250	2	rn	rn	PROPN
ma-415	251	1	|fj(z1)|	|fj(z1)|	PROPN
ma-415	251	2	|x1	|x1	ADP
ma-415	251	3	−	−	PROPN
ma-415	251	4	z1|n	z1|n	PROPN
ma-415	251	5	dz1	dz1	VERB
ma-415	251	6	.	.	PUNCT
ma-415	252	1	(	(	PUNCT
ma-415	252	2	∗	∗	NOUN
ma-415	252	3	)	)	PUNCT
ma-415	252	4	next	next	ADV
ma-415	252	5	,	,	PUNCT
ma-415	252	6	we	we	PRON
ma-415	252	7	consider	consider	VERB
ma-415	252	8	β01	β01	NOUN
ma-415	252	9	.	.	PUNCT
ma-415	253	1	since	since	SCONJ
ma-415	253	2	j	j	PROPN
ma-415	253	3	≤	≤	PROPN
ma-415	254	1	k	k	NOUN
ma-415	255	1	−	−	PROPN
ma-415	255	2	2	2	NUM
ma-415	255	3	,	,	PUNCT
ma-415	255	4	by	by	ADP
ma-415	255	5	applying	apply	VERB
ma-415	255	6	hölder	hölder	NOUN
ma-415	255	7	’s	’s	PART
ma-415	255	8	inequality	inequality	NOUN
ma-415	255	9	(	(	PUNCT
ma-415	255	10	lemma	lemma	PROPN
ma-415	255	11	2.3	2.3	NUM
ma-415	255	12	)	)	PUNCT
ma-415	255	13	,	,	PUNCT
ma-415	255	14	we	we	PRON
ma-415	255	15	obtain	obtain	VERB
ma-415	255	16	µ∗,σψ	µ∗,σψ	NOUN
ma-415	255	17	,	,	PUNCT
ma-415	255	18	λ(f	λ(f	PROPN
ma-415	255	19	)	)	PUNCT
ma-415	255	20	(	(	PUNCT
ma-415	255	21	x	x	NOUN
ma-415	255	22	)	)	PUNCT
ma-415	255	23	.	.	PUNCT
ma-415	256	1	∫	∫	PROPN
ma-415	256	2	rn	rn	PROPN
ma-415	257	1	|fj(z1)|	|fj(z1)|	PROPN
ma-415	257	2	|x1	|x1	ADP
ma-415	257	3	−	−	PROPN
ma-415	257	4	z1|n	z1|n	PROPN
ma-415	257	5	dz	dz	X
ma-415	257	6	.	.	PUNCT
ma-415	258	1	2−kn‖χj‖lp′1(·)(rn	2−kn‖χj‖lp′1(·)(rn	NUM
ma-415	258	2	)	)	PUNCT
ma-415	259	1	‖fj‖lp1(·)(rn	‖fj‖lp1(·)(rn	PROPN
ma-415	259	2	)	)	PUNCT
ma-415	259	3	.	.	PUNCT
ma-415	260	1	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	VERB
ma-415	260	2	eur	eur	PROPN
ma-415	260	3	.	.	PUNCT
ma-415	261	1	j.	j.	PROPN
ma-415	261	2	math	math	PROPN
ma-415	261	3	.	.	PUNCT
ma-415	262	1	anal	anal	PROPN
ma-415	262	2	.	.	PUNCT
ma-415	263	1	10.28924	10.28924	NUM
ma-415	263	2	/	/	SYM
ma-415	263	3	ada	ada	PROPN
ma-415	263	4	/	/	SYM
ma-415	263	5	ma.5.22	ma.5.22	NOUN
ma-415	263	6	10then	10then	ADV
ma-415	263	7	,	,	PUNCT
ma-415	263	8	by	by	ADP
ma-415	263	9	lemmas	lemmas	PROPN
ma-415	263	10	2.5	2.5	NUM
ma-415	263	11	2.7	2.7	NUM
ma-415	263	12	,	,	PUNCT
ma-415	263	13	we	we	PRON
ma-415	263	14	deduce	deduce	VERB
ma-415	263	15	that	that	SCONJ
ma-415	263	16	∞∑	∞∑	NUM
ma-415	263	17	k=−∞	k=−∞	NOUN
ma-415	263	18	∥∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥∥	NUM
ma-415	263	19			PROPN
ma-415	263	20	2kα(·)|	2kα(·)|	CCONJ
ma-415	263	21	k−2∑	k−2∑	PROPN
ma-415	263	22	j=−∞	j=−∞	PROPN
ma-415	263	23	µ∗,σψ	µ∗,σψ	PROPN
ma-415	263	24	,	,	PUNCT
ma-415	263	25	λ(fj)χk	λ(fj)χk	VERB
ma-415	264	1	|	|	INTJ
ma-415	264	2	β0	β0	NOUN
ma-415	264	3			PROPN
ma-415	265	1	q2(·)∥∥∥∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥∥∥∥	PROPN
ma-415	265	2	l	l	NOUN
ma-415	265	3	p1	p1	NOUN
ma-415	265	4	(	(	PUNCT
ma-415	265	5	·	·	PUNCT
ma-415	265	6	)	)	PUNCT
ma-415	265	7	q2	q2	NOUN
ma-415	265	8	(	(	PUNCT
ma-415	265	9	·	·	PUNCT
ma-415	265	10	)	)	PUNCT
ma-415	265	11	.	.	PUNCT
ma-415	266	1	∞∑	∞∑	NUM
ma-415	266	2	k=−∞	k=−∞	NOUN
ma-415	266	3	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	X
ma-415	266	4	2kα(·)|	2kα(·)|	CCONJ
ma-415	266	5	k−2∑	k−2∑	PROPN
ma-415	266	6	j=−∞	j=−∞	PROPN
ma-415	266	7	µ∗,σψ	µ∗,σψ	PROPN
ma-415	266	8	,	,	PUNCT
ma-415	266	9	λ(fj)χk	λ(fj)χk	NOUN
ma-415	266	10	|	|	ADV
ma-415	266	11	β0	β0	ADJ
ma-415	266	12	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	PROPN
ma-415	266	13	(	(	PUNCT
ma-415	266	14	q01	q01	NOUN
ma-415	266	15	2	2	NUM
ma-415	266	16	)	)	PUNCT
ma-415	266	17	k	k	PROPN
ma-415	266	18	lp1	lp1	PROPN
ma-415	266	19	(	(	PUNCT
ma-415	266	20	·	·	PUNCT
ma-415	266	21	)	)	PUNCT
ma-415	266	22	.	.	PUNCT
ma-415	267	1	∞∑	∞∑	NUM
ma-415	267	2	k=−∞	k=−∞	PROPN
ma-415	267	3	2kα	2kα	PROPN
ma-415	267	4	(	(	PUNCT
ma-415	267	5	·	·	PUNCT
ma-415	267	6	)	)	PUNCT
ma-415	267	7	k−2∑	k−2∑	PROPN
ma-415	267	8	j=−∞	j=−∞	ADP
ma-415	267	9	∥∥∥∥	∥∥∥∥	NUM
ma-415	267	10	fjβ0	fjβ0	PROPN
ma-415	267	11	∥∥∥∥	∥∥∥∥	PROPN
ma-415	267	12	lp1(·)(rn	lp1(·)(rn	NOUN
ma-415	267	13	)	)	PUNCT
ma-415	268	1	‖χbj‖lp′1(·)‖χbk‖lp1	‖χbj‖lp′1(·)‖χbk‖lp1	PROPN
ma-415	268	2	(	(	PUNCT
ma-415	268	3	·	·	PUNCT
ma-415	268	4	)	)	PUNCT
ma-415	269	1	2−kn	2−kn	NUM
ma-415	269	2	(q01	(q01	NOUN
ma-415	269	3	2	2	NUM
ma-415	269	4	)	)	PUNCT
ma-415	269	5	k	k	NOUN
ma-415	269	6	.	.	PUNCT
ma-415	270	1	∞∑	∞∑	NUM
ma-415	270	2	k=−∞	k=−∞	PROPN
ma-415	270	3	2kα	2kα	PROPN
ma-415	270	4	(	(	PUNCT
ma-415	270	5	·	·	PUNCT
ma-415	270	6	)	)	PUNCT
ma-415	270	7	k−2∑	k−2∑	PROPN
ma-415	270	8	j=−∞	j=−∞	ADP
ma-415	270	9	∥∥∥∥	∥∥∥∥	NUM
ma-415	270	10	fjβ0	fjβ0	PROPN
ma-415	270	11	∥∥∥∥	∥∥∥∥	PROPN
ma-415	270	12	lp1(·)(rn	lp1(·)(rn	NOUN
ma-415	270	13	)	)	PUNCT
ma-415	270	14	‖χbj‖lp′1	‖χbj‖lp′1	PROPN
ma-415	270	15	(	(	PUNCT
ma-415	270	16	·	·	PUNCT
ma-415	270	17	)	)	PUNCT
ma-415	270	18	‖χbk‖lp′1	‖χbk‖lp′1	PROPN
ma-415	270	19	(	(	PUNCT
ma-415	270	20	·	·	PUNCT
ma-415	270	21	)	)	PUNCT
ma-415	270	22	(q01	(q01	NOUN
ma-415	270	23	2	2	NUM
ma-415	270	24	)	)	PUNCT
ma-415	270	25	k	k	NOUN
ma-415	270	26	.	.	PUNCT
ma-415	271	1	∞∑	∞∑	NUM
ma-415	271	2	k=−∞	k=−∞	PROPN
ma-415	271	3	2kα	2kα	PROPN
ma-415	271	4	(	(	PUNCT
ma-415	271	5	·	·	PUNCT
ma-415	271	6	)	)	PUNCT
ma-415	271	7	k−2∑	k−2∑	PROPN
ma-415	271	8	j=−∞	j=−∞	ADP
ma-415	271	9	2(j−k)nδ11	2(j−k)nδ11	NUM
ma-415	271	10	∥∥∥∥	∥∥∥∥	NUM
ma-415	271	11	fjβ0	fjβ0	VERB
ma-415	271	12	∥∥∥∥	∥∥∥∥	PROPN
ma-415	271	13	lp1(·)(rn	lp1(·)(rn	NOUN
ma-415	271	14	)	)	PUNCT
ma-415	271	15	(q01	(q01	NOUN
ma-415	271	16	2	2	NUM
ma-415	271	17	)	)	PUNCT
ma-415	271	18	k	k	NOUN
ma-415	271	19	.	.	PUNCT
ma-415	272	1	∞∑	∞∑	NUM
ma-415	272	2	k=−∞	k=−∞	NOUN
ma-415	272	3			X
ma-415	272	4	k−2∑	k−2∑	NOUN
ma-415	272	5	j=−∞	j=−∞	ADV
ma-415	272	6	2(k−j)(−nδ11+α+	2(k−j)(−nδ11+α+	NUM
ma-415	272	7	)	)	PUNCT
ma-415	272	8	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ma-415	273	1	(	(	PUNCT
ma-415	273	2	|2jα(·)f	|2jα(·)f	NOUN
ma-415	273	3	χj	χj	INTJ
ma-415	273	4	|	|	ADV
ma-415	273	5	β0	β0	PROPN
ma-415	273	6	)	)	PUNCT
ma-415	273	7	q1	q1	PROPN
ma-415	273	8	(	(	PUNCT
ma-415	273	9	·	·	PUNCT
ma-415	273	10	)	)	PUNCT
ma-415	273	11	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	274	1	1	1	NUM
ma-415	274	2	(	(	PUNCT
ma-415	274	3	q1)+	q1)+	PROPN
ma-415	274	4	lp1(·)q1(·)(rn	lp1(·)q1(·)(rn	PROPN
ma-415	274	5	)	)	PUNCT
ma-415	275	1			NUM
ma-415	275	2	(	(	PUNCT
ma-415	275	3	q01	q01	NOUN
ma-415	275	4	2	2	NUM
ma-415	275	5	)	)	PUNCT
ma-415	275	6	k	k	NOUN
ma-415	275	7	,	,	PUNCT
ma-415	275	8	where	where	SCONJ
ma-415	275	9	(	(	PUNCT
ma-415	275	10	q01	q01	NOUN
ma-415	275	11	2	2	NUM
ma-415	275	12	)	)	PUNCT
ma-415	275	13	k	k	NOUN
ma-415	275	14	=	=	SYM
ma-415	275	15			X
ma-415	275	16	(	(	PUNCT
ma-415	275	17	q2)−	q2)−	PROPN
ma-415	275	18	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	275	19	2kα(·)|	2kα(·)|	ADP
ma-415	275	20	k−2∑	k−2∑	PROPN
ma-415	275	21	j=−∞	j=−∞	PROPN
ma-415	275	22	µ∗,σψ	µ∗,σψ	PROPN
ma-415	275	23	,	,	PUNCT
ma-415	275	24	λ(fj	λ(fj	NUM
ma-415	275	25	)	)	PUNCT
ma-415	275	26	χk	χk	NOUN
ma-415	275	27	|	|	ADV
ma-415	275	28	β0	β0	PROPN
ma-415	275	29			PROPN
ma-415	275	30	q2	q2	PROPN
ma-415	275	31	(	(	PUNCT
ma-415	275	32	·	·	PUNCT
ma-415	275	33	)	)	PUNCT
ma-415	275	34	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ma-415	276	1	l	l	PROPN
ma-415	276	2	p1	p1	PROPN
ma-415	276	3	(	(	PUNCT
ma-415	276	4	·	·	PUNCT
ma-415	276	5	)	)	PUNCT
ma-415	276	6	q2	q2	NOUN
ma-415	276	7	(	(	PUNCT
ma-415	276	8	·	·	PUNCT
ma-415	276	9	)	)	PUNCT
ma-415	276	10	≥	≥	NOUN
ma-415	276	11	1	1	NUM
ma-415	276	12	,	,	PUNCT
ma-415	276	13	(	(	PUNCT
ma-415	276	14	q2)+	q2)+	VERB
ma-415	276	15	otherwise	otherwise	ADV
ma-415	276	16	.	.	PUNCT
ma-415	277	1	if	if	SCONJ
ma-415	277	2	(	(	PUNCT
ma-415	277	3	q1)+	q1)+	PROPN
ma-415	277	4	6	6	NUM
ma-415	277	5	1	1	NUM
ma-415	277	6	,	,	PUNCT
ma-415	277	7	then	then	ADV
ma-415	277	8	by	by	ADP
ma-415	277	9	lemma	lemma	PROPN
ma-415	277	10	2.6	2.6	NUM
ma-415	277	11	,	,	PUNCT
ma-415	277	12	we	we	PRON
ma-415	277	13	have	have	VERB
ma-415	277	14	∞∑	∞∑	NUM
ma-415	277	15	k=−∞	k=−∞	NOUN
ma-415	277	16	∥∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥∥	NUM
ma-415	277	17			PROPN
ma-415	278	1	2kα(·)|	2kα(·)|	CCONJ
ma-415	278	2	k−2∑	k−2∑	PROPN
ma-415	278	3	j=−∞	j=−∞	PROPN
ma-415	278	4	µ∗,σψ	µ∗,σψ	PROPN
ma-415	278	5	,	,	PUNCT
ma-415	278	6	λ(fj)χk	λ(fj)χk	VERB
ma-415	279	1	|	|	INTJ
ma-415	279	2	β0	β0	NOUN
ma-415	279	3			PROPN
ma-415	280	1	q2(·)∥∥∥∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥∥∥∥	PROPN
ma-415	280	2	l	l	NOUN
ma-415	280	3	p1	p1	NOUN
ma-415	280	4	(	(	PUNCT
ma-415	280	5	·	·	PUNCT
ma-415	280	6	)	)	PUNCT
ma-415	280	7	q2	q2	NOUN
ma-415	280	8	(	(	PUNCT
ma-415	280	9	·	·	PUNCT
ma-415	280	10	)	)	PUNCT
ma-415	280	11	.	.	PUNCT
ma-415	281	1	∞∑	∞∑	NUM
ma-415	281	2	k=−∞	k=−∞	NOUN
ma-415	281	3			X
ma-415	281	4	k−2∑	k−2∑	NOUN
ma-415	281	5	j=−∞	j=−∞	NOUN
ma-415	281	6	2(k−j)(q1)+(α+−nδ11	2(k−j)(q1)+(α+−nδ11	NUM
ma-415	281	7	)	)	PUNCT
ma-415	281	8	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ma-415	281	9	(	(	PUNCT
ma-415	281	10	|2jα(·)f	|2jα(·)f	NOUN
ma-415	281	11	χj	χj	INTJ
ma-415	281	12	|	|	ADV
ma-415	281	13	β0	β0	PROPN
ma-415	281	14	)	)	PUNCT
ma-415	281	15	q1	q1	PROPN
ma-415	281	16	(	(	PUNCT
ma-415	281	17	·	·	PUNCT
ma-415	281	18	)	)	PUNCT
ma-415	281	19	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	281	20	lp1(·)q1(·)(rn	lp1(·)q1(·)(rn	X
ma-415	281	21	)	)	PUNCT
ma-415	281	22			NUM
ma-415	281	23	(	(	PUNCT
ma-415	281	24	q01	q01	NOUN
ma-415	281	25	2	2	NUM
ma-415	281	26	)	)	PUNCT
ma-415	281	27	k	k	NOUN
ma-415	281	28	(	(	PUNCT
ma-415	281	29	q1)+	q1)+	PROPN
ma-415	281	30	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	PROPN
ma-415	281	31	eur	eur	PROPN
ma-415	281	32	.	.	PUNCT
ma-415	282	1	j.	j.	PROPN
ma-415	282	2	math	math	PROPN
ma-415	282	3	.	.	PUNCT
ma-415	283	1	anal	anal	PROPN
ma-415	283	2	.	.	PUNCT
ma-415	284	1	10.28924	10.28924	NUM
ma-415	284	2	/	/	SYM
ma-415	284	3	ada	ada	PROPN
ma-415	284	4	/	/	SYM
ma-415	284	5	ma.5.22	ma.5.22	NOUN
ma-415	284	6	11	11	NUM
ma-415	284	7	.	.	PUNCT
ma-415	285	1			X
ma-415	286	1	∞∑	∞∑	NUM
ma-415	286	2	j=−∞	j=−∞	NOUN
ma-415	286	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	287	1	(	(	PUNCT
ma-415	287	2	|2jα(·)f	|2jα(·)f	NOUN
ma-415	287	3	χj	χj	INTJ
ma-415	287	4	|	|	ADV
ma-415	287	5	β0	β0	PROPN
ma-415	287	6	)	)	PUNCT
ma-415	287	7	q1	q1	PROPN
ma-415	287	8	(	(	PUNCT
ma-415	287	9	·	·	PUNCT
ma-415	287	10	)	)	PUNCT
ma-415	287	11	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ma-415	288	1	lp1(·)q1(·)(rn	lp1(·)q1(·)(rn	X
ma-415	288	2	)	)	PUNCT
ma-415	289	1	∞∑	∞∑	NUM
ma-415	289	2	k	k	X
ma-415	289	3	=	=	PROPN
ma-415	289	4	j+2	j+2	ADJ
ma-415	289	5	2(k−j)(q1)+(α+−nδ11	2(k−j)(q1)+(α+−nδ11	NUM
ma-415	289	6	)	)	PUNCT
ma-415	289	7			NUM
ma-415	289	8	q•	q•	NOUN
ma-415	289	9	.	.	PUNCT
ma-415	290	1	1	1	NUM
ma-415	290	2	,	,	PUNCT
ma-415	290	3	here	here	ADV
ma-415	290	4	q•	q•	VERB
ma-415	290	5	=	=	SYM
ma-415	290	6	min	min	PROPN
ma-415	290	7	k∈n	k∈n	PROPN
ma-415	290	8	(	(	PUNCT
ma-415	290	9	q01	q01	NOUN
ma-415	290	10	2	2	NUM
ma-415	290	11	)	)	PUNCT
ma-415	290	12	k	k	PROPN
ma-415	290	13	(	(	PUNCT
ma-415	290	14	q1)+	q1)+	PROPN
ma-415	290	15	.if	.if	PUNCT
ma-415	291	1	(	(	PUNCT
ma-415	291	2	q1)+	q1)+	PROPN
ma-415	291	3	>	>	X
ma-415	291	4	1	1	NUM
ma-415	291	5	,	,	PUNCT
ma-415	291	6	using	use	VERB
ma-415	291	7	hölder	hölder	NOUN
ma-415	291	8	’s	’s	PART
ma-415	291	9	inequality	inequality	NOUN
ma-415	291	10	,	,	PUNCT
ma-415	291	11	we	we	PRON
ma-415	291	12	deduce	deduce	VERB
ma-415	291	13	that	that	SCONJ
ma-415	291	14	∞∑	∞∑	NUM
ma-415	291	15	k=−∞	k=−∞	NOUN
ma-415	291	16	∥∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥∥	NUM
ma-415	291	17			PROPN
ma-415	291	18	2kα(·)|	2kα(·)|	CCONJ
ma-415	291	19	k−2∑	k−2∑	PROPN
ma-415	291	20	j=−∞	j=−∞	PROPN
ma-415	291	21	µ∗,σψ	µ∗,σψ	PROPN
ma-415	291	22	,	,	PUNCT
ma-415	291	23	λ(fj)χk	λ(fj)χk	VERB
ma-415	292	1	|	|	INTJ
ma-415	292	2	β0	β0	NOUN
ma-415	292	3			PROPN
ma-415	293	1	q2(·)∥∥∥∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥∥∥∥	PROPN
ma-415	293	2	l	l	NOUN
ma-415	293	3	p1	p1	NOUN
ma-415	293	4	(	(	PUNCT
ma-415	293	5	·	·	PUNCT
ma-415	293	6	)	)	PUNCT
ma-415	293	7	q2	q2	NOUN
ma-415	293	8	(	(	PUNCT
ma-415	293	9	·	·	PUNCT
ma-415	293	10	)	)	PUNCT
ma-415	293	11	.	.	PUNCT
ma-415	294	1	∞∑	∞∑	NUM
ma-415	294	2	k=−∞	k=−∞	NOUN
ma-415	294	3			X
ma-415	294	4	k−2∑	k−2∑	PROPN
ma-415	294	5	j=−∞	j=−∞	ADP
ma-415	294	6	2(k−j)(α+−nδ11	2(k−j)(α+−nδ11	NUM
ma-415	294	7	)	)	PUNCT
ma-415	294	8	(	(	PUNCT
ma-415	294	9	q1)+	q1)+	PROPN
ma-415	294	10	2	2	NUM
ma-415	294	11	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ma-415	294	12	(	(	PUNCT
ma-415	294	13	|2jα(·)f	|2jα(·)f	NOUN
ma-415	294	14	χj	χj	INTJ
ma-415	294	15	|	|	ADV
ma-415	294	16	β0	β0	PROPN
ma-415	294	17	)	)	PUNCT
ma-415	294	18	q1	q1	PROPN
ma-415	294	19	(	(	PUNCT
ma-415	294	20	·	·	PUNCT
ma-415	294	21	)	)	PUNCT
ma-415	294	22	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	295	1	lp1(·)q1(·)(rn	lp1(·)q1(·)(rn	X
ma-415	295	2	)	)	PUNCT
ma-415	296	1			NUM
ma-415	296	2	(	(	PUNCT
ma-415	296	3	q01	q01	NOUN
ma-415	296	4	2	2	NUM
ma-415	296	5	)	)	PUNCT
ma-415	296	6	k	k	NOUN
ma-415	297	1	(	(	PUNCT
ma-415	297	2	q1)+	q1)+	PROPN
ma-415	297	3	×	×	PROPN
ma-415	297	4			PROPN
ma-415	297	5	k−2∑	k−2∑	NUM
ma-415	297	6	j=−∞	j=−∞	ADP
ma-415	297	7	2(k−j)(α+−nδ11	2(k−j)(α+−nδ11	NUM
ma-415	297	8	)	)	PUNCT
ma-415	297	9	(	(	PUNCT
ma-415	297	10	(	(	PUNCT
ma-415	297	11	q1)+)′	q1)+)′	NOUN
ma-415	297	12	2	2	NUM
ma-415	297	13			NOUN
ma-415	297	14	(	(	PUNCT
ma-415	297	15	q01	q01	NOUN
ma-415	297	16	2	2	NUM
ma-415	297	17	)	)	PUNCT
ma-415	297	18	+	+	CCONJ
ma-415	297	19	(	(	PUNCT
ma-415	297	20	(	(	PUNCT
ma-415	297	21	q1)+)′	q1)+)′	NOUN
ma-415	297	22	.	.	PUNCT
ma-415	298	1			X
ma-415	299	1	∞∑	∞∑	NUM
ma-415	299	2	j=−∞	j=−∞	NOUN
ma-415	299	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-415	300	1	(	(	PUNCT
ma-415	300	2	|2jα(·)f	|2jα(·)f	NOUN
ma-415	300	3	χj	χj	INTJ
ma-415	300	4	|	|	ADV
ma-415	300	5	β0	β0	PROPN
ma-415	300	6	)	)	PUNCT
ma-415	300	7	q1	q1	PROPN
ma-415	300	8	(	(	PUNCT
ma-415	300	9	·	·	PUNCT
ma-415	300	10	)	)	PUNCT
ma-415	300	11	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ma-415	301	1	lp1(·)q1(·)(rn	lp1(·)q1(·)(rn	X
ma-415	301	2	)	)	PUNCT
ma-415	302	1	∞∑	∞∑	NUM
ma-415	302	2	k	k	X
ma-415	302	3	=	=	PROPN
ma-415	302	4	j+2	j+2	PROPN
ma-415	302	5	2(k−j)(α+−nδ11	2(k−j)(α+−nδ11	NUM
ma-415	302	6	)	)	PUNCT
ma-415	302	7	(	(	PUNCT
ma-415	302	8	q1	q1	PROPN
ma-415	302	9	)	)	PUNCT
ma-415	302	10	+	+	CCONJ
ma-415	302	11	2	2	NUM
ma-415	302	12			NUM
ma-415	302	13	q•	q•	NOUN
ma-415	302	14	.	.	PUNCT
ma-415	303	1	1	1	X
ma-415	303	2	.	.	X
ma-415	303	3	therefore	therefore	ADV
ma-415	303	4	,	,	PUNCT
ma-415	303	5	we	we	PRON
ma-415	303	6	conclude	conclude	VERB
ma-415	303	7	the	the	DET
ma-415	303	8	estimate	estimate	NOUN
ma-415	303	9	β01	β01	NOUN
ma-415	303	10	.	.	PUNCT
ma-415	304	1	β0	β0	ADJ
ma-415	304	2	.	.	PUNCT
ma-415	305	1	‖f	‖f	PUNCT
ma-415	305	2	‖k̇α	‖k̇α	PROPN
ma-415	305	3	,	,	PUNCT
ma-415	305	4	q1	q1	PROPN
ma-415	305	5	(	(	PUNCT
ma-415	305	6	·	·	PUNCT
ma-415	305	7	)	)	PUNCT
ma-415	305	8	p1	p1	NOUN
ma-415	305	9	(	(	PUNCT
ma-415	305	10	·	·	PUNCT
ma-415	305	11	)	)	PUNCT
ma-415	305	12	(	(	PUNCT
ma-415	305	13	rn	rn	NOUN
ma-415	305	14	)	)	PUNCT
ma-415	305	15	.	.	PUNCT
ma-415	306	1	finally	finally	ADV
ma-415	306	2	,	,	PUNCT
ma-415	306	3	we	we	PRON
ma-415	306	4	estimate	estimate	VERB
ma-415	306	5	β03	β03	ADJ
ma-415	306	6	.	.	PUNCT
ma-415	307	1	since	since	SCONJ
ma-415	307	2	j	j	PROPN
ma-415	307	3	≥	≥	X
ma-415	307	4	k	k	PROPN
ma-415	307	5	+	+	CCONJ
ma-415	307	6	2	2	NUM
ma-415	307	7	,	,	PUNCT
ma-415	307	8	by	by	ADP
ma-415	307	9	(	(	PUNCT
ma-415	307	10	∗	∗	NOUN
ma-415	307	11	)	)	PUNCT
ma-415	307	12	and	and	CCONJ
ma-415	307	13	applying	apply	VERB
ma-415	307	14	hölder	hölder	NOUN
ma-415	307	15	’s	’s	PART
ma-415	307	16	inequality	inequality	NOUN
ma-415	307	17	(	(	PUNCT
ma-415	307	18	lemma	lemma	PROPN
ma-415	307	19	2.3	2.3	NUM
ma-415	307	20	)	)	PUNCT
ma-415	307	21	,	,	PUNCT
ma-415	307	22	we	we	PRON
ma-415	307	23	have	have	VERB
ma-415	307	24	µ∗,σψ	µ∗,σψ	NOUN
ma-415	307	25	,	,	PUNCT
ma-415	307	26	λ(f	λ(f	PROPN
ma-415	307	27	)	)	PUNCT
ma-415	307	28	(	(	PUNCT
ma-415	307	29	x	x	NOUN
ma-415	307	30	)	)	PUNCT
ma-415	307	31	.	.	PUNCT
ma-415	308	1	∫	∫	PROPN
ma-415	308	2	rn	rn	PROPN
ma-415	309	1	|fj(z1)|	|fj(z1)|	PROPN
ma-415	310	1	|x1	|x1	ADP
ma-415	310	2	−	−	PROPN
ma-415	310	3	z1|n	z1|n	PROPN
ma-415	310	4	dz1	dz1	VERB
ma-415	310	5	.	.	PUNCT
ma-415	311	1	2−jn‖χj‖lp′1(·)(rn	2−jn‖χj‖lp′1(·)(rn	NUM
ma-415	311	2	)	)	PUNCT
ma-415	312	1	‖fj‖lp1(·)(rn	‖fj‖lp1(·)(rn	PROPN
ma-415	312	2	)	)	PUNCT
ma-415	312	3	.	.	PUNCT
ma-415	313	1	then	then	ADV
ma-415	313	2	,	,	PUNCT
ma-415	313	3	by	by	ADP
ma-415	313	4	lemma2.5	lemma2.5	NOUN
ma-415	313	5	,	,	PUNCT
ma-415	313	6	lemma2.6	lemma2.6	X
ma-415	313	7	and	and	CCONJ
ma-415	313	8	lemma2.7	lemma2.7	PROPN
ma-415	313	9	,	,	PUNCT
ma-415	313	10	we	we	PRON
ma-415	313	11	get	get	VERB
ma-415	313	12	∞∑	∞∑	NUM
ma-415	313	13	k=−∞	k=−∞	NOUN
ma-415	313	14	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	NOUN
ma-415	313	15	2kα(·)|	2kα(·)|	CCONJ
ma-415	314	1	∞∑	∞∑	PROPN
ma-415	314	2	k+2	k+2	PROPN
ma-415	314	3	µ∗,σψ	µ∗,σψ	NOUN
ma-415	314	4	,	,	PUNCT
ma-415	314	5	λ(fj)χk	λ(fj)χk	NOUN
ma-415	314	6	|	|	NOUN
ma-415	314	7	β0	β0	NUM
ma-415	314	8			NOUN
ma-415	314	9	q2(·)∥∥∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥∥∥	PROPN
ma-415	314	10	l	l	NOUN
ma-415	314	11	p1	p1	PROPN
ma-415	314	12	(	(	PUNCT
ma-415	314	13	·	·	PUNCT
ma-415	314	14	)	)	PUNCT
ma-415	314	15	q2	q2	NOUN
ma-415	314	16	(	(	PUNCT
ma-415	314	17	·	·	PUNCT
ma-415	314	18	)	)	PUNCT
ma-415	314	19	.	.	PUNCT
ma-415	315	1	∞∑	∞∑	NUM
ma-415	315	2	k=−∞	k=−∞	NOUN
ma-415	315	3	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	NOUN
ma-415	315	4	2kα(·)|	2kα(·)|	NUM
ma-415	315	5	∞∑	∞∑	PROPN
ma-415	315	6	j	j	PROPN
ma-415	315	7	=	=	SYM
ma-415	315	8	k+2	k+2	PROPN
ma-415	315	9	µ∗,σψ	µ∗,σψ	NOUN
ma-415	315	10	,	,	PUNCT
ma-415	315	11	λ(fj)χk	λ(fj)χk	NOUN
ma-415	315	12	|	|	ADV
ma-415	315	13	β0	β0	PROPN
ma-415	315	14	∥∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥∥	PROPN
ma-415	315	15	(	(	PUNCT
ma-415	315	16	q02	q02	PROPN
ma-415	315	17	2	2	NUM
ma-415	315	18	)	)	PUNCT
ma-415	315	19	k	k	PROPN
ma-415	315	20	lp1	lp1	PROPN
ma-415	315	21	(	(	PUNCT
ma-415	315	22	·	·	PUNCT
ma-415	315	23	)	)	PUNCT
ma-415	315	24	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	VERB
ma-415	315	25	eur	eur	PROPN
ma-415	315	26	.	.	PUNCT
ma-415	316	1	j.	j.	PROPN
ma-415	316	2	math	math	PROPN
ma-415	316	3	.	.	PUNCT
ma-415	317	1	anal	anal	PROPN
ma-415	317	2	.	.	PUNCT
ma-415	318	1	10.28924	10.28924	NUM
ma-415	318	2	/	/	SYM
ma-415	318	3	ada	ada	PROPN
ma-415	318	4	/	/	SYM
ma-415	318	5	ma.5.22	ma.5.22	NOUN
ma-415	318	6	12	12	NUM
ma-415	318	7	.	.	PUNCT
ma-415	319	1	∞∑	∞∑	NUM
ma-415	319	2	k=−∞	k=−∞	NUM
ma-415	319	3	2kα	2kα	PROPN
ma-415	319	4	(	(	PUNCT
ma-415	319	5	·	·	PUNCT
ma-415	319	6	)	)	PUNCT
ma-415	320	1	∞∑	∞∑	NUM
ma-415	320	2	j	j	X
ma-415	320	3	=	=	SYM
ma-415	320	4	k+2	k+2	PROPN
ma-415	320	5	2−jn‖χbj‖lp′1(·)‖χbk‖lp1	2−jn‖χbj‖lp′1(·)‖χbk‖lp1	NUM
ma-415	320	6	(	(	PUNCT
ma-415	320	7	·	·	PUNCT
ma-415	320	8	)	)	PUNCT
ma-415	320	9	∥∥∥∥	∥∥∥∥	NUM
ma-415	320	10	fjβ0	fjβ0	PROPN
ma-415	320	11	∥∥∥∥	∥∥∥∥	PROPN
ma-415	320	12	lp1(·)(rn	lp1(·)(rn	NOUN
ma-415	320	13	)	)	PUNCT
ma-415	320	14	(q02	(q02	X
ma-415	320	15	2	2	NUM
ma-415	320	16	)	)	PUNCT
ma-415	320	17	k	k	NOUN
ma-415	320	18	.	.	PUNCT
ma-415	321	1	∞∑	∞∑	NUM
ma-415	321	2	k=−∞	k=−∞	PROPN
ma-415	321	3	2kα	2kα	PROPN
ma-415	321	4	(	(	PUNCT
ma-415	321	5	·	·	PUNCT
ma-415	321	6	)	)	PUNCT
ma-415	322	1	∞∑	∞∑	NUM
ma-415	322	2	j	j	X
ma-415	322	3	=	=	SYM
ma-415	322	4	k+2	k+2	PROPN
ma-415	322	5	2−jn	2−jn	NUM
ma-415	322	6	‖χbk‖lp1	‖χbk‖lp1	NOUN
ma-415	322	7	(	(	PUNCT
ma-415	322	8	·	·	PUNCT
ma-415	322	9	)	)	PUNCT
ma-415	322	10	‖χbj‖lp1	‖χbj‖lp1	PROPN
ma-415	322	11	(	(	PUNCT
ma-415	322	12	·	·	PUNCT
ma-415	322	13	)	)	PUNCT
ma-415	322	14	|bj	|bj	NOUN
ma-415	323	1	|	|	ADV
ma-415	323	2	∥∥∥∥	∥∥∥∥	NOUN
ma-415	323	3	fjβ0	fjβ0	VERB
ma-415	323	4	∥∥∥∥	∥∥∥∥	PROPN
ma-415	323	5	lp1(·)(rn	lp1(·)(rn	NOUN
ma-415	323	6	)	)	PUNCT
ma-415	323	7	(q02	(q02	X
ma-415	323	8	2	2	NUM
ma-415	323	9	)	)	PUNCT
ma-415	323	10	k	k	NOUN
ma-415	323	11	.	.	PUNCT
ma-415	324	1	∞∑	∞∑	NUM
ma-415	324	2	k=−∞	k=−∞	NOUN
ma-415	324	3			NOUN
ma-415	324	4	∞∑	∞∑	PROPN
ma-415	324	5	j	j	PROPN
ma-415	324	6	=	=	SYM
ma-415	324	7	k+2	k+2	PROPN
ma-415	324	8	2(k−j)(nδ12+α−	2(k−j)(nδ12+α−	PROPN
ma-415	324	9	)	)	PUNCT
ma-415	324	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	325	1	(	(	PUNCT
ma-415	325	2	2jα(·)f	2jα(·)f	NUM
ma-415	325	3	χj	χj	ADJ
ma-415	325	4	β0	β0	PROPN
ma-415	325	5	)	)	PUNCT
ma-415	325	6	q1	q1	PROPN
ma-415	325	7	(	(	PUNCT
ma-415	325	8	·	·	PUNCT
ma-415	325	9	)	)	PUNCT
ma-415	325	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-415	325	11	1	1	NUM
ma-415	325	12	(	(	PUNCT
ma-415	325	13	q1)+	q1)+	PROPN
ma-415	325	14	lp1(·)q1	lp1(·)q1	PROPN
ma-415	325	15	(	(	PUNCT
ma-415	325	16	·	·	PUNCT
ma-415	325	17	)	)	PUNCT
ma-415	325	18			NOUN
ma-415	325	19	(	(	PUNCT
ma-415	325	20	q02	q02	PROPN
ma-415	325	21	2	2	NUM
ma-415	325	22	)	)	PUNCT
ma-415	325	23	k	k	NOUN
ma-415	325	24	,	,	PUNCT
ma-415	325	25	where	where	SCONJ
ma-415	325	26	(	(	PUNCT
ma-415	325	27	q02	q02	PROPN
ma-415	325	28	2	2	NUM
ma-415	325	29	)	)	PUNCT
ma-415	325	30	k	k	NOUN
ma-415	326	1	=	=	PUNCT
ma-415	326	2			X
ma-415	326	3	(	(	PUNCT
ma-415	326	4	q2)−	q2)−	PROPN
ma-415	326	5	∥∥∥∥∥∥∥	∥∥∥∥∥∥∥	PROPN
ma-415	326	6	2kα(·)|	2kα(·)|	ADP
ma-415	326	7	∞∑	∞∑	PROPN
ma-415	326	8	j	j	PROPN
ma-415	326	9	=	=	SYM
ma-415	326	10	k+2	k+2	PROPN
ma-415	326	11	µ∗,σψ	µ∗,σψ	PROPN
ma-415	326	12	,	,	PUNCT
ma-415	326	13	λ(fj	λ(fj	NUM
ma-415	326	14	)	)	PUNCT
ma-415	326	15	χk	χk	NOUN
ma-415	327	1	|	|	ADV
ma-415	327	2	β0	β0	NOUN
ma-415	327	3	q2(·)∥∥∥∥∥∥∥	q2(·)∥∥∥∥∥∥∥	PROPN
ma-415	327	4	l	l	PROPN
ma-415	327	5	p1	p1	PROPN
ma-415	327	6	(	(	PUNCT
ma-415	327	7	·	·	PUNCT
ma-415	327	8	)	)	PUNCT
ma-415	327	9	q2	q2	NOUN
ma-415	327	10	(	(	PUNCT
ma-415	327	11	·	·	PUNCT
ma-415	327	12	)	)	PUNCT
ma-415	327	13	≥	≥	NOUN
ma-415	327	14	1	1	NUM
ma-415	327	15	,	,	PUNCT
ma-415	327	16	(	(	PUNCT
ma-415	327	17	q2)+	q2)+	NOUN
ma-415	327	18	,	,	PUNCT
ma-415	327	19	otherwise.notice	otherwise.notice	VERB
ma-415	327	20	that	that	PRON
ma-415	327	21	α−	α−	ADP
ma-415	327	22	>	>	X
ma-415	327	23	−nδ12	−nδ12	PROPN
ma-415	327	24	,	,	PUNCT
ma-415	327	25	and	and	CCONJ
ma-415	327	26	applying	apply	VERB
ma-415	327	27	the	the	DET
ma-415	327	28	same	same	ADJ
ma-415	327	29	estimation	estimation	NOUN
ma-415	327	30	technique	technique	NOUN
ma-415	327	31	used	use	VERB
ma-415	327	32	for	for	ADP
ma-415	327	33	β01	β01	NOUN
ma-415	327	34	,	,	PUNCT
ma-415	327	35	we	we	PRON
ma-415	327	36	get	get	VERB
ma-415	327	37	that	that	DET
ma-415	327	38	β03	β03	ADJ
ma-415	327	39	.	.	PUNCT
ma-415	328	1	β0	β0	ADJ
ma-415	328	2	.	.	PUNCT
ma-415	329	1	‖f	‖f	PUNCT
ma-415	329	2	‖k̇α	‖k̇α	PROPN
ma-415	329	3	,	,	PUNCT
ma-415	329	4	q1	q1	PROPN
ma-415	329	5	(	(	PUNCT
ma-415	329	6	·	·	PUNCT
ma-415	329	7	)	)	PUNCT
ma-415	329	8	p1	p1	NOUN
ma-415	329	9	(	(	PUNCT
ma-415	329	10	·	·	PUNCT
ma-415	329	11	)	)	PUNCT
ma-415	329	12	(	(	PUNCT
ma-415	329	13	rn	rn	NOUN
ma-415	329	14	)	)	PUNCT
ma-415	329	15	.	.	PUNCT
ma-415	330	1	thus	thus	ADV
ma-415	330	2	,	,	PUNCT
ma-415	330	3	the	the	DET
ma-415	330	4	theorem	theorem	NOUN
ma-415	330	5	3.4	3.4	NUM
ma-415	330	6	is	be	AUX
ma-415	330	7	proven	prove	VERB
ma-415	330	8	.	.	PUNCT
ma-415	331	1	�	�	PROPN
ma-415	331	2	author	author	NOUN
ma-415	331	3	contributions	contribution	NOUN
ma-415	331	4	:	:	PUNCT
ma-415	331	5	all	all	DET
ma-415	331	6	authors	author	NOUN
ma-415	331	7	contributed	contribute	VERB
ma-415	331	8	equally	equally	ADV
ma-415	331	9	to	to	ADP
ma-415	331	10	the	the	DET
ma-415	331	11	writing	writing	NOUN
ma-415	331	12	of	of	ADP
ma-415	331	13	this	this	DET
ma-415	331	14	paper	paper	NOUN
ma-415	331	15	.	.	PUNCT
ma-415	332	1	all	all	DET
ma-415	332	2	authors	author	NOUN
ma-415	332	3	readand	readand	PROPN
ma-415	332	4	approved	approve	VERB
ma-415	332	5	the	the	DET
ma-415	332	6	final	final	ADJ
ma-415	332	7	manuscript	manuscript	NOUN
ma-415	332	8	.	.	PUNCT
ma-415	333	1	conflicts	conflict	NOUN
ma-415	333	2	of	of	ADP
ma-415	333	3	interest	interest	NOUN
ma-415	333	4	:	:	PUNCT
ma-415	333	5	the	the	DET
ma-415	333	6	authors	author	NOUN
ma-415	333	7	declare	declare	VERB
ma-415	333	8	that	that	SCONJ
ma-415	333	9	there	there	PRON
ma-415	333	10	is	be	VERB
ma-415	333	11	no	no	DET
ma-415	333	12	conflict	conflict	NOUN
ma-415	333	13	of	of	ADP
ma-415	333	14	interest	interest	NOUN
ma-415	333	15	regarding	regard	VERB
ma-415	333	16	the	the	DET
ma-415	333	17	publi	publi	NOUN
ma-415	333	18	-	-	PUNCT
ma-415	333	19	cation	cation	NOUN
ma-415	333	20	of	of	ADP
ma-415	333	21	this	this	DET
ma-415	333	22	article	article	NOUN
ma-415	333	23	.	.	PUNCT
ma-415	334	1	references	reference	NOUN
ma-415	334	2	[	[	X
ma-415	334	3	1	1	NUM
ma-415	334	4	]	]	PUNCT
ma-415	334	5	m.	m.	NOUN
ma-415	334	6	sakamoto	sakamoto	PROPN
ma-415	334	7	,	,	PUNCT
ma-415	334	8	k.	k.	PROPN
ma-415	334	9	yabuta	yabuta	PROPN
ma-415	334	10	,	,	PUNCT
ma-415	334	11	boundedness	boundedness	NOUN
ma-415	334	12	of	of	ADP
ma-415	334	13	marcinkiewicz	marcinkiewicz	PROPN
ma-415	334	14	functions	function	NOUN
ma-415	334	15	,	,	PUNCT
ma-415	334	16	studia	studia	PROPN
ma-415	334	17	math	math	NOUN
ma-415	334	18	.	.	PUNCT
ma-415	335	1	135	135	NUM
ma-415	335	2	(	(	PUNCT
ma-415	335	3	1999	1999	NUM
ma-415	335	4	)	)	PUNCT
ma-415	335	5	,	,	PUNCT
ma-415	335	6	103–142	103–142	NUM
ma-415	335	7	.	.	PUNCT
ma-415	336	1	http	http	ADJ
ma-415	336	2	:	:	PUNCT
ma-415	336	3	//eudml.org	//eudml.org	ADJ
ma-415	336	4	/	/	SYM
ma-415	336	5	doc/216646[2	doc/216646[2	NOUN
ma-415	336	6	]	]	X
ma-415	336	7	q.	q.	PROPN
ma-415	336	8	xue	xue	PROPN
ma-415	336	9	,	,	PUNCT
ma-415	336	10	y.	y.	PROPN
ma-415	336	11	ding	ding	PROPN
ma-415	336	12	,	,	PUNCT
ma-415	336	13	wieghted	wieghte	VERB
ma-415	336	14	lp	lp	NOUN
ma-415	336	15	boundedness	boundedness	NOUN
ma-415	336	16	for	for	ADP
ma-415	336	17	parametrized	parametrized	ADJ
ma-415	336	18	littlewood	littlewood	NOUN
ma-415	336	19	–	–	PUNCT
ma-415	336	20	paley	paley	NOUN
ma-415	336	21	operator	operator	NOUN
ma-415	336	22	,	,	PUNCT
ma-415	336	23	taiwan	taiwan	PROPN
ma-415	336	24	.	.	PUNCT
ma-415	337	1	j.	j.	PROPN
ma-415	337	2	math	math	PROPN
ma-415	337	3	.	.	PUNCT
ma-415	338	1	11	11	NUM
ma-415	338	2	(	(	PUNCT
ma-415	338	3	2007),1143–1165	2007),1143–1165	NUM
ma-415	338	4	.	.	PUNCT
ma-415	338	5	https://doi.org/10.11650/twjm/1500404809[3	https://doi.org/10.11650/twjm/1500404809[3	PROPN
ma-415	338	6	]	]	PUNCT
ma-415	339	1	f.	f.	PROPN
ma-415	339	2	deringoz	deringoz	PROPN
ma-415	339	3	,	,	PUNCT
ma-415	339	4	v.s.	v.s.	X
ma-415	339	5	guliyev	guliyev	PROPN
ma-415	339	6	,	,	PUNCT
ma-415	339	7	m.a	m.a	PROPN
ma-415	339	8	.	.	PROPN
ma-415	339	9	ragusa	ragusa	PROPN
ma-415	339	10	,	,	PUNCT
ma-415	339	11	intrinsic	intrinsic	ADJ
ma-415	339	12	square	square	ADJ
ma-415	339	13	functions	function	NOUN
ma-415	339	14	on	on	ADP
ma-415	339	15	vanishing	vanish	VERB
ma-415	339	16	generalized	generalized	ADJ
ma-415	339	17	orlicz	orlicz	ADJ
ma-415	339	18	-	-	PUNCT
ma-415	339	19	morrey	morrey	NOUN
ma-415	339	20	spaces	space	NOUN
ma-415	339	21	,	,	PUNCT
ma-415	339	22	set	set	NOUN
ma-415	339	23	-	-	PUNCT
ma-415	339	24	valued	value	VERB
ma-415	339	25	var	var	NOUN
ma-415	339	26	.	.	PUNCT
ma-415	340	1	anal	anal	ADJ
ma-415	340	2	.	.	PUNCT
ma-415	341	1	25	25	NUM
ma-415	341	2	(	(	PUNCT
ma-415	341	3	2017	2017	NUM
ma-415	341	4	)	)	PUNCT
ma-415	341	5	,	,	PUNCT
ma-415	341	6	807–828	807–828	NUM
ma-415	341	7	.	.	PUNCT
ma-415	341	8	https://doi.org/10.1007/s11228-017-0422-y[4	https://doi.org/10.1007/s11228-017-0422-y[4	PROPN
ma-415	341	9	]	]	X
ma-415	341	10	b.	b.	PROPN
ma-415	341	11	li	li	PROPN
ma-415	341	12	,	,	PUNCT
ma-415	341	13	weighted	weight	VERB
ma-415	341	14	norm	norm	NOUN
ma-415	341	15	inequalities	inequality	NOUN
ma-415	341	16	for	for	ADP
ma-415	341	17	parametric	parametric	ADJ
ma-415	341	18	littlewood	littlewood	PROPN
ma-415	341	19	–	–	PUNCT
ma-415	341	20	paley	paley	ADJ
ma-415	341	21	operators	operator	NOUN
ma-415	341	22	,	,	PUNCT
ma-415	341	23	math	math	NOUN
ma-415	341	24	.	.	PUNCT
ma-415	342	1	inequal	inequal	PROPN
ma-415	342	2	.	.	PUNCT
ma-415	343	1	appl	appl	PROPN
ma-415	343	2	.	.	PUNCT
ma-415	344	1	22	22	NUM
ma-415	344	2	(	(	PUNCT
ma-415	344	3	2019	2019	NUM
ma-415	344	4	)	)	PUNCT
ma-415	344	5	,	,	PUNCT
ma-415	344	6	1205–1220	1205–1220	NUM
ma-415	344	7	.	.	PUNCT
ma-415	345	1	https://doi.org/10.7153/mia-2019-22-34[5	https://doi.org/10.7153/mia-2019-22-34[5	NOUN
ma-415	345	2	]	]	X
ma-415	345	3	a.	a.	PROPN
ma-415	345	4	abdalmonem	abdalmonem	PROPN
ma-415	345	5	,	,	PUNCT
ma-415	345	6	o.	o.	PROPN
ma-415	345	7	abdalrhman	abdalrhman	PROPN
ma-415	345	8	,	,	PUNCT
ma-415	345	9	s.	s.	PROPN
ma-415	345	10	tao	tao	PROPN
ma-415	345	11	,	,	PUNCT
ma-415	345	12	commutators	commutator	NOUN
ma-415	345	13	of	of	ADP
ma-415	345	14	fractional	fractional	ADJ
ma-415	345	15	integral	integral	ADJ
ma-415	345	16	with	with	ADP
ma-415	345	17	variable	variable	ADJ
ma-415	345	18	kernel	kernel	NOUN
ma-415	345	19	on	on	ADP
ma-415	345	20	variable	variable	ADJ
ma-415	345	21	exponentherz	exponentherz	NOUN
ma-415	345	22	and	and	CCONJ
ma-415	345	23	lebesgue	lebesgue	NOUN
ma-415	345	24	spaces	space	NOUN
ma-415	345	25	,	,	PUNCT
ma-415	345	26	int	int	NOUN
ma-415	345	27	.	.	PUNCT
ma-415	346	1	j.	j.	PROPN
ma-415	346	2	math	math	PROPN
ma-415	346	3	.	.	PUNCT
ma-415	347	1	appl	appl	PROPN
ma-415	347	2	.	.	PROPN
ma-415	348	1	4	4	NUM
ma-415	348	2	(	(	PUNCT
ma-415	348	3	2016	2016	NUM
ma-415	348	4	)	)	PUNCT
ma-415	348	5	,	,	PUNCT
ma-415	348	6	29–40	29–40	NUM
ma-415	348	7	.	.	PUNCT
ma-415	349	1	https://ijmaa.in/index.php/ijmaa/article/	https://ijmaa.in/index.php/ijmaa/article/	PROPN
ma-415	349	2	view/970[6	view/970[6	PROPN
ma-415	349	3	]	]	PUNCT
ma-415	349	4	j.	j.	PROPN
ma-415	349	5	chen	chen	PROPN
ma-415	349	6	,	,	PUNCT
ma-415	349	7	y.	y.	PROPN
ma-415	349	8	ding	ding	PROPN
ma-415	349	9	,	,	PUNCT
ma-415	349	10	d.	d.	PROPN
ma-415	349	11	fan	fan	PROPN
ma-415	349	12	,	,	PUNCT
ma-415	349	13	littlewood	littlewood	PROPN
ma-415	349	14	–	–	PUNCT
ma-415	349	15	paley	paley	ADJ
ma-415	349	16	operator	operator	NOUN
ma-415	349	17	with	with	ADP
ma-415	349	18	variable	variable	ADJ
ma-415	349	19	kernel	kernel	NOUN
ma-415	349	20	,	,	PUNCT
ma-415	349	21	sci	sci	PROPN
ma-415	349	22	.	.	PUNCT
ma-415	349	23	china	china	PROPN
ma-415	349	24	ser	ser	PROPN
ma-415	349	25	.	.	PUNCT
ma-415	350	1	a	a	DET
ma-415	350	2	49	49	NUM
ma-415	350	3	(	(	PUNCT
ma-415	350	4	2006	2006	NUM
ma-415	350	5	)	)	PUNCT
ma-415	350	6	,	,	PUNCT
ma-415	350	7	639–650	639–650	NUM
ma-415	350	8	.	.	PUNCT
ma-415	351	1	https://doi.org/10.1007/s11425-006-0639-y	https://doi.org/10.1007/s11425-006-0639-y	NOUN
ma-415	351	2	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	PROPN
ma-415	351	3	http://eudml.org/doc/216646	http://eudml.org/doc/216646	PROPN
ma-415	351	4	http://eudml.org/doc/216646	http://eudml.org/doc/216646	PROPN
ma-415	351	5	https://doi.org/10.11650/twjm/1500404809	https://doi.org/10.11650/twjm/1500404809	PROPN
ma-415	351	6	https://doi.org/10.1007/s11228-017-0422-y	https://doi.org/10.1007/s11228-017-0422-y	ADV
ma-415	351	7	https://doi.org/10.7153/mia-2019-22-34	https://doi.org/10.7153/mia-2019-22-34	ADJ
ma-415	351	8	https://ijmaa.in/index.php/ijmaa/article/view/970	https://ijmaa.in/index.php/ijmaa/article/view/970	PROPN
ma-415	351	9	https://ijmaa.in/index.php/ijmaa/article/view/970	https://ijmaa.in/index.php/ijmaa/article/view/970	PROPN
ma-415	351	10	https://doi.org/10.1007/s11425-006-0639-y	https://doi.org/10.1007/s11425-006-0639-y	PROPN
ma-415	351	11	eur	eur	PROPN
ma-415	351	12	.	.	PUNCT
ma-415	352	1	j.	j.	PROPN
ma-415	352	2	math	math	PROPN
ma-415	352	3	.	.	PUNCT
ma-415	353	1	anal	anal	PROPN
ma-415	353	2	.	.	PUNCT
ma-415	354	1	10.28924	10.28924	NUM
ma-415	354	2	/	/	SYM
ma-415	354	3	ada	ada	PROPN
ma-415	354	4	/	/	SYM
ma-415	354	5	ma.5.22	ma.5.22	NOUN
ma-415	354	6	13	13	NUM
ma-415	354	7	[	[	X
ma-415	354	8	7	7	NUM
ma-415	354	9	]	]	PUNCT
ma-415	354	10	x.	x.	PROPN
ma-415	354	11	shao	shao	PROPN
ma-415	354	12	,	,	PUNCT
ma-415	354	13	s.	s.	PROPN
ma-415	354	14	tao	tao	PROPN
ma-415	354	15	,	,	PUNCT
ma-415	354	16	weighted	weight	VERB
ma-415	354	17	estimates	estimate	NOUN
ma-415	354	18	of	of	ADP
ma-415	354	19	variable	variable	ADJ
ma-415	354	20	kernel	kernel	NOUN
ma-415	354	21	fractional	fractional	PROPN
ma-415	354	22	integral	integral	ADJ
ma-415	354	23	and	and	CCONJ
ma-415	354	24	its	its	PRON
ma-415	354	25	commutators	commutator	NOUN
ma-415	354	26	on	on	ADP
ma-415	354	27	vanish	vanish	VERB
ma-415	354	28	-	-	PUNCT
ma-415	354	29	ing	ing	NOUN
ma-415	354	30	generalized	generalize	VERB
ma-415	354	31	morrey	morrey	NOUN
ma-415	354	32	spaces	space	NOUN
ma-415	354	33	with	with	ADP
ma-415	354	34	variable	variable	ADJ
ma-415	354	35	exponent	exponent	NOUN
ma-415	354	36	,	,	PUNCT
ma-415	354	37	chin	chin	PROPN
ma-415	354	38	.	.	PUNCT
ma-415	355	1	ann	ann	PROPN
ma-415	355	2	.	.	PUNCT
ma-415	355	3	math	math	PROPN
ma-415	355	4	.	.	PUNCT
ma-415	356	1	ser	ser	PROPN
ma-415	356	2	.	.	PUNCT
ma-415	357	1	b	b	ADP
ma-415	357	2	42	42	NUM
ma-415	357	3	(	(	PUNCT
ma-415	357	4	2021	2021	NUM
ma-415	357	5	)	)	PUNCT
ma-415	357	6	,	,	PUNCT
ma-415	357	7	451–470	451–470	NUM
ma-415	357	8	.	.	PUNCT
ma-415	358	1	https	https	NOUN
ma-415	358	2	:	:	PUNCT
ma-415	358	3	//doi.org/10.1007	//doi.org/10.1007	PROPN
ma-415	358	4	/	/	SYM
ma-415	358	5	s11401	s11401	NOUN
ma-415	358	6	-	-	PUNCT
ma-415	358	7	021	021	NUM
ma-415	358	8	-	-	PUNCT
ma-415	358	9	0268	0268	NUM
ma-415	358	10	-	-	SYM
ma-415	358	11	3[8	3[8	NUM
ma-415	358	12	]	]	X
ma-415	358	13	h.	h.	PROPN
ma-415	358	14	wang	wang	PROPN
ma-415	358	15	,	,	PUNCT
ma-415	358	16	estimates	estimate	NOUN
ma-415	358	17	of	of	ADP
ma-415	358	18	some	some	DET
ma-415	358	19	integral	integral	ADJ
ma-415	358	20	operators	operator	NOUN
ma-415	358	21	with	with	ADP
ma-415	358	22	bounded	bounded	ADJ
ma-415	358	23	variable	variable	ADJ
ma-415	358	24	kernels	kernel	NOUN
ma-415	358	25	on	on	ADP
ma-415	358	26	the	the	DET
ma-415	358	27	hardy	hardy	ADJ
ma-415	358	28	and	and	CCONJ
ma-415	358	29	weak	weak	ADJ
ma-415	358	30	hardy	hardy	ADJ
ma-415	358	31	spacesover	spacesover	NOUN
ma-415	358	32	rn	rn	PROPN
ma-415	358	33	,	,	PUNCT
ma-415	358	34	acta	acta	PROPN
ma-415	358	35	math	math	PROPN
ma-415	358	36	.	.	PUNCT
ma-415	359	1	sin	sin	NOUN
ma-415	359	2	.	.	PUNCT
ma-415	360	1	engl	engl	PROPN
ma-415	360	2	.	.	PUNCT
ma-415	360	3	ser	ser	PROPN
ma-415	360	4	.	.	PROPN
ma-415	361	1	32	32	NUM
ma-415	361	2	(	(	PUNCT
ma-415	361	3	2016	2016	NUM
ma-415	361	4	)	)	PUNCT
ma-415	361	5	,	,	PUNCT
ma-415	361	6	411–438	411–438	NUM
ma-415	361	7	.	.	PUNCT
ma-415	362	1	https://doi.org/10.1007/s10114-016-4617-1[9	https://doi.org/10.1007/s10114-016-4617-1[9	PROPN
ma-415	362	2	]	]	X
ma-415	362	3	a.	a.	PROPN
ma-415	362	4	abdalmonem	abdalmonem	PROPN
ma-415	362	5	,	,	PUNCT
ma-415	362	6	o.	o.	PROPN
ma-415	362	7	abdalrhman	abdalrhman	PROPN
ma-415	362	8	,	,	PUNCT
ma-415	362	9	s.	s.	PROPN
ma-415	362	10	tao	tao	PROPN
ma-415	362	11	,	,	PUNCT
ma-415	362	12	boundedness	boundedness	NOUN
ma-415	362	13	of	of	ADP
ma-415	362	14	littlewood	littlewood	PROPN
ma-415	362	15	–	–	PUNCT
ma-415	362	16	paley	paley	ADJ
ma-415	362	17	operators	operator	NOUN
ma-415	362	18	with	with	ADP
ma-415	362	19	variable	variable	ADJ
ma-415	362	20	kernel	kernel	NOUN
ma-415	362	21	on	on	ADP
ma-415	362	22	theweighted	theweighte	VERB
ma-415	362	23	herz	herz	PROPN
ma-415	362	24	–	–	PUNCT
ma-415	362	25	morrey	morrey	PROPN
ma-415	362	26	spaces	space	VERB
ma-415	362	27	with	with	ADP
ma-415	362	28	variable	variable	ADJ
ma-415	362	29	exponent	exponent	NOUN
ma-415	362	30	,	,	PUNCT
ma-415	362	31	surv	surv	NOUN
ma-415	362	32	.	.	PUNCT
ma-415	363	1	math	math	NOUN
ma-415	363	2	.	.	PUNCT
ma-415	364	1	appl	appl	PROPN
ma-415	364	2	.	.	PROPN
ma-415	365	1	15	15	NUM
ma-415	365	2	(	(	PUNCT
ma-415	365	3	2020	2020	NUM
ma-415	365	4	)	)	PUNCT
ma-415	365	5	,	,	PUNCT
ma-415	365	6	295–313	295–313	NUM
ma-415	365	7	.	.	PUNCT
ma-415	366	1	https://www	https://www	PROPN
ma-415	366	2	.	.	PUNCT
ma-415	367	1	utgjiu.ro/math/sma/v15/v15.html[10	utgjiu.ro/math/sma/v15/v15.html[10	PROPN
ma-415	367	2	]	]	PUNCT
ma-415	368	1	a.	a.	PROPN
ma-415	368	2	almeida	almeida	PROPN
ma-415	368	3	,	,	PUNCT
ma-415	368	4	d.	d.	PROPN
ma-415	368	5	drihem	drihem	PROPN
ma-415	368	6	,	,	PUNCT
ma-415	368	7	maximal	maximal	ADJ
ma-415	368	8	,	,	PUNCT
ma-415	368	9	potential	potential	ADJ
ma-415	368	10	and	and	CCONJ
ma-415	368	11	singular	singular	ADJ
ma-415	368	12	type	type	NOUN
ma-415	368	13	operators	operator	NOUN
ma-415	368	14	on	on	ADP
ma-415	368	15	herz	herz	PROPN
ma-415	368	16	spaces	space	NOUN
ma-415	368	17	with	with	ADP
ma-415	368	18	variable	variable	ADJ
ma-415	368	19	exponents	exponent	NOUN
ma-415	368	20	,	,	PUNCT
ma-415	368	21	j.math	j.math	NOUN
ma-415	368	22	.	.	PUNCT
ma-415	369	1	anal	anal	PROPN
ma-415	369	2	.	.	PUNCT
ma-415	369	3	appl	appl	PROPN
ma-415	369	4	.	.	PROPN
ma-415	370	1	394	394	NUM
ma-415	370	2	(	(	PUNCT
ma-415	370	3	2012	2012	NUM
ma-415	370	4	)	)	PUNCT
ma-415	370	5	,	,	PUNCT
ma-415	370	6	781–795	781–795	NUM
ma-415	370	7	.	.	PUNCT
ma-415	371	1	https://doi.org/10.1016/j.jmaa.2012.04.043[11	https://doi.org/10.1016/j.jmaa.2012.04.043[11	PROPN
ma-415	371	2	]	]	PUNCT
ma-415	371	3	e.	e.	PROPN
ma-415	371	4	stein	stein	PROPN
ma-415	371	5	,	,	PUNCT
ma-415	371	6	singular	singular	PROPN
ma-415	371	7	integrals	integral	NOUN
ma-415	371	8	and	and	CCONJ
ma-415	371	9	differentiability	differentiability	NOUN
ma-415	371	10	properties	property	NOUN
ma-415	371	11	of	of	ADP
ma-415	371	12	functions	function	NOUN
ma-415	371	13	,	,	PUNCT
ma-415	371	14	princeton	princeton	PROPN
ma-415	371	15	univ	univ	PROPN
ma-415	371	16	.	.	PUNCT
ma-415	372	1	press	press	PROPN
ma-415	372	2	,	,	PUNCT
ma-415	372	3	princeton	princeton	PROPN
ma-415	372	4	(	(	PUNCT
ma-415	372	5	1970	1970	NUM
ma-415	372	6	)	)	PUNCT
ma-415	372	7	.	.	PUNCT
ma-415	373	1	https://doi.org/10.1112/blms/5.1.121[12	https://doi.org/10.1112/blms/5.1.121[12	NOUN
ma-415	373	2	]	]	PUNCT
ma-415	373	3	m.	m.	NOUN
ma-415	373	4	izuki	izuki	PROPN
ma-415	373	5	,	,	PUNCT
ma-415	373	6	t.	t.	PROPN
ma-415	373	7	noi	noi	PROPN
ma-415	373	8	,	,	PUNCT
ma-415	373	9	boundedness	boundedness	NOUN
ma-415	373	10	of	of	ADP
ma-415	373	11	some	some	DET
ma-415	373	12	integral	integral	ADJ
ma-415	373	13	operators	operator	NOUN
ma-415	373	14	and	and	CCONJ
ma-415	373	15	commutators	commutator	NOUN
ma-415	373	16	on	on	ADP
ma-415	373	17	generalized	generalize	VERB
ma-415	373	18	herz	herz	PROPN
ma-415	373	19	spaces	space	NOUN
ma-415	373	20	with	with	ADP
ma-415	373	21	variableexponents	variableexponent	NOUN
ma-415	373	22	,	,	PUNCT
ma-415	373	23	ocami	ocami	ADP
ma-415	373	24	preprint	preprint	NOUN
ma-415	373	25	ser	ser	NOUN
ma-415	373	26	.	.	PROPN
ma-415	373	27	11	11	NUM
ma-415	373	28	(	(	PUNCT
ma-415	373	29	2011	2011	NUM
ma-415	373	30	)	)	PUNCT
ma-415	373	31	,	,	PUNCT
ma-415	373	32	1–23	1–23	NOUN
ma-415	373	33	.	.	PUNCT
ma-415	374	1	https://ocu-omu.repo.nii.ac.jp/records/201676[13	https://ocu-omu.repo.nii.ac.jp/records/201676[13	NOUN
ma-415	374	2	]	]	PUNCT
ma-415	375	1	y.	y.	PROPN
ma-415	375	2	shu	shu	PROPN
ma-415	375	3	,	,	PUNCT
ma-415	375	4	l.	l.	PROPN
ma-415	375	5	wang	wang	PROPN
ma-415	375	6	,	,	PUNCT
ma-415	375	7	d.	d.	PROPN
ma-415	375	8	xia	xia	PROPN
ma-415	375	9	,	,	PUNCT
ma-415	375	10	sublinear	sublinear	VERB
ma-415	375	11	operators	operator	NOUN
ma-415	375	12	with	with	ADP
ma-415	375	13	rough	rough	ADJ
ma-415	375	14	kernel	kernel	NOUN
ma-415	375	15	on	on	ADP
ma-415	375	16	herz	herz	PROPN
ma-415	375	17	spaces	space	NOUN
ma-415	375	18	with	with	ADP
ma-415	375	19	variable	variable	ADJ
ma-415	375	20	exponent	exponent	NOUN
ma-415	375	21	,	,	PUNCT
ma-415	375	22	anal	anal	NOUN
ma-415	375	23	.	.	PUNCT
ma-415	376	1	theoryappl	theoryappl	ADJ
ma-415	376	2	.	.	PUNCT
ma-415	377	1	38	38	NUM
ma-415	377	2	(	(	PUNCT
ma-415	377	3	2022	2022	NUM
ma-415	377	4	)	)	PUNCT
ma-415	377	5	,	,	PUNCT
ma-415	377	6	79–91.[14	79–91.[14	NUM
ma-415	377	7	]	]	X
ma-415	377	8	m.a	m.a	PROPN
ma-415	377	9	.	.	PROPN
ma-415	377	10	ragusa	ragusa	PROPN
ma-415	377	11	,	,	PUNCT
ma-415	377	12	homogeneous	homogeneous	ADJ
ma-415	377	13	herz	herz	ADJ
ma-415	377	14	spaces	space	NOUN
ma-415	377	15	and	and	CCONJ
ma-415	377	16	regularity	regularity	NOUN
ma-415	377	17	results	result	NOUN
ma-415	377	18	,	,	PUNCT
ma-415	377	19	nonlinear	nonlinear	ADJ
ma-415	377	20	anal	anal	NOUN
ma-415	377	21	.	.	PUNCT
ma-415	378	1	71	71	NUM
ma-415	378	2	(	(	PUNCT
ma-415	378	3	2009	2009	NUM
ma-415	378	4	)	)	PUNCT
ma-415	379	1	,	,	PUNCT
ma-415	379	2	e1909	e1909	PROPN
ma-415	379	3	–	–	PUNCT
ma-415	379	4	e1914	e1914	PROPN
ma-415	379	5	.	.	PUNCT
ma-415	379	6	https	https	NOUN
ma-415	379	7	:	:	PUNCT
ma-415	380	1	//doi.org/10.1016	//doi.org/10.1016	PROPN
ma-415	380	2	/	/	SYM
ma-415	380	3	j.na.2009.02.075[15	j.na.2009.02.075[15	VERB
ma-415	380	4	]	]	PUNCT
ma-415	380	5	a.	a.	NOUN
ma-415	380	6	scapellato	scapellato	PROPN
ma-415	380	7	,	,	PUNCT
ma-415	380	8	homogeneous	homogeneous	ADJ
ma-415	380	9	herz	herz	PROPN
ma-415	380	10	spaces	space	NOUN
ma-415	380	11	with	with	ADP
ma-415	380	12	variable	variable	ADJ
ma-415	380	13	exponents	exponent	NOUN
ma-415	380	14	and	and	CCONJ
ma-415	380	15	regularity	regularity	NOUN
ma-415	380	16	results	result	NOUN
ma-415	380	17	,	,	PUNCT
ma-415	380	18	electron	electron	NOUN
ma-415	380	19	.	.	PUNCT
ma-415	381	1	j.	j.	PROPN
ma-415	381	2	qual	qual	PROPN
ma-415	381	3	.	.	PUNCT
ma-415	381	4	theorydiffer	theorydiffer	NOUN
ma-415	381	5	.	.	PUNCT
ma-415	382	1	equ	equ	PROPN
ma-415	382	2	.	.	PROPN
ma-415	382	3	2018	2018	NUM
ma-415	382	4	(	(	PUNCT
ma-415	382	5	2018	2018	NUM
ma-415	382	6	)	)	PUNCT
ma-415	382	7	,	,	PUNCT
ma-415	382	8	1–11	1–11	PROPN
ma-415	382	9	.	.	PUNCT
ma-415	383	1	https://doi.org/10.14232/ejqtde.2018.1.82[16	https://doi.org/10.14232/ejqtde.2018.1.82[16	PROPN
ma-415	383	2	]	]	PUNCT
ma-415	383	3	a.	a.	NOUN
ma-415	383	4	scapellato	scapellato	PROPN
ma-415	383	5	,	,	PUNCT
ma-415	383	6	regularity	regularity	NOUN
ma-415	383	7	of	of	ADP
ma-415	383	8	solutions	solution	NOUN
ma-415	383	9	to	to	ADP
ma-415	383	10	elliptic	elliptic	ADJ
ma-415	383	11	equations	equation	NOUN
ma-415	383	12	on	on	ADP
ma-415	383	13	herz	herz	PROPN
ma-415	383	14	spaces	space	NOUN
ma-415	383	15	with	with	ADP
ma-415	383	16	variable	variable	ADJ
ma-415	383	17	exponents	exponent	NOUN
ma-415	383	18	,	,	PUNCT
ma-415	383	19	bound	bind	VERB
ma-415	383	20	.	.	PUNCT
ma-415	384	1	valueprobl	valueprobl	PROPN
ma-415	384	2	.	.	PUNCT
ma-415	385	1	2019	2019	NUM
ma-415	385	2	(	(	PUNCT
ma-415	385	3	2019	2019	NUM
ma-415	385	4	)	)	PUNCT
ma-415	385	5	,	,	PUNCT
ma-415	385	6	1–13	1–13	NOUN
ma-415	385	7	.	.	PUNCT
ma-415	386	1	https://doi.org/10.1186/s13661-018-1116-6[17	https://doi.org/10.1186/s13661-018-1116-6[17	PROPN
ma-415	386	2	]	]	X
ma-415	386	3	m.a	m.a	PROPN
ma-415	386	4	.	.	PROPN
ma-415	386	5	ragusa	ragusa	PROPN
ma-415	386	6	,	,	PUNCT
ma-415	386	7	parabolic	parabolic	PROPN
ma-415	386	8	herz	herz	PROPN
ma-415	386	9	spaces	space	NOUN
ma-415	386	10	and	and	CCONJ
ma-415	386	11	their	their	PRON
ma-415	386	12	applications	application	NOUN
ma-415	386	13	,	,	PUNCT
ma-415	386	14	appl	appl	PROPN
ma-415	386	15	.	.	PROPN
ma-415	386	16	math	math	PROPN
ma-415	386	17	.	.	PUNCT
ma-415	387	1	lett	lett	PROPN
ma-415	387	2	.	.	PUNCT
ma-415	388	1	25	25	NUM
ma-415	388	2	(	(	PUNCT
ma-415	388	3	2012	2012	NUM
ma-415	388	4	)	)	PUNCT
ma-415	388	5	,	,	PUNCT
ma-415	388	6	1270–1273	1270–1273	NUM
ma-415	388	7	.	.	PUNCT
ma-415	388	8	https	https	NOUN
ma-415	388	9	:	:	PUNCT
ma-415	388	10	//doi.org/10.1016	//doi.org/10.1016	PROPN
ma-415	388	11	/	/	SYM
ma-415	388	12	j.aml.2011.11.022[18	j.aml.2011.11.022[18	PROPN
ma-415	388	13	]	]	PUNCT
ma-415	388	14	a.	a.	PROPN
ma-415	388	15	abdalmonem	abdalmonem	PROPN
ma-415	388	16	,	,	PUNCT
ma-415	388	17	o.	o.	PROPN
ma-415	388	18	abdalrhman	abdalrhman	PROPN
ma-415	388	19	,	,	PUNCT
ma-415	388	20	s.	s.	PROPN
ma-415	388	21	tao	tao	PROPN
ma-415	388	22	,	,	PUNCT
ma-415	388	23	boundedness	boundedness	NOUN
ma-415	388	24	of	of	ADP
ma-415	388	25	fractional	fractional	ADJ
ma-415	388	26	integral	integral	ADJ
ma-415	388	27	with	with	ADP
ma-415	388	28	variable	variable	ADJ
ma-415	388	29	kernel	kernel	NOUN
ma-415	388	30	and	and	CCONJ
ma-415	388	31	their	their	PRON
ma-415	388	32	commuta	commuta	ADJ
ma-415	388	33	-	-	PUNCT
ma-415	388	34	tors	tor	NOUN
ma-415	388	35	on	on	ADP
ma-415	388	36	variable	variable	ADJ
ma-415	388	37	exponent	exponent	NOUN
ma-415	388	38	herz	herz	PROPN
ma-415	388	39	spaces	space	NOUN
ma-415	388	40	,	,	PUNCT
ma-415	388	41	appl	appl	PROPN
ma-415	388	42	.	.	PROPN
ma-415	388	43	math	math	NOUN
ma-415	388	44	.	.	PUNCT
ma-415	389	1	7	7	NUM
ma-415	389	2	(	(	PUNCT
ma-415	389	3	2016	2016	NUM
ma-415	389	4	)	)	PUNCT
ma-415	389	5	,	,	PUNCT
ma-415	389	6	1160–1172	1160–1172	NUM
ma-415	389	7	.	.	PUNCT
ma-415	390	1	https://doi.org/10.4236/am.2016	https://doi.org/10.4236/am.2016	VERB
ma-415	390	2	.	.	NOUN
ma-415	390	3	710104[19	710104[19	NUM
ma-415	390	4	]	]	PUNCT
ma-415	390	5	a.	a.	NOUN
ma-415	390	6	abdalmonem	abdalmonem	PROPN
ma-415	390	7	,	,	PUNCT
ma-415	390	8	a.	a.	PROPN
ma-415	390	9	scapellato	scapellato	PROPN
ma-415	390	10	,	,	PUNCT
ma-415	390	11	intrinsic	intrinsic	ADJ
ma-415	390	12	square	square	ADJ
ma-415	390	13	functions	function	NOUN
ma-415	390	14	and	and	CCONJ
ma-415	390	15	commutators	commutator	NOUN
ma-415	390	16	on	on	ADP
ma-415	390	17	morrey	morrey	PROPN
ma-415	390	18	–	–	PUNCT
ma-415	390	19	herz	herz	PROPN
ma-415	390	20	spaces	space	VERB
ma-415	390	21	with	with	ADP
ma-415	390	22	variableexponents	variableexponent	NOUN
ma-415	390	23	,	,	PUNCT
ma-415	390	24	math	math	NOUN
ma-415	390	25	.	.	PUNCT
ma-415	391	1	methods	method	NOUN
ma-415	391	2	appl	appl	PROPN
ma-415	391	3	.	.	PUNCT
ma-415	392	1	sci	sci	PROPN
ma-415	392	2	.	.	PROPN
ma-415	392	3	44	44	NUM
ma-415	392	4	(	(	PUNCT
ma-415	392	5	2021	2021	NUM
ma-415	392	6	)	)	PUNCT
ma-415	392	7	,	,	PUNCT
ma-415	392	8	12408–12425	12408–12425	NUM
ma-415	392	9	.	.	PUNCT
ma-415	392	10	https://doi.org/10.1002/mma.7487[20	https://doi.org/10.1002/mma.7487[20	NUM
ma-415	392	11	]	]	X
ma-415	392	12	l.	l.	PROPN
ma-415	392	13	wang	wang	PROPN
ma-415	392	14	,	,	PUNCT
ma-415	392	15	s.	s.	PROPN
ma-415	392	16	tao	tao	PROPN
ma-415	392	17	,	,	PUNCT
ma-415	392	18	parameterized	parameterized	ADJ
ma-415	392	19	littlewood	littlewood	PROPN
ma-415	392	20	–	–	PUNCT
ma-415	392	21	paley	paley	ADJ
ma-415	392	22	operators	operator	NOUN
ma-415	392	23	and	and	CCONJ
ma-415	392	24	their	their	PRON
ma-415	392	25	commutators	commutator	NOUN
ma-415	392	26	on	on	ADP
ma-415	392	27	herz	herz	PROPN
ma-415	392	28	spaces	space	NOUN
ma-415	392	29	with	with	ADP
ma-415	392	30	variableexponents	variableexponent	NOUN
ma-415	392	31	,	,	PUNCT
ma-415	392	32	turk	turk	PROPN
ma-415	392	33	.	.	PUNCT
ma-415	393	1	j.	j.	PROPN
ma-415	393	2	math	math	PROPN
ma-415	393	3	.	.	PUNCT
ma-415	394	1	40	40	NUM
ma-415	394	2	(	(	PUNCT
ma-415	394	3	2016	2016	NUM
ma-415	394	4	)	)	PUNCT
ma-415	394	5	,	,	PUNCT
ma-415	394	6	122–145	122–145	NUM
ma-415	394	7	.	.	PUNCT
ma-415	395	1	https://doi.org/10.3906/mat-1412-52[21	https://doi.org/10.3906/mat-1412-52[21	PROPN
ma-415	395	2	]	]	PUNCT
ma-415	395	3	o.	o.	PROPN
ma-415	395	4	abdalrhman	abdalrhman	PROPN
ma-415	395	5	,	,	PUNCT
ma-415	395	6	m.	m.	NOUN
ma-415	395	7	zainul	zainul	NOUN
ma-415	395	8	abidin	abidin	PROPN
ma-415	395	9	,	,	PUNCT
ma-415	395	10	boundedness	boundedness	NOUN
ma-415	395	11	of	of	ADP
ma-415	395	12	the	the	DET
ma-415	395	13	vector	vector	NOUN
ma-415	395	14	-	-	PUNCT
ma-415	395	15	valued	value	VERB
ma-415	395	16	intrinsic	intrinsic	ADJ
ma-415	395	17	square	square	ADJ
ma-415	395	18	functions	function	NOUN
ma-415	395	19	on	on	ADP
ma-415	395	20	variable	variable	ADJ
ma-415	395	21	exponentsherz	exponentsherz	PROPN
ma-415	395	22	spaces	space	NOUN
ma-415	395	23	,	,	PUNCT
ma-415	395	24	mathematics	mathematics	PROPN
ma-415	395	25	10	10	NUM
ma-415	395	26	(	(	PUNCT
ma-415	395	27	2022	2022	NUM
ma-415	395	28	)	)	PUNCT
ma-415	395	29	,	,	PUNCT
ma-415	395	30	1168	1168	NUM
ma-415	395	31	.	.	PUNCT
ma-415	396	1	https://doi.org/10.3390/math10071168[22	https://doi.org/10.3390/math10071168[22	PROPN
ma-415	396	2	]	]	X
ma-415	396	3	d.	d.	PROPN
ma-415	396	4	cruz	cruz	PROPN
ma-415	396	5	-	-	PUNCT
ma-415	396	6	uribe	uribe	PROPN
ma-415	396	7	,	,	PUNCT
ma-415	396	8	a.	a.	NOUN
ma-415	396	9	fiorenza	fiorenza	PROPN
ma-415	396	10	,	,	PUNCT
ma-415	396	11	variable	variable	ADJ
ma-415	396	12	lebesgue	lebesgue	NOUN
ma-415	396	13	spaces	space	NOUN
ma-415	396	14	.	.	PUNCT
ma-415	397	1	foundations	foundation	NOUN
ma-415	397	2	and	and	CCONJ
ma-415	397	3	harmonic	harmonic	ADJ
ma-415	397	4	analysis	analysis	NOUN
ma-415	397	5	,	,	PUNCT
ma-415	397	6	appl	appl	PROPN
ma-415	397	7	.	.	PUNCT
ma-415	398	1	numer	numer	PROPN
ma-415	398	2	.	.	PUNCT
ma-415	399	1	harmon.anal	harmon.anal	PROPN
ma-415	399	2	.	.	PROPN
ma-415	399	3	,	,	PUNCT
ma-415	399	4	springer	springer	NOUN
ma-415	399	5	,	,	PUNCT
ma-415	399	6	new	new	PROPN
ma-415	399	7	york	york	PROPN
ma-415	399	8	(	(	PUNCT
ma-415	399	9	2013	2013	NUM
ma-415	399	10	)	)	PUNCT
ma-415	399	11	.	.	PUNCT
ma-415	400	1	https://doi.org/10.1007/978-3-0348-0548-3[23	https://doi.org/10.1007/978-3-0348-0548-3[23	PROPN
ma-415	400	2	]	]	PUNCT
ma-415	400	3	m.	m.	PROPN
ma-415	400	4	izuki	izuki	PROPN
ma-415	400	5	,	,	PUNCT
ma-415	400	6	commutators	commutator	NOUN
ma-415	400	7	of	of	ADP
ma-415	400	8	fractional	fractional	ADJ
ma-415	400	9	integrals	integral	NOUN
ma-415	400	10	on	on	ADP
ma-415	400	11	lebesgue	lebesgue	NOUN
ma-415	400	12	and	and	CCONJ
ma-415	400	13	herz	herz	PROPN
ma-415	400	14	spaces	space	NOUN
ma-415	400	15	with	with	ADP
ma-415	400	16	variable	variable	ADJ
ma-415	400	17	exponent	exponent	NOUN
ma-415	400	18	,	,	PUNCT
ma-415	400	19	rend	rend	VERB
ma-415	400	20	.	.	PUNCT
ma-415	401	1	circ	circ	PROPN
ma-415	401	2	.	.	PUNCT
ma-415	402	1	mat.palermo	mat.palermo	NOUN
ma-415	402	2	59	59	NUM
ma-415	402	3	(	(	PUNCT
ma-415	402	4	2010	2010	NUM
ma-415	402	5	)	)	PUNCT
ma-415	402	6	,	,	PUNCT
ma-415	402	7	461–472	461–472	NUM
ma-415	402	8	.	.	PUNCT
ma-415	403	1	https://doi.org/10.1007/s12215-010-0034-y[24	https://doi.org/10.1007/s12215-010-0034-y[24	PROPN
ma-415	403	2	]	]	X
ma-415	403	3	d.	d.	PROPN
ma-415	403	4	cruz	cruz	PROPN
ma-415	403	5	-	-	PUNCT
ma-415	403	6	uribe	uribe	PROPN
ma-415	403	7	,	,	PUNCT
ma-415	403	8	a.	a.	NOUN
ma-415	403	9	fiorenza	fiorenza	PROPN
ma-415	403	10	,	,	PUNCT
ma-415	403	11	j.	j.	PROPN
ma-415	403	12	martell	martell	PROPN
ma-415	403	13	,	,	PUNCT
ma-415	403	14	c.	c.	NOUN
ma-415	403	15	pérez	pérez	NOUN
ma-415	403	16	,	,	PUNCT
ma-415	403	17	the	the	DET
ma-415	403	18	boundedness	boundedness	NOUN
ma-415	403	19	of	of	ADP
ma-415	403	20	classical	classical	ADJ
ma-415	403	21	operators	operator	NOUN
ma-415	403	22	on	on	ADP
ma-415	403	23	variable	variable	ADJ
ma-415	403	24	lp	lp	NOUN
ma-415	403	25	spaces	space	NOUN
ma-415	403	26	,	,	PUNCT
ma-415	403	27	ann.fenn	ann.fenn	PROPN
ma-415	403	28	.	.	PUNCT
ma-415	403	29	math	math	NOUN
ma-415	403	30	.	.	PUNCT
ma-415	404	1	31	31	NUM
ma-415	404	2	(	(	PUNCT
ma-415	404	3	2006	2006	NUM
ma-415	404	4	)	)	PUNCT
ma-415	404	5	,	,	PUNCT
ma-415	404	6	239–264	239–264	NUM
ma-415	404	7	.	.	PUNCT
ma-415	405	1	http://eudml.org/doc/126704[25	http://eudml.org/doc/126704[25	PROPN
ma-415	405	2	]	]	PUNCT
ma-415	405	3	a.	a.	PROPN
ma-415	405	4	abdalmonem	abdalmonem	PROPN
ma-415	405	5	,	,	PUNCT
ma-415	405	6	o.	o.	PROPN
ma-415	405	7	abdalrhman	abdalrhman	PROPN
ma-415	405	8	,	,	PUNCT
ma-415	405	9	h.	h.	PROPN
ma-415	405	10	mohammed	mohammed	PROPN
ma-415	405	11	,	,	PUNCT
ma-415	405	12	commutators	commutator	NOUN
ma-415	405	13	of	of	ADP
ma-415	405	14	fractional	fractional	ADJ
ma-415	405	15	integral	integral	ADJ
ma-415	405	16	with	with	ADP
ma-415	405	17	variable	variable	ADJ
ma-415	405	18	kernel	kernel	NOUN
ma-415	405	19	on	on	ADP
ma-415	405	20	variableexponent	variableexponent	ADJ
ma-415	405	21	herz	herz	PROPN
ma-415	405	22	–	–	PUNCT
ma-415	405	23	morrey	morrey	PROPN
ma-415	405	24	spaces	space	NOUN
ma-415	405	25	,	,	PUNCT
ma-415	405	26	open	open	ADJ
ma-415	405	27	j.	j.	PROPN
ma-415	405	28	math	math	PROPN
ma-415	405	29	.	.	PUNCT
ma-415	406	1	anal	anal	PROPN
ma-415	406	2	.	.	PUNCT
ma-415	407	1	(	(	PUNCT
ma-415	407	2	2019	2019	NUM
ma-415	407	3	)	)	PUNCT
ma-415	407	4	,	,	PUNCT
ma-415	407	5	19–29	19–29	NUM
ma-415	407	6	.	.	PUNCT
ma-415	408	1	https://doi.org/10.28924/ada/ma.5.22	https://doi.org/10.28924/ada/ma.5.22	PROPN
ma-415	408	2	https://doi.org/10.1007/s11401-021-0268-3	https://doi.org/10.1007/s11401-021-0268-3	NUM
ma-415	408	3	https://doi.org/10.1007/s11401-021-0268-3	https://doi.org/10.1007/s11401-021-0268-3	NUM
ma-415	409	1	https://doi.org/10.1007/s10114-016-4617-1	https://doi.org/10.1007/s10114-016-4617-1	NUM
ma-415	409	2	https://www.utgjiu.ro/math/sma/v15/v15.html	https://www.utgjiu.ro/math/sma/v15/v15.html	PROPN
ma-415	409	3	https://www.utgjiu.ro/math/sma/v15/v15.html	https://www.utgjiu.ro/math/sma/v15/v15.html	PROPN
ma-415	409	4	https://doi.org/10.1016/j.jmaa.2012.04.043	https://doi.org/10.1016/j.jmaa.2012.04.043	PROPN
ma-415	409	5	https://doi.org/10.1112/blms/5.1.121	https://doi.org/10.1112/blms/5.1.121	VERB
ma-415	409	6	https://ocu-omu.repo.nii.ac.jp/records/201676	https://ocu-omu.repo.nii.ac.jp/records/201676	PROPN
ma-415	409	7	https://doi.org/10.1016/j.na.2009.02.075	https://doi.org/10.1016/j.na.2009.02.075	PROPN
ma-415	409	8	https://doi.org/10.1016/j.na.2009.02.075	https://doi.org/10.1016/j.na.2009.02.075	X
ma-415	409	9	https://doi.org/10.14232/ejqtde.2018.1.82	https://doi.org/10.14232/ejqtde.2018.1.82	X
ma-415	409	10	https://doi.org/10.1186/s13661-018-1116-6	https://doi.org/10.1186/s13661-018-1116-6	X
ma-415	409	11	https://doi.org/10.1016/j.aml.2011.11.022	https://doi.org/10.1016/j.aml.2011.11.022	NOUN
ma-415	409	12	https://doi.org/10.1016/j.aml.2011.11.022	https://doi.org/10.1016/j.aml.2011.11.022	NOUN
ma-415	409	13	https://doi.org/10.4236/am.2016.710104	https://doi.org/10.4236/am.2016.710104	NOUN
ma-415	409	14	https://doi.org/10.4236/am.2016.710104	https://doi.org/10.4236/am.2016.710104	PROPN
ma-415	410	1	https://doi.org/10.1002/mma.7487	https://doi.org/10.1002/mma.7487	PROPN
ma-415	410	2	https://doi.org/10.3906/mat-1412-52	https://doi.org/10.3906/mat-1412-52	PROPN
ma-415	410	3	https://doi.org/10.3390/math10071168	https://doi.org/10.3390/math10071168	VERB
ma-415	410	4	https://doi.org/10.1007/978-3-0348-0548-3	https://doi.org/10.1007/978-3-0348-0548-3	PROPN
ma-415	410	5	https://doi.org/10.1007/s12215-010-0034-y	https://doi.org/10.1007/s12215-010-0034-y	PROPN
ma-415	410	6	http://eudml.org/doc/126704	http://eudml.org/doc/126704	PROPN
ma-415	410	7	1	1	NUM
ma-415	410	8	.	.	PUNCT
ma-415	411	1	introduction	introduction	NOUN
ma-415	411	2	2	2	NUM
ma-415	411	3	.	.	PUNCT
ma-415	411	4	mathematical	mathematical	ADJ
ma-415	411	5	background	background	NOUN
ma-415	411	6	3	3	NUM
ma-415	411	7	.	.	PUNCT
ma-415	412	1	boundedness	boundedness	NOUN
ma-415	412	2	of	of	ADP
ma-415	412	3	the	the	DET
ma-415	412	4	parameterized	parameterized	ADJ
ma-415	412	5	littlewood	littlewood	PROPN
ma-415	412	6	-	-	PUNCT
ma-415	412	7	paley	paley	PROPN
ma-415	412	8	operators	operator	NOUN
ma-415	412	9	author	author	NOUN
ma-415	412	10	contributions	contribution	NOUN
ma-415	412	11	:	:	PUNCT
ma-415	412	12	conflicts	conflict	NOUN
ma-415	412	13	of	of	ADP
ma-415	412	14	interest	interest	NOUN
ma-415	412	15	:	:	PUNCT
ma-415	412	16	references	reference	NOUN