id	sid	tid	token	lemma	pos
ejpam-6667	1	1	european	european	PROPN
ejpam-6667	1	2	journal	journal	PROPN
ejpam-6667	1	3	of	of	ADP
ejpam-6667	1	4	pure	pure	ADJ
ejpam-6667	1	5	and	and	CCONJ
ejpam-6667	1	6	applied	applied	ADJ
ejpam-6667	1	7	mathematics	mathematic	NOUN
ejpam-6667	1	8	2025	2025	NUM
ejpam-6667	1	9	,	,	PUNCT
ejpam-6667	1	10	vol	vol	NOUN
ejpam-6667	1	11	.	.	PROPN
ejpam-6667	1	12	18	18	NUM
ejpam-6667	1	13	,	,	PUNCT
ejpam-6667	1	14	issue	issue	NOUN
ejpam-6667	1	15	4	4	NUM
ejpam-6667	1	16	,	,	PUNCT
ejpam-6667	1	17	article	article	NOUN
ejpam-6667	1	18	number	number	NOUN
ejpam-6667	1	19	6667	6667	NUM
ejpam-6667	1	20	issn	issn	PROPN
ejpam-6667	1	21	1307	1307	NUM
ejpam-6667	1	22	-	-	SYM
ejpam-6667	1	23	5543	5543	NUM
ejpam-6667	1	24	–	–	PUNCT
ejpam-6667	1	25	ejpam.com	ejpam.com	X
ejpam-6667	1	26	published	publish	VERB
ejpam-6667	1	27	by	by	ADP
ejpam-6667	1	28	new	new	PROPN
ejpam-6667	1	29	york	york	PROPN
ejpam-6667	1	30	business	business	PROPN
ejpam-6667	1	31	global	global	PROPN
ejpam-6667	1	32	some	some	DET
ejpam-6667	1	33	new	new	ADJ
ejpam-6667	1	34	weighted	weight	VERB
ejpam-6667	1	35	results	result	NOUN
ejpam-6667	1	36	for	for	ADP
ejpam-6667	1	37	the	the	DET
ejpam-6667	1	38	hardy	hardy	ADJ
ejpam-6667	1	39	operator	operator	NOUN
ejpam-6667	1	40	on	on	ADP
ejpam-6667	1	41	variable	variable	ADJ
ejpam-6667	1	42	-	-	PUNCT
ejpam-6667	1	43	exponent	exponent	NOUN
ejpam-6667	1	44	λ	λ	NOUN
ejpam-6667	1	45	-	-	ADJ
ejpam-6667	1	46	central	central	ADJ
ejpam-6667	1	47	morrey	morrey	NOUN
ejpam-6667	1	48	space	space	NOUN
ejpam-6667	1	49	muhammad	muhammad	PROPN
ejpam-6667	1	50	asim1	asim1	PROPN
ejpam-6667	1	51	,	,	PUNCT
ejpam-6667	1	52	khaled	khaled	PROPN
ejpam-6667	1	53	suwais2	suwais2	PROPN
ejpam-6667	1	54	,	,	PUNCT
ejpam-6667	1	55	nabil	nabil	PROPN
ejpam-6667	1	56	mlaiki3,∗	mlaiki3,∗	PROPN
ejpam-6667	1	57	1	1	NUM
ejpam-6667	1	58	department	department	NOUN
ejpam-6667	1	59	of	of	ADP
ejpam-6667	1	60	nusash	nusash	PROPN
ejpam-6667	1	61	,	,	PUNCT
ejpam-6667	1	62	national	national	ADJ
ejpam-6667	1	63	university	university	PROPN
ejpam-6667	1	64	of	of	ADP
ejpam-6667	1	65	technology	technology	NOUN
ejpam-6667	1	66	(	(	PUNCT
ejpam-6667	1	67	nutech	nutech	NOUN
ejpam-6667	1	68	)	)	PUNCT
ejpam-6667	1	69	,	,	PUNCT
ejpam-6667	1	70	islamabad	islamabad	NOUN
ejpam-6667	1	71	44000	44000	NUM
ejpam-6667	1	72	,	,	PUNCT
ejpam-6667	1	73	pakistan	pakistan	PROPN
ejpam-6667	1	74	2	2	NUM
ejpam-6667	1	75	faculty	faculty	NOUN
ejpam-6667	1	76	of	of	ADP
ejpam-6667	1	77	computer	computer	NOUN
ejpam-6667	1	78	studies	study	NOUN
ejpam-6667	1	79	,	,	PUNCT
ejpam-6667	1	80	arab	arab	ADJ
ejpam-6667	1	81	open	open	PROPN
ejpam-6667	1	82	university	university	PROPN
ejpam-6667	1	83	,	,	PUNCT
ejpam-6667	1	84	riyadh	riyadh	PROPN
ejpam-6667	1	85	11681	11681	NUM
ejpam-6667	1	86	,	,	PUNCT
ejpam-6667	1	87	saudi	saudi	PROPN
ejpam-6667	1	88	arabia	arabia	PROPN
ejpam-6667	1	89	3	3	NUM
ejpam-6667	1	90	department	department	NOUN
ejpam-6667	1	91	of	of	ADP
ejpam-6667	1	92	mathematics	mathematic	NOUN
ejpam-6667	1	93	and	and	CCONJ
ejpam-6667	1	94	sciences	science	NOUN
ejpam-6667	1	95	,	,	PUNCT
ejpam-6667	1	96	prince	prince	PROPN
ejpam-6667	1	97	sultan	sultan	PROPN
ejpam-6667	1	98	university	university	PROPN
ejpam-6667	1	99	,	,	PUNCT
ejpam-6667	1	100	riyadh	riyadh	PROPN
ejpam-6667	1	101	11586	11586	NUM
ejpam-6667	1	102	,	,	PUNCT
ejpam-6667	1	103	saudi	saudi	PROPN
ejpam-6667	1	104	arabia	arabia	PROPN
ejpam-6667	1	105	abstract	abstract	NOUN
ejpam-6667	1	106	.	.	PUNCT
ejpam-6667	2	1	the	the	DET
ejpam-6667	2	2	main	main	ADJ
ejpam-6667	2	3	purpose	purpose	NOUN
ejpam-6667	2	4	of	of	ADP
ejpam-6667	2	5	this	this	DET
ejpam-6667	2	6	study	study	NOUN
ejpam-6667	2	7	is	be	AUX
ejpam-6667	2	8	to	to	PART
ejpam-6667	2	9	demonstrate	demonstrate	VERB
ejpam-6667	2	10	that	that	SCONJ
ejpam-6667	2	11	the	the	DET
ejpam-6667	2	12	fractional	fractional	ADJ
ejpam-6667	2	13	hardy	hardy	ADJ
ejpam-6667	2	14	operators	operator	NOUN
ejpam-6667	2	15	are	be	AUX
ejpam-6667	2	16	bounded	bound	VERB
ejpam-6667	2	17	on	on	ADP
ejpam-6667	2	18	the	the	DET
ejpam-6667	2	19	weighted	weight	VERB
ejpam-6667	2	20	variable	variable	ADJ
ejpam-6667	2	21	central	central	ADJ
ejpam-6667	2	22	morrey	morrey	PROPN
ejpam-6667	2	23	space	space	NOUN
ejpam-6667	2	24	.	.	PUNCT
ejpam-6667	3	1	when	when	SCONJ
ejpam-6667	3	2	the	the	DET
ejpam-6667	3	3	symbol	symbol	NOUN
ejpam-6667	3	4	functions	function	NOUN
ejpam-6667	3	5	belong	belong	VERB
ejpam-6667	3	6	to	to	ADP
ejpam-6667	3	7	the	the	DET
ejpam-6667	3	8	λ	λ	ADJ
ejpam-6667	3	9	-	-	ADJ
ejpam-6667	3	10	central	central	ADJ
ejpam-6667	3	11	bmo	bmo	NOUN
ejpam-6667	3	12	space	space	NOUN
ejpam-6667	3	13	with	with	ADP
ejpam-6667	3	14	a	a	DET
ejpam-6667	3	15	variable	variable	ADJ
ejpam-6667	3	16	exponent	exponent	NOUN
ejpam-6667	3	17	,	,	PUNCT
ejpam-6667	3	18	the	the	DET
ejpam-6667	3	19	estimates	estimate	NOUN
ejpam-6667	3	20	for	for	ADP
ejpam-6667	3	21	their	their	PRON
ejpam-6667	3	22	commutators	commutator	NOUN
ejpam-6667	3	23	are	be	AUX
ejpam-6667	3	24	similar	similar	ADJ
ejpam-6667	3	25	.	.	PUNCT
ejpam-6667	4	1	2020	2020	NUM
ejpam-6667	4	2	mathematics	mathematic	NOUN
ejpam-6667	4	3	subject	subject	NOUN
ejpam-6667	4	4	classifications	classification	NOUN
ejpam-6667	4	5	:	:	PUNCT
ejpam-6667	4	6	42b35	42b35	NUM
ejpam-6667	4	7	,	,	PUNCT
ejpam-6667	4	8	26d10	26d10	NUM
ejpam-6667	4	9	,	,	PUNCT
ejpam-6667	4	10	47b38	47b38	NUM
ejpam-6667	4	11	,	,	PUNCT
ejpam-6667	4	12	47g10	47g10	NUM
ejpam-6667	4	13	key	key	ADJ
ejpam-6667	4	14	words	word	NOUN
ejpam-6667	4	15	and	and	CCONJ
ejpam-6667	4	16	phrases	phrase	NOUN
ejpam-6667	4	17	:	:	PUNCT
ejpam-6667	4	18	fractional	fractional	ADJ
ejpam-6667	4	19	operators	operator	NOUN
ejpam-6667	4	20	,	,	PUNCT
ejpam-6667	4	21	weighted	weight	VERB
ejpam-6667	4	22	morrey	morrey	PROPN
ejpam-6667	4	23	space	space	NOUN
ejpam-6667	4	24	,	,	PUNCT
ejpam-6667	4	25	variable	variable	ADJ
ejpam-6667	4	26	exponent	exponent	NOUN
ejpam-6667	4	27	,	,	PUNCT
ejpam-6667	4	28	integral	integral	ADJ
ejpam-6667	4	29	operators	operator	NOUN
ejpam-6667	4	30	1	1	NUM
ejpam-6667	4	31	.	.	PUNCT
ejpam-6667	5	1	introduction	introduction	NOUN
ejpam-6667	5	2	let	let	VERB
ejpam-6667	5	3	l1	l1	PROPN
ejpam-6667	5	4	loc(rn	loc(rn	PRON
ejpam-6667	5	5	)	)	PUNCT
ejpam-6667	5	6	denote	denote	VERB
ejpam-6667	5	7	the	the	DET
ejpam-6667	5	8	set	set	NOUN
ejpam-6667	5	9	consisting	consisting	NOUN
ejpam-6667	5	10	of	of	ADP
ejpam-6667	5	11	all	all	DET
ejpam-6667	5	12	complex	complex	NOUN
ejpam-6667	5	13	-	-	PUNCT
ejpam-6667	5	14	valued	value	VERB
ejpam-6667	5	15	integrable	integrable	ADJ
ejpam-6667	5	16	functions	function	NOUN
ejpam-6667	5	17	on	on	ADP
ejpam-6667	5	18	rn	rn	PROPN
ejpam-6667	5	19	,	,	PUNCT
ejpam-6667	5	20	in	in	ADP
ejpam-6667	5	21	[	[	PUNCT
ejpam-6667	5	22	1	1	NUM
ejpam-6667	5	23	]	]	PUNCT
ejpam-6667	5	24	,	,	PUNCT
ejpam-6667	5	25	the	the	DET
ejpam-6667	5	26	hardy	hardy	ADJ
ejpam-6667	5	27	operator	operator	NOUN
ejpam-6667	5	28	is	be	AUX
ejpam-6667	5	29	defined	define	VERB
ejpam-6667	5	30	as	as	SCONJ
ejpam-6667	5	31	follows	follow	VERB
ejpam-6667	5	32	:	:	PUNCT
ejpam-6667	5	33	hf(x	hf(x	X
ejpam-6667	5	34	)	)	PUNCT
ejpam-6667	5	35	=	=	SYM
ejpam-6667	6	1	1	1	NUM
ejpam-6667	6	2	x	x	SYM
ejpam-6667	6	3	∫	∫	PROPN
ejpam-6667	6	4	x	x	SYM
ejpam-6667	6	5	0	0	NUM
ejpam-6667	6	6	f(t)dt	f(t)dt	PROPN
ejpam-6667	6	7	,	,	PUNCT
ejpam-6667	6	8	x	x	X
ejpam-6667	6	9	>	>	X
ejpam-6667	6	10	0	0	NUM
ejpam-6667	6	11	,	,	PUNCT
ejpam-6667	6	12	which	which	PRON
ejpam-6667	6	13	was	be	AUX
ejpam-6667	6	14	generalized	generalize	VERB
ejpam-6667	6	15	by	by	ADP
ejpam-6667	6	16	faris	faris	PROPN
ejpam-6667	6	17	[	[	X
ejpam-6667	6	18	2	2	NUM
ejpam-6667	6	19	]	]	PUNCT
ejpam-6667	6	20	to	to	ADP
ejpam-6667	6	21	n	n	CCONJ
ejpam-6667	6	22	-	-	PUNCT
ejpam-6667	6	23	dimensional	dimensional	ADJ
ejpam-6667	6	24	euclidean	euclidean	ADJ
ejpam-6667	6	25	space	space	NOUN
ejpam-6667	6	26	and	and	CCONJ
ejpam-6667	6	27	defined	define	VERB
ejpam-6667	6	28	as	as	ADP
ejpam-6667	6	29	:	:	PUNCT
ejpam-6667	6	30	hf(x	hf(x	X
ejpam-6667	6	31	)	)	PUNCT
ejpam-6667	6	32	=	=	SYM
ejpam-6667	6	33	1	1	NUM
ejpam-6667	6	34	vn|x|n	vn|x|n	NOUN
ejpam-6667	6	35	∫	∫	PROPN
ejpam-6667	6	36	|y|<|x|	|y|<|x|	PROPN
ejpam-6667	6	37	f(y)dy	f(y)dy	NOUN
ejpam-6667	6	38	,	,	PUNCT
ejpam-6667	6	39	where	where	SCONJ
ejpam-6667	6	40	x	x	PUNCT
ejpam-6667	6	41	∈	∈	PROPN
ejpam-6667	6	42	rn	rn	PROPN
ejpam-6667	6	43	\	\	PROPN
ejpam-6667	6	44	{	{	PUNCT
ejpam-6667	6	45	0	0	NUM
ejpam-6667	6	46	}	}	PUNCT
ejpam-6667	6	47	,	,	PUNCT
ejpam-6667	6	48	f	f	PROPN
ejpam-6667	6	49	∈	∈	PROPN
ejpam-6667	6	50	l1	l1	PROPN
ejpam-6667	6	51	loc(rn	loc(rn	PROPN
ejpam-6667	6	52	)	)	PUNCT
ejpam-6667	6	53	,	,	PUNCT
ejpam-6667	6	54	and	and	CCONJ
ejpam-6667	6	55	vn	vn	PROPN
ejpam-6667	6	56	represents	represent	VERB
ejpam-6667	6	57	the	the	DET
ejpam-6667	6	58	volume	volume	NOUN
ejpam-6667	6	59	of	of	ADP
ejpam-6667	6	60	the	the	DET
ejpam-6667	6	61	unit	unit	NOUN
ejpam-6667	6	62	ball	ball	NOUN
ejpam-6667	6	63	.	.	PUNCT
ejpam-6667	7	1	the	the	DET
ejpam-6667	7	2	n	n	ADV
ejpam-6667	7	3	-	-	PUNCT
ejpam-6667	7	4	dimensional	dimensional	ADJ
ejpam-6667	7	5	fractional	fractional	ADJ
ejpam-6667	7	6	hardy	hardy	ADJ
ejpam-6667	7	7	operator	operator	NOUN
ejpam-6667	7	8	hα	hα	NOUN
ejpam-6667	7	9	and	and	CCONJ
ejpam-6667	7	10	its	its	PRON
ejpam-6667	7	11	dual	dual	ADJ
ejpam-6667	7	12	operator	operator	NOUN
ejpam-6667	7	13	are	be	AUX
ejpam-6667	7	14	defined	define	VERB
ejpam-6667	7	15	as	as	SCONJ
ejpam-6667	7	16	follows	follow	VERB
ejpam-6667	7	17	:	:	PUNCT
ejpam-6667	7	18	hαf(x	hαf(x	NOUN
ejpam-6667	7	19	)	)	PUNCT
ejpam-6667	8	1	=	=	PRON
ejpam-6667	8	2	|x|α−n	|x|α−n	PRON
ejpam-6667	8	3	∫	∫	PROPN
ejpam-6667	8	4	|y|<|x|	|y|<|x|	PROPN
ejpam-6667	8	5	f(y)dy	f(y)dy	PART
ejpam-6667	8	6	,	,	PUNCT
ejpam-6667	8	7	h∗	h∗	PROPN
ejpam-6667	8	8	αf(x	αf(x	NUM
ejpam-6667	8	9	)	)	PUNCT
ejpam-6667	8	10	=	=	SYM
ejpam-6667	8	11	∫	∫	PROPN
ejpam-6667	8	12	|y|>|x|	|y|>|x|	X
ejpam-6667	8	13	|y|α−nf(y)dy	|y|α−nf(y)dy	NOUN
ejpam-6667	8	14	.	.	PUNCT
ejpam-6667	9	1	∗corresponding	∗corresponde	VERB
ejpam-6667	9	2	author	author	NOUN
ejpam-6667	9	3	.	.	PUNCT
ejpam-6667	10	1	doi	doi	NOUN
ejpam-6667	10	2	:	:	PUNCT
ejpam-6667	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6667	https://doi.org/10.29020/nybg.ejpam.v18i4.6667	VERB
ejpam-6667	10	4	email	email	NOUN
ejpam-6667	10	5	addresses	address	NOUN
ejpam-6667	10	6	:	:	PUNCT
ejpam-6667	10	7	masim@math.qau.edu.pk	masim@math.qau.edu.pk	PROPN
ejpam-6667	10	8	(	(	PUNCT
ejpam-6667	10	9	m.	m.	PROPN
ejpam-6667	10	10	asim	asim	PROPN
ejpam-6667	10	11	)	)	PUNCT
ejpam-6667	10	12	,	,	PUNCT
ejpam-6667	10	13	khaled.suwais@arabou.edu.sa	khaled.suwais@arabou.edu.sa	PROPN
ejpam-6667	10	14	(	(	PUNCT
ejpam-6667	10	15	k.	k.	PROPN
ejpam-6667	10	16	suwais	suwais	PROPN
ejpam-6667	10	17	)	)	PUNCT
ejpam-6667	10	18	,	,	PUNCT
ejpam-6667	10	19	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-6667	10	20	(	(	PUNCT
ejpam-6667	10	21	n.	n.	PROPN
ejpam-6667	10	22	mlaiki	mlaiki	PROPN
ejpam-6667	10	23	)	)	PUNCT
ejpam-6667	10	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6667	11	1	1	1	NUM
ejpam-6667	11	2	copyright	copyright	NOUN
ejpam-6667	11	3	:	:	PUNCT
ejpam-6667	11	4	©	©	PROPN
ejpam-6667	11	5	2025	2025	NUM
ejpam-6667	11	6	the	the	DET
ejpam-6667	11	7	author(s	author(s	NOUN
ejpam-6667	11	8	)	)	PUNCT
ejpam-6667	11	9	.	.	PUNCT
ejpam-6667	12	1	(	(	PUNCT
ejpam-6667	12	2	cc	cc	NOUN
ejpam-6667	12	3	by	by	ADP
ejpam-6667	12	4	-	-	PUNCT
ejpam-6667	12	5	nc	nc	PROPN
ejpam-6667	12	6	4.0	4.0	NUM
ejpam-6667	12	7	)	)	PUNCT
ejpam-6667	12	8	m.	m.	NOUN
ejpam-6667	12	9	asim	asim	PROPN
ejpam-6667	12	10	,	,	PUNCT
ejpam-6667	12	11	k.	k.	PROPN
ejpam-6667	12	12	suwais	suwais	PROPN
ejpam-6667	12	13	,	,	PUNCT
ejpam-6667	12	14	n.	n.	PROPN
ejpam-6667	12	15	mlaiki	mlaiki	PROPN
ejpam-6667	12	16	/	/	SYM
ejpam-6667	12	17	eur	eur	PROPN
ejpam-6667	12	18	.	.	PUNCT
ejpam-6667	13	1	j.	j.	PROPN
ejpam-6667	13	2	pure	pure	PROPN
ejpam-6667	13	3	appl	appl	PROPN
ejpam-6667	13	4	.	.	PROPN
ejpam-6667	13	5	math	math	PROPN
ejpam-6667	13	6	,	,	PUNCT
ejpam-6667	13	7	18	18	NUM
ejpam-6667	13	8	(	(	PUNCT
ejpam-6667	13	9	4	4	NUM
ejpam-6667	13	10	)	)	PUNCT
ejpam-6667	13	11	(	(	PUNCT
ejpam-6667	13	12	2025	2025	NUM
ejpam-6667	13	13	)	)	PUNCT
ejpam-6667	13	14	,	,	PUNCT
ejpam-6667	13	15	6667	6667	NUM
ejpam-6667	13	16	2	2	NUM
ejpam-6667	13	17	of	of	ADP
ejpam-6667	13	18	20	20	NUM
ejpam-6667	13	19	let	let	VERB
ejpam-6667	13	20	b	b	NOUN
ejpam-6667	13	21	be	be	AUX
ejpam-6667	13	22	a	a	DET
ejpam-6667	13	23	locally	locally	ADV
ejpam-6667	13	24	integrable	integrable	ADJ
ejpam-6667	13	25	function	function	NOUN
ejpam-6667	13	26	,	,	PUNCT
ejpam-6667	13	27	and	and	CCONJ
ejpam-6667	13	28	define	define	VERB
ejpam-6667	13	29	the	the	DET
ejpam-6667	13	30	bmo	bmo	NOUN
ejpam-6667	13	31	norm	norm	NOUN
ejpam-6667	13	32	as	as	SCONJ
ejpam-6667	13	33	follows	follow	VERB
ejpam-6667	13	34	:	:	PUNCT
ejpam-6667	13	35	∥b∥bmo	∥b∥bmo	X
ejpam-6667	13	36	=	=	PUNCT
ejpam-6667	13	37	sup	sup	PROPN
ejpam-6667	13	38	b	b	NOUN
ejpam-6667	13	39	1	1	NUM
ejpam-6667	13	40	|b|	|b|	PROPN
ejpam-6667	13	41	∫	∫	PROPN
ejpam-6667	13	42	b	b	PROPN
ejpam-6667	13	43	|b(x)−	|b(x)−	PROPN
ejpam-6667	13	44	bb|dx	bb|dx	NOUN
ejpam-6667	13	45	,	,	PUNCT
ejpam-6667	13	46	where	where	SCONJ
ejpam-6667	13	47	the	the	DET
ejpam-6667	13	48	supremum	supremum	NOUN
ejpam-6667	13	49	is	be	AUX
ejpam-6667	13	50	taken	take	VERB
ejpam-6667	13	51	over	over	ADP
ejpam-6667	13	52	all	all	DET
ejpam-6667	13	53	balls	ball	NOUN
ejpam-6667	13	54	b	b	X
ejpam-6667	13	55	in	in	ADP
ejpam-6667	13	56	rn	rn	PROPN
ejpam-6667	13	57	,	,	PUNCT
ejpam-6667	13	58	and	and	CCONJ
ejpam-6667	13	59	bb	bb	NOUN
ejpam-6667	13	60	is	be	AUX
ejpam-6667	13	61	the	the	DET
ejpam-6667	13	62	average	average	NOUN
ejpam-6667	13	63	of	of	ADP
ejpam-6667	13	64	b	b	PROPN
ejpam-6667	13	65	on	on	ADP
ejpam-6667	13	66	b.	b.	PROPN
ejpam-6667	13	67	a	a	DET
ejpam-6667	13	68	function	function	NOUN
ejpam-6667	13	69	is	be	AUX
ejpam-6667	13	70	called	call	VERB
ejpam-6667	13	71	bounded	bounded	ADJ
ejpam-6667	13	72	mean	mean	VERB
ejpam-6667	13	73	oscillation	oscillation	NOUN
ejpam-6667	13	74	if	if	SCONJ
ejpam-6667	13	75	∥b∥bmo	∥b∥bmo	PRON
ejpam-6667	13	76	<	<	X
ejpam-6667	14	1	+	+	X
ejpam-6667	14	2	∞.	∞.	PROPN
ejpam-6667	14	3	if	if	SCONJ
ejpam-6667	14	4	b	b	PROPN
ejpam-6667	14	5	∈	∈	PROPN
ejpam-6667	14	6	bmo(rn	bmo(rn	PROPN
ejpam-6667	14	7	)	)	PUNCT
ejpam-6667	14	8	,	,	PUNCT
ejpam-6667	14	9	then	then	ADV
ejpam-6667	14	10	the	the	DET
ejpam-6667	14	11	commutator	commutator	NOUN
ejpam-6667	14	12	generated	generate	VERB
ejpam-6667	14	13	by	by	ADP
ejpam-6667	14	14	the	the	DET
ejpam-6667	14	15	hardy	hardy	ADJ
ejpam-6667	14	16	operator	operator	NOUN
ejpam-6667	14	17	is	be	AUX
ejpam-6667	14	18	defined	define	VERB
ejpam-6667	14	19	as	as	ADP
ejpam-6667	14	20	:	:	PUNCT
ejpam-6667	14	21	hbf(x	hbf(x	NOUN
ejpam-6667	14	22	)	)	PUNCT
ejpam-6667	14	23	=	=	SYM
ejpam-6667	14	24	b(x)hf(x)−h(bf)(x	b(x)hf(x)−h(bf)(x	NOUN
ejpam-6667	14	25	)	)	PUNCT
ejpam-6667	14	26	.	.	PUNCT
ejpam-6667	15	1	the	the	DET
ejpam-6667	15	2	commutator	commutator	NOUN
ejpam-6667	15	3	for	for	ADP
ejpam-6667	15	4	the	the	DET
ejpam-6667	15	5	n	n	ADV
ejpam-6667	15	6	-	-	PUNCT
ejpam-6667	15	7	dimensional	dimensional	ADJ
ejpam-6667	15	8	fractional	fractional	ADJ
ejpam-6667	15	9	hardy	hardy	ADJ
ejpam-6667	15	10	operator	operator	NOUN
ejpam-6667	15	11	hα	hα	NOUN
ejpam-6667	15	12	and	and	CCONJ
ejpam-6667	15	13	their	their	PRON
ejpam-6667	15	14	dual	dual	ADJ
ejpam-6667	15	15	operator	operator	NOUN
ejpam-6667	15	16	h∗	h∗	PROPN
ejpam-6667	15	17	α	α	PROPN
ejpam-6667	15	18	are	be	AUX
ejpam-6667	15	19	defined	define	VERB
ejpam-6667	15	20	in	in	ADP
ejpam-6667	15	21	[	[	X
ejpam-6667	15	22	3	3	NUM
ejpam-6667	15	23	]	]	PUNCT
ejpam-6667	15	24	as	as	SCONJ
ejpam-6667	15	25	follows	follow	VERB
ejpam-6667	15	26	:	:	PUNCT
ejpam-6667	16	1	hα	hα	ADP
ejpam-6667	16	2	,	,	PUNCT
ejpam-6667	16	3	bf(x	bf(x	PRON
ejpam-6667	16	4	)	)	PUNCT
ejpam-6667	16	5	=	=	SYM
ejpam-6667	16	6	b(x)hαf(x)−hα(bf)(x	b(x)hαf(x)−hα(bf)(x	PROPN
ejpam-6667	16	7	)	)	PUNCT
ejpam-6667	16	8	h∗	h∗	PROPN
ejpam-6667	16	9	α	α	X
ejpam-6667	16	10	,	,	PUNCT
ejpam-6667	16	11	bf(x	bf(x	X
ejpam-6667	16	12	)	)	PUNCT
ejpam-6667	16	13	=	=	SYM
ejpam-6667	17	1	b(x)h∗	b(x)h∗	PROPN
ejpam-6667	17	2	αf(x)−h∗	αf(x)−h∗	PROPN
ejpam-6667	17	3	α(bf)(x	α(bf)(x	PROPN
ejpam-6667	17	4	)	)	PUNCT
ejpam-6667	17	5	.	.	PUNCT
ejpam-6667	18	1	in	in	ADP
ejpam-6667	18	2	real	real	ADJ
ejpam-6667	18	3	analysis	analysis	NOUN
ejpam-6667	18	4	,	,	PUNCT
ejpam-6667	18	5	variable	variable	ADJ
ejpam-6667	18	6	exponents	exponent	NOUN
ejpam-6667	18	7	function	function	VERB
ejpam-6667	18	8	spaces	space	NOUN
ejpam-6667	18	9	are	be	AUX
ejpam-6667	18	10	being	be	AUX
ejpam-6667	18	11	observed	observe	VERB
ejpam-6667	18	12	with	with	ADP
ejpam-6667	18	13	keen	keen	ADJ
ejpam-6667	18	14	interest	interest	NOUN
ejpam-6667	18	15	.	.	PUNCT
ejpam-6667	19	1	the	the	DET
ejpam-6667	19	2	theory	theory	NOUN
ejpam-6667	19	3	of	of	ADP
ejpam-6667	19	4	variable	variable	ADJ
ejpam-6667	19	5	exponents	exponent	NOUN
ejpam-6667	19	6	has	have	VERB
ejpam-6667	19	7	great	great	ADJ
ejpam-6667	19	8	applications	application	NOUN
ejpam-6667	19	9	in	in	ADP
ejpam-6667	19	10	partial	partial	ADJ
ejpam-6667	19	11	differential	differential	ADJ
ejpam-6667	19	12	equations	equation	NOUN
ejpam-6667	19	13	and	and	CCONJ
ejpam-6667	19	14	applied	apply	VERB
ejpam-6667	19	15	mathematics	mathematic	NOUN
ejpam-6667	19	16	because	because	SCONJ
ejpam-6667	19	17	they	they	PRON
ejpam-6667	19	18	are	be	AUX
ejpam-6667	19	19	used	use	VERB
ejpam-6667	19	20	in	in	ADP
ejpam-6667	19	21	image	image	NOUN
ejpam-6667	19	22	restoration	restoration	NOUN
ejpam-6667	19	23	and	and	CCONJ
ejpam-6667	19	24	the	the	DET
ejpam-6667	19	25	modeling	modeling	NOUN
ejpam-6667	19	26	of	of	ADP
ejpam-6667	19	27	electrorheological	electrorheological	ADJ
ejpam-6667	19	28	fluids	fluid	NOUN
ejpam-6667	19	29	.	.	PUNCT
ejpam-6667	20	1	some	some	DET
ejpam-6667	20	2	basic	basic	ADJ
ejpam-6667	20	3	properties	property	NOUN
ejpam-6667	20	4	for	for	ADP
ejpam-6667	20	5	variable	variable	ADJ
ejpam-6667	20	6	exponent	exponent	NOUN
ejpam-6667	20	7	function	function	NOUN
ejpam-6667	20	8	spaces	space	NOUN
ejpam-6667	20	9	were	be	AUX
ejpam-6667	20	10	defined	define	VERB
ejpam-6667	20	11	by	by	ADP
ejpam-6667	20	12	kovacik	kovacik	PROPN
ejpam-6667	20	13	and	and	CCONJ
ejpam-6667	20	14	rakosnik	rakosnik	NOUN
ejpam-6667	20	15	[	[	X
ejpam-6667	20	16	4	4	NUM
ejpam-6667	20	17	]	]	PUNCT
ejpam-6667	20	18	.	.	PUNCT
ejpam-6667	21	1	the	the	DET
ejpam-6667	21	2	boundedness	boundedness	NOUN
ejpam-6667	21	3	of	of	ADP
ejpam-6667	21	4	hardy	hardy	ADJ
ejpam-6667	21	5	operators	operator	NOUN
ejpam-6667	21	6	on	on	ADP
ejpam-6667	21	7	some	some	DET
ejpam-6667	21	8	function	function	NOUN
ejpam-6667	21	9	spaces	space	NOUN
ejpam-6667	21	10	is	be	AUX
ejpam-6667	21	11	one	one	NUM
ejpam-6667	21	12	of	of	ADP
ejpam-6667	21	13	the	the	DET
ejpam-6667	21	14	main	main	ADJ
ejpam-6667	21	15	problems	problem	NOUN
ejpam-6667	21	16	in	in	ADP
ejpam-6667	21	17	this	this	DET
ejpam-6667	21	18	theory	theory	NOUN
ejpam-6667	21	19	.	.	PUNCT
ejpam-6667	22	1	the	the	DET
ejpam-6667	22	2	boundedness	boundedness	NOUN
ejpam-6667	22	3	of	of	ADP
ejpam-6667	22	4	the	the	DET
ejpam-6667	22	5	hardy	hardy	ADJ
ejpam-6667	22	6	operator	operator	NOUN
ejpam-6667	22	7	on	on	ADP
ejpam-6667	22	8	lebesgue	lebesgue	NOUN
ejpam-6667	22	9	spaces	space	NOUN
ejpam-6667	22	10	and	and	CCONJ
ejpam-6667	22	11	sobolev	sobolev	NOUN
ejpam-6667	22	12	spaces	space	NOUN
ejpam-6667	22	13	with	with	ADP
ejpam-6667	22	14	variable	variable	ADJ
ejpam-6667	22	15	exponents	exponent	NOUN
ejpam-6667	22	16	can	can	AUX
ejpam-6667	22	17	be	be	AUX
ejpam-6667	22	18	verified	verify	VERB
ejpam-6667	22	19	in	in	ADP
ejpam-6667	22	20	[	[	X
ejpam-6667	22	21	5–7	5–7	NOUN
ejpam-6667	22	22	]	]	PUNCT
ejpam-6667	22	23	.	.	PUNCT
ejpam-6667	23	1	the	the	DET
ejpam-6667	23	2	boundedness	boundedness	NOUN
ejpam-6667	23	3	of	of	ADP
ejpam-6667	23	4	the	the	DET
ejpam-6667	23	5	commutator	commutator	NOUN
ejpam-6667	23	6	of	of	ADP
ejpam-6667	23	7	the	the	DET
ejpam-6667	23	8	hardy	hardy	ADJ
ejpam-6667	23	9	operator	operator	NOUN
ejpam-6667	23	10	on	on	ADP
ejpam-6667	23	11	λ	λ	NOUN
ejpam-6667	23	12	-	-	ADJ
ejpam-6667	23	13	central	central	ADJ
ejpam-6667	23	14	morrey	morrey	NOUN
ejpam-6667	23	15	space	space	NOUN
ejpam-6667	23	16	and	and	CCONJ
ejpam-6667	23	17	the	the	DET
ejpam-6667	23	18	variable	variable	ADJ
ejpam-6667	23	19	exponent	exponent	NOUN
ejpam-6667	23	20	herz	herz	PROPN
ejpam-6667	23	21	space	space	PROPN
ejpam-6667	23	22	k̇α	k̇α	PROPN
ejpam-6667	23	23	,	,	PUNCT
ejpam-6667	23	24	p	p	NOUN
ejpam-6667	23	25	q	q	ADJ
ejpam-6667	23	26	(	(	PUNCT
ejpam-6667	23	27	·	·	PUNCT
ejpam-6667	23	28	)	)	PUNCT
ejpam-6667	23	29	is	be	AUX
ejpam-6667	23	30	discussed	discuss	VERB
ejpam-6667	23	31	in	in	ADP
ejpam-6667	23	32	[	[	PUNCT
ejpam-6667	23	33	8–13	8–13	NOUN
ejpam-6667	23	34	]	]	PUNCT
ejpam-6667	23	35	.	.	PUNCT
ejpam-6667	24	1	more	more	ADV
ejpam-6667	24	2	generalized	generalized	ADJ
ejpam-6667	24	3	results	result	NOUN
ejpam-6667	24	4	,	,	PUNCT
ejpam-6667	24	5	incorporating	incorporate	VERB
ejpam-6667	24	6	weights	weight	NOUN
ejpam-6667	24	7	and	and	CCONJ
ejpam-6667	24	8	variable	variable	ADJ
ejpam-6667	24	9	exponents	exponent	NOUN
ejpam-6667	24	10	,	,	PUNCT
ejpam-6667	24	11	can	can	AUX
ejpam-6667	24	12	be	be	AUX
ejpam-6667	24	13	found	find	VERB
ejpam-6667	24	14	in	in	ADP
ejpam-6667	24	15	[	[	X
ejpam-6667	24	16	14–29	14–29	NUM
ejpam-6667	24	17	]	]	PUNCT
ejpam-6667	24	18	.	.	PUNCT
ejpam-6667	25	1	some	some	PRON
ejpam-6667	25	2	of	of	ADP
ejpam-6667	25	3	these	these	DET
ejpam-6667	25	4	results	result	NOUN
ejpam-6667	25	5	include	include	VERB
ejpam-6667	25	6	duality	duality	NOUN
ejpam-6667	25	7	,	,	PUNCT
ejpam-6667	25	8	boundedness	boundedness	NOUN
ejpam-6667	25	9	of	of	ADP
ejpam-6667	25	10	the	the	DET
ejpam-6667	25	11	littlewood	littlewood	PROPN
ejpam-6667	25	12	maximal	maximal	ADJ
ejpam-6667	25	13	hardy	hardy	ADJ
ejpam-6667	25	14	operator	operator	NOUN
ejpam-6667	25	15	and	and	CCONJ
ejpam-6667	25	16	sublinear	sublinear	NOUN
ejpam-6667	25	17	operator	operator	NOUN
ejpam-6667	25	18	,	,	PUNCT
ejpam-6667	25	19	wavelet	wavelet	NOUN
ejpam-6667	25	20	characterization	characterization	NOUN
ejpam-6667	25	21	,	,	PUNCT
ejpam-6667	25	22	commutator	commutator	NOUN
ejpam-6667	25	23	of	of	ADP
ejpam-6667	25	24	fractional	fractional	ADJ
ejpam-6667	25	25	and	and	CCONJ
ejpam-6667	25	26	singular	singular	NOUN
ejpam-6667	25	27	integral	integral	ADJ
ejpam-6667	25	28	,	,	PUNCT
ejpam-6667	25	29	and	and	CCONJ
ejpam-6667	25	30	more	more	ADJ
ejpam-6667	25	31	.	.	PUNCT
ejpam-6667	26	1	in	in	ADP
ejpam-6667	26	2	this	this	DET
ejpam-6667	26	3	paper	paper	NOUN
ejpam-6667	26	4	,	,	PUNCT
ejpam-6667	26	5	our	our	PRON
ejpam-6667	26	6	main	main	ADJ
ejpam-6667	26	7	focus	focus	NOUN
ejpam-6667	26	8	is	be	AUX
ejpam-6667	26	9	on	on	ADP
ejpam-6667	26	10	the	the	DET
ejpam-6667	26	11	weighted	weight	VERB
ejpam-6667	26	12	λ	λ	ADJ
ejpam-6667	26	13	-	-	ADJ
ejpam-6667	26	14	central	central	ADJ
ejpam-6667	26	15	morrey	morrey	NOUN
ejpam-6667	26	16	space	space	NOUN
ejpam-6667	26	17	,	,	PUNCT
ejpam-6667	26	18	which	which	PRON
ejpam-6667	26	19	holds	hold	VERB
ejpam-6667	26	20	importance	importance	NOUN
ejpam-6667	26	21	in	in	ADP
ejpam-6667	26	22	the	the	DET
ejpam-6667	26	23	theory	theory	NOUN
ejpam-6667	26	24	of	of	ADP
ejpam-6667	26	25	harmonic	harmonic	ADJ
ejpam-6667	26	26	analysis	analysis	NOUN
ejpam-6667	26	27	.	.	PUNCT
ejpam-6667	27	1	the	the	DET
ejpam-6667	27	2	idea	idea	NOUN
ejpam-6667	27	3	of	of	ADP
ejpam-6667	27	4	λ	λ	NOUN
ejpam-6667	27	5	-	-	ADJ
ejpam-6667	27	6	central	central	ADJ
ejpam-6667	27	7	morrey	morrey	NOUN
ejpam-6667	27	8	space	space	NOUN
ejpam-6667	27	9	and	and	CCONJ
ejpam-6667	27	10	λ	λ	NOUN
ejpam-6667	27	11	-	-	ADJ
ejpam-6667	27	12	central	central	ADJ
ejpam-6667	27	13	bmo	bmo	NOUN
ejpam-6667	27	14	space	space	NOUN
ejpam-6667	27	15	for	for	ADP
ejpam-6667	27	16	variable	variable	ADJ
ejpam-6667	27	17	exponents	exponent	NOUN
ejpam-6667	27	18	was	be	AUX
ejpam-6667	27	19	initially	initially	ADV
ejpam-6667	27	20	discussed	discuss	VERB
ejpam-6667	27	21	in	in	ADP
ejpam-6667	27	22	[	[	X
ejpam-6667	27	23	30	30	NUM
ejpam-6667	27	24	]	]	PUNCT
ejpam-6667	27	25	.	.	PUNCT
ejpam-6667	28	1	central	central	ADJ
ejpam-6667	28	2	morrey	morrey	PROPN
ejpam-6667	28	3	space	space	NOUN
ejpam-6667	28	4	,	,	PUNCT
ejpam-6667	28	5	central	central	ADJ
ejpam-6667	28	6	bmo	bmo	NOUN
ejpam-6667	28	7	,	,	PUNCT
ejpam-6667	28	8	and	and	CCONJ
ejpam-6667	28	9	their	their	PRON
ejpam-6667	28	10	corresponding	correspond	VERB
ejpam-6667	28	11	function	function	NOUN
ejpam-6667	28	12	spaces	space	NOUN
ejpam-6667	28	13	have	have	VERB
ejpam-6667	28	14	delightful	delightful	ADJ
ejpam-6667	28	15	applications	application	NOUN
ejpam-6667	28	16	in	in	ADP
ejpam-6667	28	17	exploring	explore	VERB
ejpam-6667	28	18	results	result	NOUN
ejpam-6667	28	19	for	for	ADP
ejpam-6667	28	20	operators	operator	NOUN
ejpam-6667	28	21	,	,	PUNCT
ejpam-6667	28	22	including	include	VERB
ejpam-6667	28	23	singular	singular	ADJ
ejpam-6667	28	24	integral	integral	ADJ
ejpam-6667	28	25	operators	operator	NOUN
ejpam-6667	28	26	,	,	PUNCT
ejpam-6667	28	27	as	as	SCONJ
ejpam-6667	28	28	explained	explain	VERB
ejpam-6667	28	29	in	in	ADP
ejpam-6667	28	30	[	[	X
ejpam-6667	28	31	31–38	31–38	NUM
ejpam-6667	28	32	]	]	PUNCT
ejpam-6667	28	33	.	.	PUNCT
ejpam-6667	29	1	in	in	ADP
ejpam-6667	29	2	this	this	DET
ejpam-6667	29	3	article	article	NOUN
ejpam-6667	29	4	,	,	PUNCT
ejpam-6667	29	5	we	we	PRON
ejpam-6667	29	6	utilize	utilize	VERB
ejpam-6667	29	7	the	the	DET
ejpam-6667	29	8	reisz	reisz	ADJ
ejpam-6667	29	9	type	type	NOUN
ejpam-6667	29	10	potential	potential	ADJ
ejpam-6667	29	11	operator	operator	NOUN
ejpam-6667	29	12	to	to	PART
ejpam-6667	29	13	establish	establish	VERB
ejpam-6667	29	14	the	the	DET
ejpam-6667	29	15	boundedness	boundedness	NOUN
ejpam-6667	29	16	of	of	ADP
ejpam-6667	29	17	the	the	DET
ejpam-6667	29	18	hardy	hardy	ADJ
ejpam-6667	29	19	operator	operator	NOUN
ejpam-6667	29	20	,	,	PUNCT
ejpam-6667	29	21	defined	define	VERB
ejpam-6667	29	22	as	as	SCONJ
ejpam-6667	29	23	follows	follow	VERB
ejpam-6667	29	24	:	:	PUNCT
ejpam-6667	29	25	iαf(x	iαf(x	PROPN
ejpam-6667	29	26	)	)	PUNCT
ejpam-6667	29	27	=	=	SYM
ejpam-6667	29	28	∫	∫	PROPN
ejpam-6667	29	29	rn	rn	PROPN
ejpam-6667	29	30	f(y	f(y	PROPN
ejpam-6667	29	31	)	)	PUNCT
ejpam-6667	29	32	|x−	|x−	PROPN
ejpam-6667	30	1	y|n−α	y|n−α	PROPN
ejpam-6667	30	2	dy	dy	PROPN
ejpam-6667	30	3	,	,	PUNCT
ejpam-6667	30	4	f	f	PROPN
ejpam-6667	30	5	is	be	AUX
ejpam-6667	30	6	locally	locally	ADV
ejpam-6667	30	7	integrable	integrable	ADJ
ejpam-6667	30	8	function	function	NOUN
ejpam-6667	30	9	,	,	PUNCT
ejpam-6667	30	10	0	0	PUNCT
ejpam-6667	30	11	<	<	X
ejpam-6667	30	12	α	α	X
ejpam-6667	30	13	<	<	X
ejpam-6667	30	14	n	n	NOUN
ejpam-6667	31	1	and	and	CCONJ
ejpam-6667	31	2	x	x	PROPN
ejpam-6667	31	3	∈	∈	PROPN
ejpam-6667	31	4	rn	rn	PROPN
ejpam-6667	31	5	\	\	PROPN
ejpam-6667	31	6	{	{	PUNCT
ejpam-6667	31	7	0	0	NUM
ejpam-6667	31	8	}	}	PUNCT
ejpam-6667	31	9	.	.	PUNCT
ejpam-6667	32	1	permit	permit	VERB
ejpam-6667	32	2	me	i	PRON
ejpam-6667	32	3	to	to	PART
ejpam-6667	32	4	elucidate	elucidate	VERB
ejpam-6667	32	5	the	the	DET
ejpam-6667	32	6	structural	structural	ADJ
ejpam-6667	32	7	framework	framework	NOUN
ejpam-6667	32	8	of	of	ADP
ejpam-6667	32	9	the	the	DET
ejpam-6667	32	10	present	present	ADJ
ejpam-6667	32	11	manuscript	manuscript	NOUN
ejpam-6667	32	12	.	.	PUNCT
ejpam-6667	33	1	in	in	ADP
ejpam-6667	33	2	section	section	NOUN
ejpam-6667	33	3	3	3	NUM
ejpam-6667	33	4	,	,	PUNCT
ejpam-6667	33	5	a	a	DET
ejpam-6667	33	6	recapitulation	recapitulation	NOUN
ejpam-6667	33	7	shall	shall	AUX
ejpam-6667	33	8	be	be	AUX
ejpam-6667	33	9	furnished	furnish	VERB
ejpam-6667	33	10	of	of	ADP
ejpam-6667	33	11	certain	certain	ADJ
ejpam-6667	33	12	pivotal	pivotal	ADJ
ejpam-6667	33	13	lemmas	lemma	NOUN
ejpam-6667	33	14	and	and	CCONJ
ejpam-6667	33	15	propositions	proposition	NOUN
ejpam-6667	33	16	,	,	PUNCT
ejpam-6667	33	17	articulated	articulate	VERB
ejpam-6667	33	18	within	within	ADP
ejpam-6667	33	19	the	the	DET
ejpam-6667	33	20	analytical	analytical	ADJ
ejpam-6667	33	21	milieu	milieu	NOUN
ejpam-6667	33	22	of	of	ADP
ejpam-6667	33	23	weighted	weight	VERB
ejpam-6667	33	24	lebesgue	lebesgue	NOUN
ejpam-6667	33	25	space	space	NOUN
ejpam-6667	33	26	endowed	endow	VERB
ejpam-6667	33	27	with	with	ADP
ejpam-6667	33	28	variable	variable	ADJ
ejpam-6667	33	29	m.	m.	NOUN
ejpam-6667	33	30	asim	asim	PROPN
ejpam-6667	33	31	,	,	PUNCT
ejpam-6667	33	32	k.	k.	PROPN
ejpam-6667	33	33	suwais	suwais	PROPN
ejpam-6667	33	34	,	,	PUNCT
ejpam-6667	33	35	n.	n.	PROPN
ejpam-6667	33	36	mlaiki	mlaiki	PROPN
ejpam-6667	33	37	/	/	SYM
ejpam-6667	33	38	eur	eur	PROPN
ejpam-6667	33	39	.	.	PUNCT
ejpam-6667	34	1	j.	j.	PROPN
ejpam-6667	34	2	pure	pure	PROPN
ejpam-6667	34	3	appl	appl	PROPN
ejpam-6667	34	4	.	.	PROPN
ejpam-6667	34	5	math	math	PROPN
ejpam-6667	34	6	,	,	PUNCT
ejpam-6667	34	7	18	18	NUM
ejpam-6667	34	8	(	(	PUNCT
ejpam-6667	34	9	4	4	NUM
ejpam-6667	34	10	)	)	PUNCT
ejpam-6667	34	11	(	(	PUNCT
ejpam-6667	34	12	2025	2025	NUM
ejpam-6667	34	13	)	)	PUNCT
ejpam-6667	34	14	,	,	PUNCT
ejpam-6667	34	15	6667	6667	NUM
ejpam-6667	34	16	3	3	NUM
ejpam-6667	34	17	of	of	ADP
ejpam-6667	34	18	20	20	NUM
ejpam-6667	34	19	exponents	exponent	NOUN
ejpam-6667	34	20	.	.	PUNCT
ejpam-6667	35	1	moving	move	VERB
ejpam-6667	35	2	on	on	ADP
ejpam-6667	35	3	to	to	ADP
ejpam-6667	35	4	section	section	NOUN
ejpam-6667	35	5	4.1	4.1	NUM
ejpam-6667	35	6	,	,	PUNCT
ejpam-6667	35	7	we	we	PRON
ejpam-6667	35	8	will	will	AUX
ejpam-6667	35	9	establish	establish	VERB
ejpam-6667	35	10	the	the	DET
ejpam-6667	35	11	boundedness	boundedness	NOUN
ejpam-6667	35	12	of	of	ADP
ejpam-6667	35	13	fractional	fractional	ADJ
ejpam-6667	35	14	hardy	hardy	ADJ
ejpam-6667	35	15	operators	operator	NOUN
ejpam-6667	35	16	in	in	ADP
ejpam-6667	35	17	the	the	DET
ejpam-6667	35	18	weighted	weight	VERB
ejpam-6667	35	19	central	central	ADJ
ejpam-6667	35	20	morrey	morrey	PROPN
ejpam-6667	35	21	space	space	NOUN
ejpam-6667	35	22	concerning	concern	VERB
ejpam-6667	35	23	variable	variable	ADJ
ejpam-6667	35	24	exponents	exponent	NOUN
ejpam-6667	35	25	.	.	PUNCT
ejpam-6667	36	1	in	in	ADP
ejpam-6667	36	2	section	section	NOUN
ejpam-6667	36	3	4.2	4.2	NUM
ejpam-6667	36	4	,	,	PUNCT
ejpam-6667	36	5	we	we	PRON
ejpam-6667	36	6	will	will	AUX
ejpam-6667	36	7	investigate	investigate	VERB
ejpam-6667	36	8	the	the	DET
ejpam-6667	36	9	estimates	estimate	NOUN
ejpam-6667	36	10	of	of	ADP
ejpam-6667	36	11	commutators	commutator	NOUN
ejpam-6667	36	12	induced	induce	VERB
ejpam-6667	36	13	by	by	ADP
ejpam-6667	36	14	hardy	hardy	ADJ
ejpam-6667	36	15	operators	operator	NOUN
ejpam-6667	36	16	and	and	CCONJ
ejpam-6667	36	17	weighted	weight	VERB
ejpam-6667	36	18	λ	λ	PROPN
ejpam-6667	36	19	-	-	ADJ
ejpam-6667	36	20	central	central	ADJ
ejpam-6667	36	21	bmo	bmo	NOUN
ejpam-6667	36	22	functions	function	NOUN
ejpam-6667	36	23	on	on	ADP
ejpam-6667	36	24	the	the	DET
ejpam-6667	36	25	central	central	ADJ
ejpam-6667	36	26	morrey	morrey	PROPN
ejpam-6667	36	27	space	space	NOUN
ejpam-6667	36	28	.	.	PUNCT
ejpam-6667	37	1	additionally	additionally	ADV
ejpam-6667	37	2	,	,	PUNCT
ejpam-6667	37	3	|s|	|s|	PROPN
ejpam-6667	37	4	and	and	CCONJ
ejpam-6667	37	5	χs	χs	PROPN
ejpam-6667	37	6	represent	represent	VERB
ejpam-6667	37	7	the	the	DET
ejpam-6667	37	8	lebesgue	lebesgue	ADJ
ejpam-6667	37	9	measure	measure	NOUN
ejpam-6667	37	10	and	and	CCONJ
ejpam-6667	37	11	characteristic	characteristic	ADJ
ejpam-6667	37	12	function	function	NOUN
ejpam-6667	37	13	of	of	ADP
ejpam-6667	37	14	a	a	DET
ejpam-6667	37	15	measurable	measurable	ADJ
ejpam-6667	37	16	set	set	NOUN
ejpam-6667	37	17	s	s	PROPN
ejpam-6667	37	18	⊂	⊂	PROPN
ejpam-6667	37	19	rn	rn	PROPN
ejpam-6667	37	20	,	,	PUNCT
ejpam-6667	37	21	respectively	respectively	ADV
ejpam-6667	37	22	.	.	PUNCT
ejpam-6667	38	1	when	when	SCONJ
ejpam-6667	38	2	we	we	PRON
ejpam-6667	38	3	write	write	VERB
ejpam-6667	38	4	g	g	PROPN
ejpam-6667	38	5	≈	≈	PROPN
ejpam-6667	38	6	h	h	PROPN
ejpam-6667	38	7	,	,	PUNCT
ejpam-6667	38	8	it	it	PRON
ejpam-6667	38	9	indicates	indicate	VERB
ejpam-6667	38	10	the	the	DET
ejpam-6667	38	11	existence	existence	NOUN
ejpam-6667	38	12	of	of	ADP
ejpam-6667	38	13	constants	constant	NOUN
ejpam-6667	38	14	c1	c1	PROPN
ejpam-6667	38	15	and	and	CCONJ
ejpam-6667	38	16	c2	c2	PROPN
ejpam-6667	38	17	,	,	PUNCT
ejpam-6667	38	18	both	both	CCONJ
ejpam-6667	38	19	greater	great	ADJ
ejpam-6667	38	20	than	than	ADP
ejpam-6667	38	21	zero	zero	NUM
ejpam-6667	38	22	,	,	PUNCT
ejpam-6667	38	23	such	such	ADJ
ejpam-6667	38	24	that	that	DET
ejpam-6667	38	25	c1	c1	PROPN
ejpam-6667	38	26	g	g	PROPN
ejpam-6667	38	27	≤	≤	NUM
ejpam-6667	38	28	h	h	NOUN
ejpam-6667	38	29	≤	≤	NUM
ejpam-6667	38	30	c2	c2	PROPN
ejpam-6667	38	31	g.	g.	PROPN
ejpam-6667	38	32	we	we	PRON
ejpam-6667	38	33	define	define	VERB
ejpam-6667	38	34	sj	sj	PROPN
ejpam-6667	38	35	=	=	SYM
ejpam-6667	38	36	s(0	s(0	PROPN
ejpam-6667	38	37	,	,	PUNCT
ejpam-6667	38	38	2j	2j	NUM
ejpam-6667	38	39	)	)	PUNCT
ejpam-6667	38	40	=	=	PRON
ejpam-6667	39	1	{	{	PUNCT
ejpam-6667	39	2	x	x	PUNCT
ejpam-6667	39	3	∈	∈	PROPN
ejpam-6667	39	4	rn	rn	NOUN
ejpam-6667	39	5	:	:	PUNCT
ejpam-6667	39	6	|x|	|x|	PROPN
ejpam-6667	39	7	≤	≤	NUM
ejpam-6667	39	8	2j	2j	NUM
ejpam-6667	39	9	}	}	PUNCT
ejpam-6667	39	10	,	,	PUNCT
ejpam-6667	39	11	and	and	CCONJ
ejpam-6667	39	12	for	for	ADP
ejpam-6667	39	13	j	j	PROPN
ejpam-6667	39	14	∈	∈	PROPN
ejpam-6667	39	15	z	z	PROPN
ejpam-6667	39	16	,	,	PUNCT
ejpam-6667	39	17	we	we	PRON
ejpam-6667	39	18	set	set	VERB
ejpam-6667	39	19	χj	χj	PROPN
ejpam-6667	39	20	=	=	PROPN
ejpam-6667	39	21	χaj	χaj	PROPN
ejpam-6667	39	22	.	.	PUNCT
ejpam-6667	40	1	2	2	X
ejpam-6667	40	2	.	.	NUM
ejpam-6667	40	3	preliminaries	preliminary	NOUN
ejpam-6667	40	4	according	accord	VERB
ejpam-6667	40	5	to	to	ADP
ejpam-6667	40	6	some	some	DET
ejpam-6667	40	7	basic	basic	ADJ
ejpam-6667	40	8	books	book	NOUN
ejpam-6667	40	9	and	and	CCONJ
ejpam-6667	40	10	papers	paper	NOUN
ejpam-6667	40	11	[	[	X
ejpam-6667	40	12	4	4	NUM
ejpam-6667	40	13	,	,	PUNCT
ejpam-6667	40	14	39–41	39–41	NUM
ejpam-6667	40	15	]	]	PUNCT
ejpam-6667	40	16	,	,	PUNCT
ejpam-6667	40	17	we	we	PRON
ejpam-6667	40	18	have	have	AUX
ejpam-6667	40	19	established	establish	VERB
ejpam-6667	40	20	the	the	DET
ejpam-6667	40	21	lebesgue	lebesgue	ADJ
ejpam-6667	40	22	space	space	NOUN
ejpam-6667	40	23	with	with	ADP
ejpam-6667	40	24	a	a	DET
ejpam-6667	40	25	variable	variable	ADJ
ejpam-6667	40	26	exponent	exponent	NOUN
ejpam-6667	40	27	.	.	PUNCT
ejpam-6667	41	1	for	for	ADP
ejpam-6667	41	2	a	a	DET
ejpam-6667	41	3	measurable	measurable	ADJ
ejpam-6667	41	4	function	function	NOUN
ejpam-6667	41	5	p	p	X
ejpam-6667	41	6	(	(	PUNCT
ejpam-6667	41	7	·	·	PUNCT
ejpam-6667	41	8	)	)	PUNCT
ejpam-6667	41	9	:	:	PUNCT
ejpam-6667	41	10	rn	rn	PROPN
ejpam-6667	41	11	→	→	PUNCT
ejpam-6667	41	12	[	[	X
ejpam-6667	41	13	1,+∞	1,+∞	NUM
ejpam-6667	41	14	)	)	PUNCT
ejpam-6667	41	15	,	,	PUNCT
ejpam-6667	41	16	the	the	DET
ejpam-6667	41	17	lebesgue	lebesgue	NOUN
ejpam-6667	41	18	space	space	NOUN
ejpam-6667	41	19	lp(·)(rn	lp(·)(rn	PROPN
ejpam-6667	41	20	)	)	PUNCT
ejpam-6667	41	21	with	with	ADP
ejpam-6667	41	22	a	a	DET
ejpam-6667	41	23	variable	variable	ADJ
ejpam-6667	41	24	exponent	exponent	NOUN
ejpam-6667	41	25	is	be	AUX
ejpam-6667	41	26	a	a	DET
ejpam-6667	41	27	set	set	NOUN
ejpam-6667	41	28	containing	contain	VERB
ejpam-6667	41	29	complex	complex	ADJ
ejpam-6667	41	30	valued	value	VERB
ejpam-6667	41	31	function	function	NOUN
ejpam-6667	41	32	g	g	ADP
ejpam-6667	41	33	such	such	ADJ
ejpam-6667	41	34	that	that	DET
ejpam-6667	41	35	pp(g	pp(g	NOUN
ejpam-6667	41	36	)	)	PUNCT
ejpam-6667	42	1	=	=	SYM
ejpam-6667	42	2	∫	∫	PROPN
ejpam-6667	42	3	rn	rn	PROPN
ejpam-6667	42	4	|g(x)|p(x)dx	|g(x)|p(x)dx	PROPN
ejpam-6667	42	5	<	<	X
ejpam-6667	42	6	+	+	PROPN
ejpam-6667	42	7	∞.	∞.	PROPN
ejpam-6667	42	8	lp	lp	ADJ
ejpam-6667	42	9	(	(	PUNCT
ejpam-6667	42	10	·	·	PUNCT
ejpam-6667	42	11	)	)	PUNCT
ejpam-6667	42	12	is	be	AUX
ejpam-6667	42	13	a	a	DET
ejpam-6667	42	14	banach	banach	NOUN
ejpam-6667	42	15	function	function	NOUN
ejpam-6667	42	16	space	space	NOUN
ejpam-6667	42	17	with	with	ADP
ejpam-6667	42	18	respect	respect	NOUN
ejpam-6667	42	19	to	to	ADP
ejpam-6667	42	20	the	the	DET
ejpam-6667	42	21	norm	norm	NOUN
ejpam-6667	42	22	∥g∥lp	∥g∥lp	X
ejpam-6667	42	23	(	(	PUNCT
ejpam-6667	42	24	·	·	PUNCT
ejpam-6667	42	25	)	)	PUNCT
ejpam-6667	43	1	=	=	VERB
ejpam-6667	43	2	inf{ω	inf{ω	VERB
ejpam-6667	43	3	>	>	X
ejpam-6667	43	4	0	0	PUNCT
ejpam-6667	44	1	:	:	PUNCT
ejpam-6667	44	2	pp	pp	ADJ
ejpam-6667	44	3	(	(	PUNCT
ejpam-6667	44	4	g	g	PROPN
ejpam-6667	44	5	ω	ω	PROPN
ejpam-6667	44	6	)	)	PUNCT
ejpam-6667	44	7	≤	≤	NUM
ejpam-6667	44	8	1	1	NUM
ejpam-6667	44	9	}	}	PUNCT
ejpam-6667	44	10	.	.	PUNCT
ejpam-6667	45	1	the	the	DET
ejpam-6667	45	2	set	set	NOUN
ejpam-6667	45	3	p	p	NOUN
ejpam-6667	45	4	represents	represent	VERB
ejpam-6667	45	5	a	a	DET
ejpam-6667	45	6	set	set	NOUN
ejpam-6667	45	7	consisting	consist	VERB
ejpam-6667	45	8	of	of	ADP
ejpam-6667	45	9	all	all	DET
ejpam-6667	45	10	measurable	measurable	ADJ
ejpam-6667	45	11	function	function	NOUN
ejpam-6667	45	12	p	p	X
ejpam-6667	45	13	(	(	PUNCT
ejpam-6667	45	14	·	·	PUNCT
ejpam-6667	45	15	)	)	PUNCT
ejpam-6667	45	16	such	such	ADJ
ejpam-6667	45	17	that	that	DET
ejpam-6667	45	18	p−	p−	NOUN
ejpam-6667	45	19	=	=	PUNCT
ejpam-6667	45	20	ess	ess	PROPN
ejpam-6667	45	21	inf	inf	PROPN
ejpam-6667	45	22	p(x	p(x	PROPN
ejpam-6667	45	23	)	)	PUNCT
ejpam-6667	45	24	>	>	X
ejpam-6667	46	1	1	1	NUM
ejpam-6667	46	2	x	x	SYM
ejpam-6667	46	3	∈	∈	PROPN
ejpam-6667	46	4	rn	rn	PROPN
ejpam-6667	46	5	+	+	PROPN
ejpam-6667	46	6	∞	∞	PROPN
ejpam-6667	46	7	>	>	X
ejpam-6667	46	8	p+	p+	PROPN
ejpam-6667	46	9	=	=	SYM
ejpam-6667	46	10	ess	ess	PROPN
ejpam-6667	46	11	sup	sup	PROPN
ejpam-6667	46	12	p(x	p(x	PROPN
ejpam-6667	46	13	)	)	PUNCT
ejpam-6667	46	14	x	x	SYM
ejpam-6667	46	15	∈	∈	PROPN
ejpam-6667	46	16	rn	rn	PROPN
ejpam-6667	46	17	.	.	PUNCT
ejpam-6667	47	1	a	a	DET
ejpam-6667	47	2	function	function	NOUN
ejpam-6667	47	3	p	p	X
ejpam-6667	47	4	(	(	PUNCT
ejpam-6667	47	5	·	·	PUNCT
ejpam-6667	47	6	)	)	PUNCT
ejpam-6667	47	7	is	be	AUX
ejpam-6667	47	8	said	say	VERB
ejpam-6667	47	9	to	to	PART
ejpam-6667	47	10	be	be	AUX
ejpam-6667	47	11	globally	globally	ADV
ejpam-6667	47	12	log	log	VERB
ejpam-6667	47	13	holder	holder	NOUN
ejpam-6667	47	14	continuous	continuous	ADJ
ejpam-6667	47	15	(	(	PUNCT
ejpam-6667	47	16	lh(rn	lh(rn	PROPN
ejpam-6667	47	17	)	)	PUNCT
ejpam-6667	47	18	)	)	PUNCT
ejpam-6667	48	1	if	if	SCONJ
ejpam-6667	48	2	it	it	PRON
ejpam-6667	48	3	fulfills	fulfill	VERB
ejpam-6667	48	4	the	the	DET
ejpam-6667	48	5	following	follow	VERB
ejpam-6667	48	6	conditions	condition	NOUN
ejpam-6667	48	7	:	:	PUNCT
ejpam-6667	48	8	|p(y)−	|p(y)−	NOUN
ejpam-6667	48	9	p(x)|	p(x)|	NOUN
ejpam-6667	48	10	≲	≲	PROPN
ejpam-6667	48	11	1	1	NUM
ejpam-6667	48	12	log(|y	log(|y	NOUN
ejpam-6667	48	13	−	−	PROPN
ejpam-6667	48	14	x|	x|	PROPN
ejpam-6667	48	15	)	)	PUNCT
ejpam-6667	48	16	,	,	PUNCT
ejpam-6667	48	17	x	x	X
ejpam-6667	48	18	,	,	PUNCT
ejpam-6667	48	19	y	y	PROPN
ejpam-6667	48	20	∈	∈	PROPN
ejpam-6667	48	21	rn	rn	PROPN
ejpam-6667	48	22	:	:	PUNCT
ejpam-6667	48	23	|y	|y	NOUN
ejpam-6667	48	24	−	−	PROPN
ejpam-6667	48	25	x|	x|	PROPN
ejpam-6667	48	26	≤	≤	NUM
ejpam-6667	48	27	1	1	NUM
ejpam-6667	48	28	2	2	NUM
ejpam-6667	48	29	(	(	PUNCT
ejpam-6667	48	30	1	1	NUM
ejpam-6667	48	31	)	)	PUNCT
ejpam-6667	48	32	|p∞	|p∞	NOUN
ejpam-6667	48	33	−	−	NOUN
ejpam-6667	49	1	p(x)|	p(x)|	VERB
ejpam-6667	49	2	≲	≲	PROPN
ejpam-6667	49	3	1	1	NUM
ejpam-6667	49	4	log(e+	log(e+	PROPN
ejpam-6667	49	5	|x|	|x|	PROPN
ejpam-6667	49	6	)	)	PUNCT
ejpam-6667	49	7	,	,	PUNCT
ejpam-6667	49	8	(	(	PUNCT
ejpam-6667	49	9	2	2	X
ejpam-6667	49	10	)	)	PUNCT
ejpam-6667	49	11	for	for	ADP
ejpam-6667	49	12	some	some	DET
ejpam-6667	49	13	real	real	ADJ
ejpam-6667	49	14	number	number	NOUN
ejpam-6667	49	15	p∞.	p∞.	ADP
ejpam-6667	49	16	the	the	DET
ejpam-6667	49	17	hardy	hardy	ADJ
ejpam-6667	49	18	maximal	maximal	ADJ
ejpam-6667	49	19	littlewood	littlewood	NOUN
ejpam-6667	49	20	operator	operator	NOUN
ejpam-6667	49	21	denoted	denote	VERB
ejpam-6667	49	22	by	by	ADP
ejpam-6667	49	23	m	m	PROPN
ejpam-6667	49	24	,	,	PUNCT
ejpam-6667	49	25	is	be	AUX
ejpam-6667	49	26	defined	define	VERB
ejpam-6667	49	27	as	as	ADP
ejpam-6667	49	28	:	:	PUNCT
ejpam-6667	49	29	mg(x	mg(x	NUM
ejpam-6667	49	30	)	)	PUNCT
ejpam-6667	50	1	=	=	SYM
ejpam-6667	50	2	sup	sup	NOUN
ejpam-6667	50	3	1	1	NUM
ejpam-6667	50	4	|b|	|b|	PROPN
ejpam-6667	50	5	∫	∫	PROPN
ejpam-6667	51	1	b	b	PROPN
ejpam-6667	52	1	g(t)dt	g(t)dt	PROPN
ejpam-6667	52	2	,	,	PUNCT
ejpam-6667	52	3	where	where	SCONJ
ejpam-6667	52	4	b	b	NOUN
ejpam-6667	52	5	is	be	AUX
ejpam-6667	52	6	a	a	DET
ejpam-6667	52	7	ball	ball	NOUN
ejpam-6667	52	8	and	and	CCONJ
ejpam-6667	52	9	x	x	PART
ejpam-6667	52	10	∈	∈	PROPN
ejpam-6667	52	11	b.	b.	NOUN
ejpam-6667	53	1	it	it	PRON
ejpam-6667	53	2	is	be	AUX
ejpam-6667	53	3	known	know	VERB
ejpam-6667	53	4	that	that	SCONJ
ejpam-6667	53	5	m	m	PROPN
ejpam-6667	53	6	is	be	AUX
ejpam-6667	53	7	bounded	bound	VERB
ejpam-6667	53	8	on	on	ADP
ejpam-6667	53	9	lp(·)(rn	lp(·)(rn	PROPN
ejpam-6667	53	10	)	)	PUNCT
ejpam-6667	53	11	,	,	PUNCT
ejpam-6667	53	12	for	for	ADP
ejpam-6667	53	13	p	p	PRON
ejpam-6667	53	14	(	(	PUNCT
ejpam-6667	53	15	·	·	PUNCT
ejpam-6667	53	16	)	)	PUNCT
ejpam-6667	53	17	∈	∈	PROPN
ejpam-6667	53	18	p(rn	p(rn	PROPN
ejpam-6667	53	19	)	)	PUNCT
ejpam-6667	53	20	⋂	⋂	PROPN
ejpam-6667	53	21	lh(rn	lh(rn	PROPN
ejpam-6667	53	22	)	)	PUNCT
ejpam-6667	54	1	[	[	X
ejpam-6667	54	2	42–44	42–44	NUM
ejpam-6667	54	3	]	]	PUNCT
ejpam-6667	54	4	.	.	PUNCT
ejpam-6667	54	5	m.	m.	PROPN
ejpam-6667	54	6	asim	asim	PROPN
ejpam-6667	54	7	,	,	PUNCT
ejpam-6667	54	8	k.	k.	PROPN
ejpam-6667	54	9	suwais	suwais	PROPN
ejpam-6667	54	10	,	,	PUNCT
ejpam-6667	54	11	n.	n.	PROPN
ejpam-6667	54	12	mlaiki	mlaiki	PROPN
ejpam-6667	54	13	/	/	SYM
ejpam-6667	54	14	eur	eur	PROPN
ejpam-6667	54	15	.	.	PUNCT
ejpam-6667	55	1	j.	j.	PROPN
ejpam-6667	55	2	pure	pure	PROPN
ejpam-6667	55	3	appl	appl	PROPN
ejpam-6667	55	4	.	.	PROPN
ejpam-6667	55	5	math	math	PROPN
ejpam-6667	55	6	,	,	PUNCT
ejpam-6667	55	7	18	18	NUM
ejpam-6667	55	8	(	(	PUNCT
ejpam-6667	55	9	4	4	NUM
ejpam-6667	55	10	)	)	PUNCT
ejpam-6667	55	11	(	(	PUNCT
ejpam-6667	55	12	2025	2025	NUM
ejpam-6667	55	13	)	)	PUNCT
ejpam-6667	55	14	,	,	PUNCT
ejpam-6667	55	15	6667	6667	NUM
ejpam-6667	55	16	4	4	NUM
ejpam-6667	55	17	of	of	ADP
ejpam-6667	55	18	20	20	NUM
ejpam-6667	55	19	let	let	VERB
ejpam-6667	55	20	w	w	NOUN
ejpam-6667	55	21	be	be	AUX
ejpam-6667	55	22	a	a	DET
ejpam-6667	55	23	weight	weight	NOUN
ejpam-6667	55	24	,	,	PUNCT
ejpam-6667	55	25	and	and	CCONJ
ejpam-6667	55	26	q	q	ADJ
ejpam-6667	55	27	(	(	PUNCT
ejpam-6667	55	28	·	·	PUNCT
ejpam-6667	55	29	)	)	PUNCT
ejpam-6667	55	30	∈	∈	PROPN
ejpam-6667	55	31	p(rn	p(rn	PROPN
ejpam-6667	55	32	)	)	PUNCT
ejpam-6667	55	33	.	.	PUNCT
ejpam-6667	56	1	then	then	ADV
ejpam-6667	56	2	lp(·)(w	lp(·)(w	VERB
ejpam-6667	56	3	)	)	PUNCT
ejpam-6667	56	4	represents	represent	VERB
ejpam-6667	56	5	the	the	DET
ejpam-6667	56	6	weighted	weight	VERB
ejpam-6667	56	7	variable	variable	ADJ
ejpam-6667	56	8	exponent	exponent	NOUN
ejpam-6667	56	9	lebesgue	lebesgue	NOUN
ejpam-6667	56	10	spaces	space	VERB
ejpam-6667	56	11	variable	variable	ADJ
ejpam-6667	56	12	exponent	exponent	NOUN
ejpam-6667	56	13	,	,	PUNCT
ejpam-6667	56	14	which	which	PRON
ejpam-6667	56	15	contains	contain	VERB
ejpam-6667	56	16	all	all	DET
ejpam-6667	56	17	complex	complex	ADJ
ejpam-6667	56	18	valued	value	VERB
ejpam-6667	56	19	measurable	measurable	ADJ
ejpam-6667	56	20	function	function	NOUN
ejpam-6667	57	1	f	f	PROPN
ejpam-6667	57	2	such	such	ADJ
ejpam-6667	57	3	that	that	SCONJ
ejpam-6667	57	4	fw	fw	PROPN
ejpam-6667	57	5	1	1	NUM
ejpam-6667	57	6	p	p	X
ejpam-6667	57	7	(	(	PUNCT
ejpam-6667	57	8	·	·	PUNCT
ejpam-6667	57	9	)	)	PUNCT
ejpam-6667	57	10	∈	∈	PROPN
ejpam-6667	57	11	lp(·)(w	lp(·)(w	NOUN
ejpam-6667	57	12	)	)	PUNCT
ejpam-6667	57	13	.	.	PUNCT
ejpam-6667	58	1	lp(·)(w	lp(·)(w	PROPN
ejpam-6667	58	2	)	)	PUNCT
ejpam-6667	58	3	forms	form	VERB
ejpam-6667	58	4	a	a	DET
ejpam-6667	58	5	banach	banach	NOUN
ejpam-6667	58	6	function	function	NOUN
ejpam-6667	58	7	space	space	NOUN
ejpam-6667	58	8	with	with	ADP
ejpam-6667	58	9	respect	respect	NOUN
ejpam-6667	58	10	to	to	ADP
ejpam-6667	58	11	the	the	DET
ejpam-6667	58	12	given	give	VERB
ejpam-6667	58	13	norm	norm	NOUN
ejpam-6667	58	14	∥f∥lp(·)(w	∥f∥lp(·)(w	NOUN
ejpam-6667	58	15	)	)	PUNCT
ejpam-6667	58	16	=	=	SYM
ejpam-6667	58	17	∥fw	∥fw	PROPN
ejpam-6667	58	18	1	1	NUM
ejpam-6667	58	19	p	p	X
ejpam-6667	58	20	(	(	PUNCT
ejpam-6667	58	21	·	·	PUNCT
ejpam-6667	58	22	)	)	PUNCT
ejpam-6667	58	23	∥lp	∥lp	PROPN
ejpam-6667	58	24	(	(	PUNCT
ejpam-6667	58	25	·	·	PUNCT
ejpam-6667	58	26	)	)	PUNCT
ejpam-6667	58	27	.	.	PUNCT
ejpam-6667	59	1	since	since	SCONJ
ejpam-6667	59	2	,	,	PUNCT
ejpam-6667	59	3	p	p	NOUN
ejpam-6667	59	4	′	′	X
ejpam-6667	59	5	(	(	PUNCT
ejpam-6667	59	6	·	·	PUNCT
ejpam-6667	59	7	)	)	PUNCT
ejpam-6667	59	8	is	be	AUX
ejpam-6667	59	9	the	the	DET
ejpam-6667	59	10	conjugate	conjugate	NOUN
ejpam-6667	59	11	of	of	ADP
ejpam-6667	59	12	p	p	X
ejpam-6667	59	13	(	(	PUNCT
ejpam-6667	59	14	·	·	PUNCT
ejpam-6667	59	15	)	)	PUNCT
ejpam-6667	59	16	and	and	CCONJ
ejpam-6667	59	17	1	1	NUM
ejpam-6667	59	18	p	p	X
ejpam-6667	59	19	(	(	PUNCT
ejpam-6667	59	20	·	·	PUNCT
ejpam-6667	59	21	)	)	PUNCT
ejpam-6667	60	1	+	+	CCONJ
ejpam-6667	60	2	1	1	NUM
ejpam-6667	60	3	p′	p′	NOUN
ejpam-6667	60	4	(	(	PUNCT
ejpam-6667	60	5	·	·	PUNCT
ejpam-6667	60	6	)	)	PUNCT
ejpam-6667	60	7	=	=	SYM
ejpam-6667	61	1	1	1	NUM
ejpam-6667	61	2	,	,	PUNCT
ejpam-6667	61	3	we	we	PRON
ejpam-6667	61	4	have	have	VERB
ejpam-6667	61	5	the	the	DET
ejpam-6667	61	6	conjugate	conjugate	ADJ
ejpam-6667	61	7	exponent	exponent	NOUN
ejpam-6667	61	8	relationship	relationship	NOUN
ejpam-6667	61	9	.	.	PUNCT
ejpam-6667	62	1	we	we	PRON
ejpam-6667	62	2	introduce	introduce	VERB
ejpam-6667	62	3	the	the	DET
ejpam-6667	62	4	concept	concept	NOUN
ejpam-6667	62	5	of	of	ADP
ejpam-6667	62	6	a	a	DET
ejpam-6667	62	7	a1	a1	NOUN
ejpam-6667	62	8	muckenhoupt	muckenhoupt	ADJ
ejpam-6667	62	9	weight	weight	NOUN
ejpam-6667	62	10	,	,	PUNCT
ejpam-6667	62	11	defined	define	VERB
ejpam-6667	62	12	as	as	SCONJ
ejpam-6667	62	13	follows	follow	VERB
ejpam-6667	62	14	:	:	PUNCT
ejpam-6667	62	15	definition	definition	NOUN
ejpam-6667	62	16	1	1	NUM
ejpam-6667	62	17	.	.	PUNCT
ejpam-6667	62	18	weight	weight	NOUN
ejpam-6667	62	19	w	w	NOUN
ejpam-6667	62	20	is	be	AUX
ejpam-6667	62	21	called	call	VERB
ejpam-6667	62	22	a	a	DET
ejpam-6667	62	23	a1	a1	NOUN
ejpam-6667	62	24	muckenhoupt	muckenhoupt	ADJ
ejpam-6667	62	25	weight	weight	NOUN
ejpam-6667	62	26	if	if	SCONJ
ejpam-6667	62	27	it	it	PRON
ejpam-6667	62	28	fulfills	fulfill	VERB
ejpam-6667	62	29	the	the	DET
ejpam-6667	62	30	condition	condition	NOUN
ejpam-6667	62	31	mw(x	mw(x	NOUN
ejpam-6667	62	32	)	)	PUNCT
ejpam-6667	63	1	≲	≲	PROPN
ejpam-6667	63	2	w(x	w(x	NUM
ejpam-6667	63	3	)	)	PUNCT
ejpam-6667	64	1	,	,	PUNCT
ejpam-6667	64	2	x	x	PROPN
ejpam-6667	64	3	∈	∈	PROPN
ejpam-6667	64	4	rn	rn	PROPN
ejpam-6667	64	5	.	.	PROPN
ejpam-6667	64	6	definition	definition	NOUN
ejpam-6667	64	7	2	2	NUM
ejpam-6667	64	8	.	.	PUNCT
ejpam-6667	65	1	let	let	VERB
ejpam-6667	65	2	p	p	PRON
ejpam-6667	65	3	(	(	PUNCT
ejpam-6667	65	4	·	·	PUNCT
ejpam-6667	65	5	)	)	PUNCT
ejpam-6667	65	6	∈	∈	PROPN
ejpam-6667	65	7	p(rn	p(rn	PROPN
ejpam-6667	65	8	)	)	PUNCT
ejpam-6667	65	9	.	.	PUNCT
ejpam-6667	66	1	a	a	DET
ejpam-6667	66	2	weight	weight	NOUN
ejpam-6667	66	3	is	be	AUX
ejpam-6667	66	4	said	say	VERB
ejpam-6667	66	5	to	to	PART
ejpam-6667	66	6	be	be	AUX
ejpam-6667	66	7	ap	ap	PROPN
ejpam-6667	66	8	(	(	PUNCT
ejpam-6667	66	9	·	·	PUNCT
ejpam-6667	66	10	)	)	PUNCT
ejpam-6667	66	11	if	if	SCONJ
ejpam-6667	66	12	it	it	PRON
ejpam-6667	66	13	satisfies	satisfy	VERB
ejpam-6667	66	14	the	the	DET
ejpam-6667	66	15	condition	condition	NOUN
ejpam-6667	66	16	:	:	PUNCT
ejpam-6667	66	17	sup	sup	PROPN
ejpam-6667	66	18	b	b	NOUN
ejpam-6667	66	19	1	1	NUM
ejpam-6667	66	20	|b|	|b|	PROPN
ejpam-6667	66	21	∥w	∥w	PROPN
ejpam-6667	66	22	1	1	NUM
ejpam-6667	66	23	p(·)χb∥lp(·)∥w−	p(·)χb∥lp(·)∥w−	NUM
ejpam-6667	66	24	1	1	NUM
ejpam-6667	66	25	p(·)χb∥lp	p(·)χb∥lp	NOUN
ejpam-6667	66	26	′	′	NUM
ejpam-6667	66	27	(	(	PUNCT
ejpam-6667	66	28	·	·	PUNCT
ejpam-6667	66	29	)	)	PUNCT
ejpam-6667	66	30	<	<	X
ejpam-6667	67	1	+	+	X
ejpam-6667	67	2	∞.	∞.	PROPN
ejpam-6667	67	3	and	and	CCONJ
ejpam-6667	67	4	a	a	DET
ejpam-6667	67	5	weight	weight	NOUN
ejpam-6667	67	6	is	be	AUX
ejpam-6667	67	7	called	call	VERB
ejpam-6667	67	8	˜ap	˜ap	PROPN
ejpam-6667	67	9	(	(	PUNCT
ejpam-6667	67	10	·	·	PUNCT
ejpam-6667	67	11	)	)	PUNCT
ejpam-6667	67	12	if	if	SCONJ
ejpam-6667	67	13	the	the	DET
ejpam-6667	67	14	following	follow	VERB
ejpam-6667	67	15	condition	condition	NOUN
ejpam-6667	67	16	holds	hold	VERB
ejpam-6667	67	17	:	:	PUNCT
ejpam-6667	67	18	sup	sup	PROPN
ejpam-6667	67	19	b	b	NOUN
ejpam-6667	67	20	1	1	NUM
ejpam-6667	67	21	|b|pb	|b|pb	NOUN
ejpam-6667	67	22	∥wχb∥l1∥w−1χb∥	∥wχb∥l1∥w−1χb∥	NOUN
ejpam-6667	68	1	l	l	NOUN
ejpam-6667	68	2	p	p	NOUN
ejpam-6667	68	3	′	′	NUM
ejpam-6667	68	4	(	(	PUNCT
ejpam-6667	68	5	·	·	PUNCT
ejpam-6667	68	6	)	)	PUNCT
ejpam-6667	69	1	p	p	X
ejpam-6667	69	2	(	(	PUNCT
ejpam-6667	69	3	·	·	PUNCT
ejpam-6667	69	4	)	)	PUNCT
ejpam-6667	69	5	<	<	X
ejpam-6667	70	1	+	+	PUNCT
ejpam-6667	70	2	∞.	∞.	PROPN
ejpam-6667	70	3	where	where	SCONJ
ejpam-6667	70	4	pb	pb	ADV
ejpam-6667	70	5	=	=	PUNCT
ejpam-6667	70	6	(	(	PUNCT
ejpam-6667	70	7	1	1	NUM
ejpam-6667	70	8	|b|	|b|	PROPN
ejpam-6667	70	9	∫	∫	PROPN
ejpam-6667	70	10	b	b	PROPN
ejpam-6667	70	11	1	1	NUM
ejpam-6667	70	12	p(x)dx	p(x)dx	NOUN
ejpam-6667	70	13	)	)	PUNCT
ejpam-6667	70	14	−1	−1	NOUN
ejpam-6667	70	15	.	.	PUNCT
ejpam-6667	71	1	based	base	VERB
ejpam-6667	71	2	on	on	ADP
ejpam-6667	71	3	this	this	DET
ejpam-6667	71	4	definition	definition	NOUN
ejpam-6667	71	5	izuki	izuki	NOUN
ejpam-6667	71	6	and	and	CCONJ
ejpam-6667	71	7	noi	noi	PROPN
ejpam-6667	71	8	[	[	X
ejpam-6667	71	9	16	16	NUM
ejpam-6667	71	10	]	]	PUNCT
ejpam-6667	71	11	have	have	AUX
ejpam-6667	71	12	proved	prove	VERB
ejpam-6667	71	13	the	the	DET
ejpam-6667	71	14	following	follow	VERB
ejpam-6667	71	15	monotone	monotone	ADJ
ejpam-6667	71	16	property	property	NOUN
ejpam-6667	71	17	.	.	PUNCT
ejpam-6667	72	1	definition	definition	NOUN
ejpam-6667	72	2	3	3	NUM
ejpam-6667	72	3	.	.	PUNCT
ejpam-6667	73	1	let	let	VERB
ejpam-6667	73	2	α	α	PRON
ejpam-6667	73	3	∈	∈	PROPN
ejpam-6667	73	4	(	(	PUNCT
ejpam-6667	73	5	0	0	NUM
ejpam-6667	73	6	,	,	PUNCT
ejpam-6667	73	7	n	n	CCONJ
ejpam-6667	73	8	)	)	PUNCT
ejpam-6667	73	9	and	and	CCONJ
ejpam-6667	73	10	p2	p2	PROPN
ejpam-6667	73	11	(	(	PUNCT
ejpam-6667	73	12	·	·	PUNCT
ejpam-6667	73	13	)	)	PUNCT
ejpam-6667	73	14	,	,	PUNCT
ejpam-6667	73	15	p1	p1	PROPN
ejpam-6667	73	16	(	(	PUNCT
ejpam-6667	73	17	·	·	PUNCT
ejpam-6667	73	18	)	)	PUNCT
ejpam-6667	73	19	∈	∈	PROPN
ejpam-6667	73	20	p(rn	p(rn	PROPN
ejpam-6667	73	21	)	)	PUNCT
ejpam-6667	73	22	,	,	PUNCT
ejpam-6667	73	23	and	and	CCONJ
ejpam-6667	73	24	1	1	NUM
ejpam-6667	73	25	p1	p1	NOUN
ejpam-6667	73	26	(	(	PUNCT
ejpam-6667	73	27	·	·	PUNCT
ejpam-6667	73	28	)	)	PUNCT
ejpam-6667	73	29	=	=	NOUN
ejpam-6667	73	30	1	1	NUM
ejpam-6667	73	31	p2	p2	NOUN
ejpam-6667	73	32	(	(	PUNCT
ejpam-6667	73	33	·	·	PUNCT
ejpam-6667	73	34	)	)	PUNCT
ejpam-6667	74	1	+	+	CCONJ
ejpam-6667	74	2	α	α	PROPN
ejpam-6667	74	3	n	n	NOUN
ejpam-6667	74	4	.	.	PUNCT
ejpam-6667	75	1	a	a	DET
ejpam-6667	75	2	weight	weight	NOUN
ejpam-6667	75	3	w	w	NOUN
ejpam-6667	75	4	is	be	AUX
ejpam-6667	75	5	known	know	VERB
ejpam-6667	75	6	as	as	ADP
ejpam-6667	75	7	a(p2	a(p2	ADJ
ejpam-6667	75	8	(	(	PUNCT
ejpam-6667	75	9	·	·	PUNCT
ejpam-6667	75	10	)	)	PUNCT
ejpam-6667	75	11	,	,	PUNCT
ejpam-6667	75	12	p1	p1	PROPN
ejpam-6667	75	13	(	(	PUNCT
ejpam-6667	75	14	·	·	PUNCT
ejpam-6667	75	15	)	)	PUNCT
ejpam-6667	75	16	)	)	PUNCT
ejpam-6667	75	17	if	if	SCONJ
ejpam-6667	75	18	it	it	PRON
ejpam-6667	75	19	satisfies	satisfy	VERB
ejpam-6667	75	20	the	the	DET
ejpam-6667	75	21	following	follow	VERB
ejpam-6667	75	22	inequality	inequality	NOUN
ejpam-6667	75	23	for	for	ADP
ejpam-6667	75	24	all	all	DET
ejpam-6667	75	25	balls	ball	NOUN
ejpam-6667	75	26	b	b	PROPN
ejpam-6667	75	27	⊂	⊂	PROPN
ejpam-6667	75	28	rn	rn	PROPN
ejpam-6667	75	29	∥w−1χb∥	∥w−1χb∥	VERB
ejpam-6667	75	30	1	1	NUM
ejpam-6667	75	31	1−α	1−α	NUM
ejpam-6667	75	32	n	n	PRON
ejpam-6667	75	33	lp	lp	NOUN
ejpam-6667	76	1	′	′	NUM
ejpam-6667	76	2	1	1	NUM
ejpam-6667	76	3	(	(	PUNCT
ejpam-6667	76	4	·	·	PUNCT
ejpam-6667	76	5	)	)	PUNCT
ejpam-6667	76	6	∥wχb∥	∥wχb∥	NOUN
ejpam-6667	77	1	1	1	NUM
ejpam-6667	77	2	1−α	1−α	NUM
ejpam-6667	77	3	n	n	PROPN
ejpam-6667	77	4	lp2	lp2	PROPN
ejpam-6667	77	5	(	(	PUNCT
ejpam-6667	77	6	·	·	PUNCT
ejpam-6667	77	7	)	)	PUNCT
ejpam-6667	77	8	≤	≤	NOUN
ejpam-6667	77	9	|b|	|b|	PROPN
ejpam-6667	77	10	.	.	PUNCT
ejpam-6667	78	1	definition	definition	NOUN
ejpam-6667	78	2	4	4	NUM
ejpam-6667	78	3	.	.	PUNCT
ejpam-6667	79	1	if	if	SCONJ
ejpam-6667	79	2	p	p	X
ejpam-6667	79	3	(	(	PUNCT
ejpam-6667	79	4	·	·	PUNCT
ejpam-6667	79	5	)	)	PUNCT
ejpam-6667	79	6	∈	∈	PROPN
ejpam-6667	79	7	p	p	NOUN
ejpam-6667	79	8	and	and	CCONJ
ejpam-6667	79	9	λ	λ	X
ejpam-6667	79	10	∈	∈	PROPN
ejpam-6667	79	11	r	r	NOUN
ejpam-6667	79	12	,	,	PUNCT
ejpam-6667	79	13	the	the	DET
ejpam-6667	79	14	weighted	weight	VERB
ejpam-6667	79	15	morrey	morrey	PROPN
ejpam-6667	79	16	space	space	NOUN
ejpam-6667	79	17	with	with	ADP
ejpam-6667	79	18	a	a	DET
ejpam-6667	79	19	variable	variable	ADJ
ejpam-6667	79	20	exponent	exponent	NOUN
ejpam-6667	79	21	ḃp(·),λ(wp	ḃp(·),λ(wp	PROPN
ejpam-6667	79	22	(	(	PUNCT
ejpam-6667	79	23	·	·	PUNCT
ejpam-6667	79	24	)	)	PUNCT
ejpam-6667	79	25	)	)	PUNCT
ejpam-6667	79	26	is	be	AUX
ejpam-6667	79	27	defined	define	VERB
ejpam-6667	79	28	as	as	ADP
ejpam-6667	79	29	:	:	PUNCT
ejpam-6667	79	30	ḃp(·),λ(w	ḃp(·),λ(w	NOUN
ejpam-6667	79	31	)	)	PUNCT
ejpam-6667	79	32	=	=	PRON
ejpam-6667	80	1	{	{	PUNCT
ejpam-6667	80	2	f	f	PROPN
ejpam-6667	80	3	∈	∈	PROPN
ejpam-6667	80	4	l	l	NOUN
ejpam-6667	81	1	p	p	X
ejpam-6667	81	2	(	(	PUNCT
ejpam-6667	81	3	·	·	PUNCT
ejpam-6667	81	4	)	)	PUNCT
ejpam-6667	81	5	loc	loc	NOUN
ejpam-6667	81	6	(	(	PUNCT
ejpam-6667	81	7	w	w	PROPN
ejpam-6667	81	8	)	)	PUNCT
ejpam-6667	81	9	:	:	PUNCT
ejpam-6667	81	10	∥f∥ḃp(·),λ(w	∥f∥ḃp(·),λ(w	X
ejpam-6667	81	11	)	)	PUNCT
ejpam-6667	81	12	<	<	X
ejpam-6667	82	1	+	+	PUNCT
ejpam-6667	82	2	∞	∞	NOUN
ejpam-6667	82	3	}	}	PUNCT
ejpam-6667	82	4	,	,	PUNCT
ejpam-6667	82	5	where	where	SCONJ
ejpam-6667	82	6	∥f∥ḃp(·),λ(w	∥f∥ḃp(·),λ(w	ADP
ejpam-6667	82	7	)	)	PUNCT
ejpam-6667	82	8	=	=	SYM
ejpam-6667	82	9	sup	sup	NUM
ejpam-6667	82	10	r>0	r>0	PROPN
ejpam-6667	82	11	∥fχb(0,r)∥lp(·)(w	∥fχb(0,r)∥lp(·)(w	NOUN
ejpam-6667	82	12	)	)	PUNCT
ejpam-6667	82	13	|b(0	|b(0	ADJ
ejpam-6667	82	14	,	,	PUNCT
ejpam-6667	82	15	r)|λ∥χb(0,r)∥lp(·)(w	r)|λ∥χb(0,r)∥lp(·)(w	PROPN
ejpam-6667	82	16	)	)	PUNCT
ejpam-6667	82	17	.	.	PUNCT
ejpam-6667	83	1	definition	definition	NOUN
ejpam-6667	83	2	5	5	NUM
ejpam-6667	83	3	.	.	PUNCT
ejpam-6667	84	1	if	if	SCONJ
ejpam-6667	84	2	p	p	X
ejpam-6667	84	3	(	(	PUNCT
ejpam-6667	84	4	·	·	PUNCT
ejpam-6667	84	5	)	)	PUNCT
ejpam-6667	84	6	∈	∈	PROPN
ejpam-6667	84	7	p	p	NOUN
ejpam-6667	84	8	and	and	CCONJ
ejpam-6667	84	9	λ	λ	X
ejpam-6667	84	10	<	<	X
ejpam-6667	84	11	1	1	NUM
ejpam-6667	84	12	n	n	NUM
ejpam-6667	84	13	the	the	DET
ejpam-6667	84	14	weighted	weight	VERB
ejpam-6667	84	15	λ−	λ−	PROPN
ejpam-6667	84	16	bmo	bmo	NOUN
ejpam-6667	84	17	space	space	NOUN
ejpam-6667	84	18	with	with	ADP
ejpam-6667	84	19	variable	variable	ADJ
ejpam-6667	84	20	exponent	exponent	NOUN
ejpam-6667	84	21	cbmop(·),λ(wp	cbmop(·),λ(wp	PROPN
ejpam-6667	84	22	(	(	PUNCT
ejpam-6667	84	23	·	·	PUNCT
ejpam-6667	84	24	)	)	PUNCT
ejpam-6667	84	25	)	)	PUNCT
ejpam-6667	84	26	is	be	AUX
ejpam-6667	84	27	defined	define	VERB
ejpam-6667	84	28	as	as	ADP
ejpam-6667	84	29	:	:	PUNCT
ejpam-6667	84	30	cbmop(·),λ(w	cbmop(·),λ(w	PROPN
ejpam-6667	84	31	)	)	PUNCT
ejpam-6667	84	32	=	=	PUNCT
ejpam-6667	85	1	{	{	PUNCT
ejpam-6667	85	2	f	f	PROPN
ejpam-6667	85	3	∈	∈	PROPN
ejpam-6667	85	4	l	l	NOUN
ejpam-6667	86	1	p	p	X
ejpam-6667	86	2	(	(	PUNCT
ejpam-6667	86	3	·	·	PUNCT
ejpam-6667	86	4	)	)	PUNCT
ejpam-6667	86	5	loc	loc	NOUN
ejpam-6667	86	6	(	(	PUNCT
ejpam-6667	86	7	w	w	PROPN
ejpam-6667	86	8	)	)	PUNCT
ejpam-6667	86	9	:	:	PUNCT
ejpam-6667	86	10	∥f∥cbmop(·),λ(w	∥f∥cbmop(·),λ(w	NOUN
ejpam-6667	86	11	)	)	PUNCT
ejpam-6667	86	12	<	<	X
ejpam-6667	87	1	+	+	PUNCT
ejpam-6667	87	2	∞	∞	NOUN
ejpam-6667	87	3	}	}	PUNCT
ejpam-6667	87	4	,	,	PUNCT
ejpam-6667	87	5	where	where	SCONJ
ejpam-6667	87	6	∥f∥cbmop(·),λ(w	∥f∥cbmop(·),λ(w	NOUN
ejpam-6667	87	7	)	)	PUNCT
ejpam-6667	87	8	=	=	SYM
ejpam-6667	87	9	sup	sup	NOUN
ejpam-6667	87	10	r>0	r>0	ADV
ejpam-6667	87	11	∥(f	∥(f	ADV
ejpam-6667	87	12	−	−	ADP
ejpam-6667	87	13	fb(0,r))χb(0,r)∥lp(·)(w	fb(0,r))χb(0,r)∥lp(·)(w	X
ejpam-6667	87	14	)	)	PUNCT
ejpam-6667	87	15	|b(0	|b(0	ADJ
ejpam-6667	87	16	,	,	PUNCT
ejpam-6667	87	17	r)|λ∥χb(0,r)∥lp(·)(w	r)|λ∥χb(0,r)∥lp(·)(w	PROPN
ejpam-6667	87	18	)	)	PUNCT
ejpam-6667	87	19	.	.	PUNCT
ejpam-6667	88	1	m.	m.	PROPN
ejpam-6667	88	2	asim	asim	PROPN
ejpam-6667	88	3	,	,	PUNCT
ejpam-6667	88	4	k.	k.	PROPN
ejpam-6667	88	5	suwais	suwais	PROPN
ejpam-6667	88	6	,	,	PUNCT
ejpam-6667	88	7	n.	n.	PROPN
ejpam-6667	88	8	mlaiki	mlaiki	PROPN
ejpam-6667	88	9	/	/	SYM
ejpam-6667	88	10	eur	eur	PROPN
ejpam-6667	88	11	.	.	PUNCT
ejpam-6667	89	1	j.	j.	PROPN
ejpam-6667	89	2	pure	pure	PROPN
ejpam-6667	89	3	appl	appl	PROPN
ejpam-6667	89	4	.	.	PROPN
ejpam-6667	89	5	math	math	PROPN
ejpam-6667	89	6	,	,	PUNCT
ejpam-6667	89	7	18	18	NUM
ejpam-6667	89	8	(	(	PUNCT
ejpam-6667	89	9	4	4	NUM
ejpam-6667	89	10	)	)	PUNCT
ejpam-6667	89	11	(	(	PUNCT
ejpam-6667	89	12	2025	2025	NUM
ejpam-6667	89	13	)	)	PUNCT
ejpam-6667	89	14	,	,	PUNCT
ejpam-6667	89	15	6667	6667	NUM
ejpam-6667	89	16	5	5	NUM
ejpam-6667	89	17	of	of	ADP
ejpam-6667	89	18	20	20	NUM
ejpam-6667	89	19	3	3	NUM
ejpam-6667	89	20	.	.	PUNCT
ejpam-6667	90	1	important	important	ADJ
ejpam-6667	90	2	lemmas	lemmas	PROPN
ejpam-6667	90	3	lemma	lemma	PROPN
ejpam-6667	90	4	1	1	NUM
ejpam-6667	90	5	.	.	PUNCT
ejpam-6667	91	1	[	[	X
ejpam-6667	91	2	16	16	NUM
ejpam-6667	91	3	]	]	PUNCT
ejpam-6667	91	4	if	if	SCONJ
ejpam-6667	91	5	p1	p1	PROPN
ejpam-6667	91	6	(	(	PUNCT
ejpam-6667	91	7	·	·	PUNCT
ejpam-6667	91	8	)	)	PUNCT
ejpam-6667	91	9	,	,	PUNCT
ejpam-6667	91	10	p2	p2	X
ejpam-6667	91	11	(	(	PUNCT
ejpam-6667	91	12	·	·	PUNCT
ejpam-6667	91	13	)	)	PUNCT
ejpam-6667	91	14	∈	∈	PROPN
ejpam-6667	91	15	p(rn	p(rn	PROPN
ejpam-6667	91	16	)	)	PUNCT
ejpam-6667	91	17	⋂	⋂	PROPN
ejpam-6667	91	18	lh(rn	lh(rn	PROPN
ejpam-6667	91	19	)	)	PUNCT
ejpam-6667	91	20	and	and	CCONJ
ejpam-6667	91	21	p1	p1	PROPN
ejpam-6667	91	22	(	(	PUNCT
ejpam-6667	91	23	·	·	PUNCT
ejpam-6667	91	24	)	)	PUNCT
ejpam-6667	91	25	<	<	X
ejpam-6667	91	26	p2	p2	X
ejpam-6667	91	27	(	(	PUNCT
ejpam-6667	91	28	·	·	PUNCT
ejpam-6667	91	29	)	)	PUNCT
ejpam-6667	91	30	,	,	PUNCT
ejpam-6667	91	31	then	then	ADV
ejpam-6667	91	32	a1	a1	PROPN
ejpam-6667	91	33	⊂	⊂	PROPN
ejpam-6667	91	34	ap1	ap1	PROPN
ejpam-6667	91	35	(	(	PUNCT
ejpam-6667	91	36	·	·	PUNCT
ejpam-6667	91	37	)	)	PUNCT
ejpam-6667	92	1	⊂	⊂	PROPN
ejpam-6667	92	2	ap2	ap2	PROPN
ejpam-6667	92	3	(	(	PUNCT
ejpam-6667	92	4	·	·	PUNCT
ejpam-6667	92	5	)	)	PUNCT
ejpam-6667	92	6	.	.	PUNCT
ejpam-6667	93	1	lemma	lemma	PROPN
ejpam-6667	93	2	2	2	NUM
ejpam-6667	93	3	.	.	PUNCT
ejpam-6667	94	1	[	[	X
ejpam-6667	94	2	16	16	NUM
ejpam-6667	94	3	]	]	X
ejpam-6667	94	4	let	let	VERB
ejpam-6667	94	5	0	0	PUNCT
ejpam-6667	94	6	<	<	X
ejpam-6667	94	7	α	α	X
ejpam-6667	94	8	<	<	X
ejpam-6667	94	9	n	n	NOUN
ejpam-6667	94	10	and	and	CCONJ
ejpam-6667	94	11	p2	p2	PROPN
ejpam-6667	94	12	(	(	PUNCT
ejpam-6667	94	13	·	·	PUNCT
ejpam-6667	94	14	)	)	PUNCT
ejpam-6667	94	15	,	,	PUNCT
ejpam-6667	94	16	p1	p1	PROPN
ejpam-6667	94	17	(	(	PUNCT
ejpam-6667	94	18	·	·	PUNCT
ejpam-6667	94	19	)	)	PUNCT
ejpam-6667	94	20	∈	∈	PROPN
ejpam-6667	94	21	p(rn	p(rn	PROPN
ejpam-6667	94	22	)	)	PUNCT
ejpam-6667	94	23	where	where	SCONJ
ejpam-6667	94	24	1	1	NUM
ejpam-6667	94	25	p1	p1	NOUN
ejpam-6667	94	26	(	(	PUNCT
ejpam-6667	94	27	·	·	PUNCT
ejpam-6667	94	28	)	)	PUNCT
ejpam-6667	94	29	=	=	NOUN
ejpam-6667	94	30	1	1	NUM
ejpam-6667	94	31	p2	p2	NOUN
ejpam-6667	94	32	(	(	PUNCT
ejpam-6667	94	33	·	·	PUNCT
ejpam-6667	94	34	)	)	PUNCT
ejpam-6667	95	1	+	+	CCONJ
ejpam-6667	95	2	α	α	PROPN
ejpam-6667	95	3	n	n	NOUN
ejpam-6667	95	4	.	.	PUNCT
ejpam-6667	96	1	then	then	ADV
ejpam-6667	96	2	w	w	PROPN
ejpam-6667	96	3	∈	∈	PROPN
ejpam-6667	96	4	a(p1	a(p1	NOUN
ejpam-6667	96	5	(	(	PUNCT
ejpam-6667	96	6	·	·	PUNCT
ejpam-6667	96	7	)	)	PUNCT
ejpam-6667	96	8	,	,	PUNCT
ejpam-6667	96	9	p2	p2	X
ejpam-6667	96	10	(	(	PUNCT
ejpam-6667	96	11	·	·	PUNCT
ejpam-6667	96	12	)	)	PUNCT
ejpam-6667	96	13	)	)	PUNCT
ejpam-6667	97	1	⇔	⇔	PROPN
ejpam-6667	97	2	wp2	wp2	PROPN
ejpam-6667	97	3	(	(	PUNCT
ejpam-6667	97	4	·	·	PUNCT
ejpam-6667	97	5	)	)	PUNCT
ejpam-6667	97	6	∈	∈	PROPN
ejpam-6667	97	7	a	a	DET
ejpam-6667	97	8	1	1	NUM
ejpam-6667	97	9	+	+	NUM
ejpam-6667	97	10	p2	p2	X
ejpam-6667	97	11	(	(	PUNCT
ejpam-6667	97	12	·	·	PUNCT
ejpam-6667	97	13	)	)	PUNCT
ejpam-6667	98	1	p	p	NOUN
ejpam-6667	98	2	′	′	NUM
ejpam-6667	98	3	1	1	NUM
ejpam-6667	98	4	(	(	PUNCT
ejpam-6667	98	5	·	·	PUNCT
ejpam-6667	98	6	)	)	PUNCT
ejpam-6667	98	7	.	.	PUNCT
ejpam-6667	99	1	lemma	lemma	PROPN
ejpam-6667	99	2	3	3	X
ejpam-6667	99	3	.	.	PUNCT
ejpam-6667	100	1	[	[	X
ejpam-6667	100	2	45	45	NUM
ejpam-6667	100	3	]	]	PUNCT
ejpam-6667	100	4	consider	consider	VERB
ejpam-6667	100	5	y	y	PROPN
ejpam-6667	100	6	is	be	AUX
ejpam-6667	100	7	a	a	DET
ejpam-6667	100	8	banach	banach	NOUN
ejpam-6667	100	9	function	function	NOUN
ejpam-6667	100	10	space	space	NOUN
ejpam-6667	100	11	.	.	PUNCT
ejpam-6667	101	1	then	then	ADV
ejpam-6667	101	2	1	1	X
ejpam-6667	101	3	.	.	X
ejpam-6667	102	1	y	y	NOUN
ejpam-6667	102	2	′	′	NOUN
ejpam-6667	102	3	will	will	AUX
ejpam-6667	102	4	also	also	ADV
ejpam-6667	102	5	be	be	AUX
ejpam-6667	102	6	a	a	DET
ejpam-6667	102	7	banach	banach	NOUN
ejpam-6667	102	8	function	function	NOUN
ejpam-6667	102	9	space	space	NOUN
ejpam-6667	102	10	.	.	PUNCT
ejpam-6667	103	1	specifically	specifically	ADV
ejpam-6667	103	2	,	,	PUNCT
ejpam-6667	103	3	∥	∥	X
ejpam-6667	103	4	·	·	PUNCT
ejpam-6667	103	5	∥(y′	∥(y′	NOUN
ejpam-6667	103	6	)	)	PUNCT
ejpam-6667	103	7	′	′	NUM
ejpam-6667	103	8	and	and	CCONJ
ejpam-6667	103	9	∥	∥	PRON
ejpam-6667	103	10	·	·	PUNCT
ejpam-6667	104	1	∥y	∥y	NOUN
ejpam-6667	104	2	are	be	AUX
ejpam-6667	104	3	both	both	ADV
ejpam-6667	104	4	equivalent	equivalent	ADJ
ejpam-6667	104	5	norms	norm	NOUN
ejpam-6667	104	6	and	and	CCONJ
ejpam-6667	104	7	satisfy	satisfy	NOUN
ejpam-6667	104	8	(	(	PUNCT
ejpam-6667	104	9	y	y	NOUN
ejpam-6667	104	10	′	′	NUM
ejpam-6667	104	11	)	)	PUNCT
ejpam-6667	105	1	′	′	NUM
ejpam-6667	106	1	=	=	PUNCT
ejpam-6667	106	2	y.	y.	NOUN
ejpam-6667	106	3	2	2	NUM
ejpam-6667	106	4	.	.	PUNCT
ejpam-6667	107	1	if	if	SCONJ
ejpam-6667	107	2	f	f	PROPN
ejpam-6667	107	3	∈	∈	PROPN
ejpam-6667	107	4	y	y	PROPN
ejpam-6667	107	5	and	and	CCONJ
ejpam-6667	107	6	g	g	PROPN
ejpam-6667	107	7	∈	∈	PROPN
ejpam-6667	107	8	y	y	PROPN
ejpam-6667	107	9	′	′	NUM
ejpam-6667	107	10	,	,	PUNCT
ejpam-6667	107	11	then	then	ADV
ejpam-6667	107	12	we	we	PRON
ejpam-6667	107	13	have∫	have∫	VERB
ejpam-6667	107	14	rn	rn	PROPN
ejpam-6667	107	15	|f(x)g(x)|dx	|f(x)g(x)|dx	NOUN
ejpam-6667	107	16	≤	≤	NOUN
ejpam-6667	107	17	∥f∥y∥g∥y′	∥f∥y∥g∥y′	NOUN
ejpam-6667	107	18	,	,	PUNCT
ejpam-6667	107	19	which	which	PRON
ejpam-6667	107	20	is	be	AUX
ejpam-6667	107	21	known	know	VERB
ejpam-6667	107	22	as	as	ADP
ejpam-6667	107	23	hölder	hölder	NOUN
ejpam-6667	107	24	inequality	inequality	NOUN
ejpam-6667	107	25	.	.	PUNCT
ejpam-6667	108	1	lemma	lemma	PROPN
ejpam-6667	108	2	4	4	NUM
ejpam-6667	108	3	.	.	PUNCT
ejpam-6667	109	1	[	[	X
ejpam-6667	109	2	45	45	NUM
ejpam-6667	109	3	]	]	PUNCT
ejpam-6667	109	4	let	let	VERB
ejpam-6667	109	5	y	y	PRON
ejpam-6667	109	6	be	be	AUX
ejpam-6667	109	7	a	a	DET
ejpam-6667	109	8	banach	banach	NOUN
ejpam-6667	109	9	function	function	NOUN
ejpam-6667	109	10	space	space	NOUN
ejpam-6667	109	11	.	.	PUNCT
ejpam-6667	110	1	then	then	ADV
ejpam-6667	110	2	1	1	NUM
ejpam-6667	110	3	≤	≤	NUM
ejpam-6667	110	4	1	1	NUM
ejpam-6667	110	5	|b|	|b|	PROPN
ejpam-6667	110	6	∥χb∥y∥χb∥y′	∥χb∥y∥χb∥y′	PROPN
ejpam-6667	110	7	.	.	PUNCT
ejpam-6667	111	1	this	this	PRON
ejpam-6667	111	2	holds	hold	VERB
ejpam-6667	111	3	for	for	ADP
ejpam-6667	111	4	all	all	DET
ejpam-6667	111	5	balls	ball	NOUN
ejpam-6667	111	6	b.	b.	PROPN
ejpam-6667	111	7	lemma	lemma	PROPN
ejpam-6667	111	8	5	5	NUM
ejpam-6667	111	9	.	.	PUNCT
ejpam-6667	112	1	[	[	X
ejpam-6667	112	2	46	46	NUM
ejpam-6667	112	3	]	]	X
ejpam-6667	112	4	if	if	SCONJ
ejpam-6667	112	5	m	m	NOUN
ejpam-6667	112	6	is	be	AUX
ejpam-6667	112	7	weakly	weakly	ADV
ejpam-6667	112	8	bounded	bounded	ADJ
ejpam-6667	112	9	on	on	ADP
ejpam-6667	112	10	a	a	DET
ejpam-6667	112	11	banach	banach	NOUN
ejpam-6667	112	12	function	function	NOUN
ejpam-6667	112	13	space	space	NOUN
ejpam-6667	112	14	y	y	PROPN
ejpam-6667	112	15	,	,	PUNCT
ejpam-6667	112	16	i.e	i.e	X
ejpam-6667	112	17	,	,	PUNCT
ejpam-6667	112	18	∥χ{mf	∥χ{mf	PROPN
ejpam-6667	112	19	>	>	X
ejpam-6667	112	20	λ}∥y	λ}∥y	PRON
ejpam-6667	112	21	≤	≤	NOUN
ejpam-6667	112	22	λ−1∥f∥y	λ−1∥f∥y	VERB
ejpam-6667	112	23	,	,	PUNCT
ejpam-6667	112	24	(	(	PUNCT
ejpam-6667	112	25	3	3	X
ejpam-6667	112	26	)	)	PUNCT
ejpam-6667	112	27	where	where	SCONJ
ejpam-6667	112	28	λ	λ	X
ejpam-6667	112	29	>	>	X
ejpam-6667	112	30	0	0	PUNCT
ejpam-6667	112	31	and	and	CCONJ
ejpam-6667	112	32	f	f	PROPN
ejpam-6667	112	33	∈	∈	PROPN
ejpam-6667	112	34	y	y	PROPN
ejpam-6667	112	35	,	,	PUNCT
ejpam-6667	112	36	then	then	ADV
ejpam-6667	112	37	sup	sup	PROPN
ejpam-6667	112	38	1	1	NUM
ejpam-6667	112	39	|b|	|b|	PROPN
ejpam-6667	112	40	∥χb∥y∥χb∥y′	∥χb∥y∥χb∥y′	VERB
ejpam-6667	112	41	<	<	X
ejpam-6667	112	42	+	+	PROPN
ejpam-6667	112	43	∞.	∞.	PROPN
ejpam-6667	112	44	(	(	PUNCT
ejpam-6667	112	45	4	4	NUM
ejpam-6667	112	46	)	)	PUNCT
ejpam-6667	112	47	now	now	ADV
ejpam-6667	112	48	we	we	PRON
ejpam-6667	112	49	define	define	VERB
ejpam-6667	112	50	weighted	weight	VERB
ejpam-6667	112	51	banach	banach	NOUN
ejpam-6667	112	52	function	function	NOUN
ejpam-6667	112	53	space	space	NOUN
ejpam-6667	112	54	and	and	CCONJ
ejpam-6667	112	55	explain	explain	VERB
ejpam-6667	112	56	some	some	PRON
ejpam-6667	112	57	of	of	ADP
ejpam-6667	112	58	their	their	PRON
ejpam-6667	112	59	properties	property	NOUN
ejpam-6667	112	60	.	.	PUNCT
ejpam-6667	113	1	for	for	ADP
ejpam-6667	113	2	a	a	DET
ejpam-6667	113	3	function	function	NOUN
ejpam-6667	113	4	w	w	PROPN
ejpam-6667	113	5	(	(	PUNCT
ejpam-6667	113	6	x	x	NOUN
ejpam-6667	113	7	)	)	PUNCT
ejpam-6667	113	8	∈	∈	PROPN
ejpam-6667	113	9	(	(	PUNCT
ejpam-6667	113	10	0,+∞	0,+∞	NUM
ejpam-6667	113	11	)	)	PUNCT
ejpam-6667	113	12	,	,	PUNCT
ejpam-6667	113	13	w	w	PROPN
ejpam-6667	113	14	(	(	PUNCT
ejpam-6667	113	15	x	x	X
ejpam-6667	113	16	)	)	PUNCT
ejpam-6667	113	17	∈	∈	PROPN
ejpam-6667	113	18	yloc	yloc	NOUN
ejpam-6667	113	19	and	and	CCONJ
ejpam-6667	113	20	w−1(x	w−1(x	PROPN
ejpam-6667	113	21	)	)	PUNCT
ejpam-6667	113	22	∈	∈	PROPN
ejpam-6667	113	23	y	y	PROPN
ejpam-6667	113	24	′	′	PROPN
ejpam-6667	113	25	loc	loc	PROPN
ejpam-6667	113	26	,	,	PUNCT
ejpam-6667	113	27	where	where	SCONJ
ejpam-6667	113	28	yloc(rn	yloc(rn	NOUN
ejpam-6667	113	29	)	)	PUNCT
ejpam-6667	113	30	comprises	comprise	NOUN
ejpam-6667	113	31	of	of	ADP
ejpam-6667	113	32	all	all	DET
ejpam-6667	113	33	measurable	measurable	ADJ
ejpam-6667	113	34	functions	function	NOUN
ejpam-6667	113	35	f	f	PRON
ejpam-6667	113	36	such	such	ADJ
ejpam-6667	113	37	that	that	DET
ejpam-6667	113	38	fχb	fχb	NOUN
ejpam-6667	113	39	∈	∈	PROPN
ejpam-6667	113	40	y	y	PROPN
ejpam-6667	113	41	for	for	ADP
ejpam-6667	113	42	any	any	DET
ejpam-6667	113	43	compact	compact	ADJ
ejpam-6667	113	44	set	set	NOUN
ejpam-6667	113	45	b	b	NOUN
ejpam-6667	113	46	with	with	ADP
ejpam-6667	113	47	|b|	|b|	PROPN
ejpam-6667	113	48	<	<	X
ejpam-6667	113	49	+	+	PUNCT
ejpam-6667	113	50	∞.	∞.	PROPN
ejpam-6667	113	51	then	then	ADV
ejpam-6667	113	52	the	the	DET
ejpam-6667	113	53	weighted	weighted	ADJ
ejpam-6667	113	54	banach	banach	NOUN
ejpam-6667	113	55	function	function	NOUN
ejpam-6667	113	56	space	space	NOUN
ejpam-6667	113	57	is	be	AUX
ejpam-6667	113	58	defined	define	VERB
ejpam-6667	113	59	as	as	ADP
ejpam-6667	113	60	y(rn	y(rn	PROPN
ejpam-6667	113	61	,	,	PUNCT
ejpam-6667	113	62	w	w	PROPN
ejpam-6667	113	63	)	)	PUNCT
ejpam-6667	114	1	=	=	PRON
ejpam-6667	114	2	{	{	PUNCT
ejpam-6667	114	3	f	f	PROPN
ejpam-6667	114	4	∈	∈	PROPN
ejpam-6667	114	5	m	m	VERB
ejpam-6667	114	6	:	:	PUNCT
ejpam-6667	114	7	fw	fw	PROPN
ejpam-6667	114	8	∈	∈	PROPN
ejpam-6667	114	9	y	y	PROPN
ejpam-6667	114	10	}	}	PUNCT
ejpam-6667	114	11	.	.	PUNCT
ejpam-6667	115	1	then	then	ADV
ejpam-6667	115	2	the	the	DET
ejpam-6667	115	3	accompanying	accompanying	ADJ
ejpam-6667	115	4	lemma	lemma	PROPN
ejpam-6667	115	5	is	be	AUX
ejpam-6667	115	6	true	true	ADJ
ejpam-6667	115	7	.	.	PUNCT
ejpam-6667	116	1	lemma	lemma	PROPN
ejpam-6667	116	2	6	6	NUM
ejpam-6667	116	3	.	.	PUNCT
ejpam-6667	117	1	[	[	X
ejpam-6667	117	2	47	47	NUM
ejpam-6667	117	3	]	]	SYM
ejpam-6667	117	4	1	1	NUM
ejpam-6667	117	5	.	.	PUNCT
ejpam-6667	117	6	y(rn	y(rn	PROPN
ejpam-6667	117	7	,	,	PUNCT
ejpam-6667	117	8	w	w	PROPN
ejpam-6667	117	9	)	)	PUNCT
ejpam-6667	117	10	is	be	AUX
ejpam-6667	117	11	a	a	DET
ejpam-6667	117	12	banach	banach	NOUN
ejpam-6667	117	13	function	function	NOUN
ejpam-6667	117	14	space	space	NOUN
ejpam-6667	117	15	with	with	ADP
ejpam-6667	117	16	the	the	DET
ejpam-6667	117	17	given	give	VERB
ejpam-6667	117	18	norm	norm	NOUN
ejpam-6667	117	19	∥f∥y(rn	∥f∥y(rn	PROPN
ejpam-6667	117	20	,	,	PUNCT
ejpam-6667	117	21	w	w	NOUN
ejpam-6667	117	22	)	)	PUNCT
ejpam-6667	117	23	=	=	PUNCT
ejpam-6667	117	24	∥fw∥y	∥fw∥y	PROPN
ejpam-6667	117	25	.	.	PUNCT
ejpam-6667	118	1	2	2	X
ejpam-6667	118	2	.	.	X
ejpam-6667	118	3	the	the	DET
ejpam-6667	118	4	associated	associated	ADJ
ejpam-6667	118	5	space	space	NOUN
ejpam-6667	118	6	of	of	ADP
ejpam-6667	118	7	the	the	DET
ejpam-6667	118	8	weighted	weight	VERB
ejpam-6667	118	9	banach	banach	NOUN
ejpam-6667	118	10	function	function	NOUN
ejpam-6667	118	11	space	space	NOUN
ejpam-6667	118	12	y(rn	y(rn	PROPN
ejpam-6667	118	13	,	,	PUNCT
ejpam-6667	118	14	w	w	PROPN
ejpam-6667	118	15	)	)	PUNCT
ejpam-6667	118	16	is	be	AUX
ejpam-6667	118	17	also	also	ADV
ejpam-6667	118	18	a	a	DET
ejpam-6667	118	19	banach	banach	NOUN
ejpam-6667	118	20	function	function	NOUN
ejpam-6667	118	21	space	space	NOUN
ejpam-6667	118	22	.	.	PUNCT
ejpam-6667	119	1	m.	m.	PROPN
ejpam-6667	119	2	asim	asim	PROPN
ejpam-6667	119	3	,	,	PUNCT
ejpam-6667	119	4	k.	k.	PROPN
ejpam-6667	119	5	suwais	suwais	PROPN
ejpam-6667	119	6	,	,	PUNCT
ejpam-6667	119	7	n.	n.	PROPN
ejpam-6667	119	8	mlaiki	mlaiki	PROPN
ejpam-6667	119	9	/	/	SYM
ejpam-6667	119	10	eur	eur	PROPN
ejpam-6667	119	11	.	.	PUNCT
ejpam-6667	120	1	j.	j.	PROPN
ejpam-6667	120	2	pure	pure	PROPN
ejpam-6667	120	3	appl	appl	PROPN
ejpam-6667	120	4	.	.	PROPN
ejpam-6667	120	5	math	math	PROPN
ejpam-6667	120	6	,	,	PUNCT
ejpam-6667	120	7	18	18	NUM
ejpam-6667	120	8	(	(	PUNCT
ejpam-6667	120	9	4	4	NUM
ejpam-6667	120	10	)	)	PUNCT
ejpam-6667	120	11	(	(	PUNCT
ejpam-6667	120	12	2025	2025	NUM
ejpam-6667	120	13	)	)	PUNCT
ejpam-6667	120	14	,	,	PUNCT
ejpam-6667	120	15	6667	6667	NUM
ejpam-6667	120	16	6	6	NUM
ejpam-6667	120	17	of	of	ADP
ejpam-6667	120	18	20	20	NUM
ejpam-6667	120	19	remark	remark	NOUN
ejpam-6667	120	20	1	1	NUM
ejpam-6667	120	21	.	.	PUNCT
ejpam-6667	121	1	take	take	VERB
ejpam-6667	121	2	q	q	ADJ
ejpam-6667	121	3	(	(	PUNCT
ejpam-6667	121	4	·	·	PUNCT
ejpam-6667	121	5	)	)	PUNCT
ejpam-6667	121	6	∈	∈	PROPN
ejpam-6667	121	7	p(rn	p(rn	PROPN
ejpam-6667	121	8	)	)	PUNCT
ejpam-6667	121	9	.	.	PUNCT
ejpam-6667	122	1	now	now	ADV
ejpam-6667	122	2	,	,	PUNCT
ejpam-6667	122	3	by	by	ADP
ejpam-6667	122	4	the	the	DET
ejpam-6667	122	5	definition	definition	NOUN
ejpam-6667	122	6	of	of	ADP
ejpam-6667	122	7	the	the	DET
ejpam-6667	122	8	weighted	weight	VERB
ejpam-6667	122	9	banach	banach	NOUN
ejpam-6667	122	10	function	function	NOUN
ejpam-6667	122	11	space	space	NOUN
ejpam-6667	122	12	y(rn	y(rn	PROPN
ejpam-6667	122	13	,	,	PUNCT
ejpam-6667	122	14	w	w	NOUN
ejpam-6667	122	15	)	)	PUNCT
ejpam-6667	122	16	,	,	PUNCT
ejpam-6667	122	17	lq(·)(wq	lq(·)(wq	X
ejpam-6667	122	18	(	(	PUNCT
ejpam-6667	122	19	·	·	PUNCT
ejpam-6667	122	20	)	)	PUNCT
ejpam-6667	122	21	)	)	PUNCT
ejpam-6667	123	1	and	and	CCONJ
ejpam-6667	123	2	lq	lq	INTJ
ejpam-6667	123	3	′	′	NUM
ejpam-6667	123	4	(	(	PUNCT
ejpam-6667	123	5	·	·	PUNCT
ejpam-6667	123	6	)	)	PUNCT
ejpam-6667	123	7	(	(	PUNCT
ejpam-6667	123	8	w−q	w−q	INTJ
ejpam-6667	123	9	′	′	NUM
ejpam-6667	123	10	(	(	PUNCT
ejpam-6667	123	11	·	·	PUNCT
ejpam-6667	123	12	)	)	PUNCT
ejpam-6667	123	13	)	)	PUNCT
ejpam-6667	123	14	,	,	PUNCT
ejpam-6667	123	15	we	we	PRON
ejpam-6667	123	16	observe	observe	VERB
ejpam-6667	123	17	that	that	SCONJ
ejpam-6667	123	18	1	1	X
ejpam-6667	123	19	.	.	PUNCT
ejpam-6667	123	20	let	let	VERB
ejpam-6667	123	21	y	y	PROPN
ejpam-6667	123	22	=	=	PUNCT
ejpam-6667	123	23	lq(·)(rn	lq(·)(rn	PROPN
ejpam-6667	123	24	)	)	PUNCT
ejpam-6667	123	25	and	and	CCONJ
ejpam-6667	123	26	w	w	PROPN
ejpam-6667	123	27	=	=	SYM
ejpam-6667	123	28	w	w	PROPN
ejpam-6667	123	29	,	,	PUNCT
ejpam-6667	123	30	then	then	ADV
ejpam-6667	123	31	we	we	PRON
ejpam-6667	123	32	have	have	VERB
ejpam-6667	123	33	lq(·)(rn	lq(·)(rn	PROPN
ejpam-6667	123	34	,	,	PUNCT
ejpam-6667	123	35	w	w	NOUN
ejpam-6667	123	36	)	)	PUNCT
ejpam-6667	123	37	=	=	SYM
ejpam-6667	123	38	lq(·)(wq	lq(·)(wq	X
ejpam-6667	123	39	(	(	PUNCT
ejpam-6667	123	40	·	·	PUNCT
ejpam-6667	123	41	)	)	PUNCT
ejpam-6667	123	42	)	)	PUNCT
ejpam-6667	123	43	.	.	PUNCT
ejpam-6667	124	1	2	2	X
ejpam-6667	124	2	.	.	X
ejpam-6667	124	3	for	for	ADP
ejpam-6667	124	4	y	y	PROPN
ejpam-6667	124	5	=	=	PUNCT
ejpam-6667	124	6	lq	lq	NOUN
ejpam-6667	124	7	′	′	NUM
ejpam-6667	124	8	(	(	PUNCT
ejpam-6667	124	9	·	·	PUNCT
ejpam-6667	124	10	)	)	PUNCT
ejpam-6667	124	11	(	(	PUNCT
ejpam-6667	124	12	rn	rn	NOUN
ejpam-6667	124	13	)	)	PUNCT
ejpam-6667	124	14	and	and	CCONJ
ejpam-6667	124	15	w	w	PROPN
ejpam-6667	124	16	=	=	SYM
ejpam-6667	124	17	w	w	PROPN
ejpam-6667	124	18	,	,	PUNCT
ejpam-6667	124	19	we	we	PRON
ejpam-6667	124	20	obtain	obtain	VERB
ejpam-6667	124	21	lq	lq	NOUN
ejpam-6667	124	22	′	′	NUM
ejpam-6667	124	23	(	(	PUNCT
ejpam-6667	124	24	·	·	PUNCT
ejpam-6667	124	25	)	)	PUNCT
ejpam-6667	124	26	(	(	PUNCT
ejpam-6667	124	27	rn	rn	PROPN
ejpam-6667	124	28	,	,	PUNCT
ejpam-6667	124	29	w−1	w−1	PROPN
ejpam-6667	124	30	)	)	PUNCT
ejpam-6667	124	31	=	=	PUNCT
ejpam-6667	125	1	lq	lq	NOUN
ejpam-6667	125	2	′	′	NUM
ejpam-6667	125	3	(	(	PUNCT
ejpam-6667	125	4	·	·	PUNCT
ejpam-6667	125	5	)	)	PUNCT
ejpam-6667	125	6	(	(	PUNCT
ejpam-6667	125	7	w−q	w−q	INTJ
ejpam-6667	125	8	′	′	NUM
ejpam-6667	125	9	(	(	PUNCT
ejpam-6667	125	10	·	·	PUNCT
ejpam-6667	125	11	)	)	PUNCT
ejpam-6667	125	12	)	)	PUNCT
ejpam-6667	125	13	.	.	PUNCT
ejpam-6667	126	1	therefore	therefore	ADV
ejpam-6667	126	2	,	,	PUNCT
ejpam-6667	126	3	from	from	ADP
ejpam-6667	126	4	lemma	lemma	PROPN
ejpam-6667	126	5	6	6	NUM
ejpam-6667	126	6	,	,	PUNCT
ejpam-6667	126	7	we	we	PRON
ejpam-6667	126	8	have	have	VERB
ejpam-6667	126	9	(	(	PUNCT
ejpam-6667	126	10	lq(·)(wq	lq(·)(wq	ADJ
ejpam-6667	126	11	(	(	PUNCT
ejpam-6667	126	12	·	·	PUNCT
ejpam-6667	126	13	)	)	PUNCT
ejpam-6667	126	14	)	)	PUNCT
ejpam-6667	126	15	)	)	PUNCT
ejpam-6667	127	1	′	′	NUM
ejpam-6667	128	1	=	=	SYM
ejpam-6667	128	2	(	(	PUNCT
ejpam-6667	128	3	lq(·)(rn	lq(·)(rn	PROPN
ejpam-6667	128	4	,	,	PUNCT
ejpam-6667	128	5	w−1	w−1	PROPN
ejpam-6667	128	6	)	)	PUNCT
ejpam-6667	128	7	)	)	PUNCT
ejpam-6667	129	1	′	′	NUM
ejpam-6667	130	1	=	=	PUNCT
ejpam-6667	130	2	lq	lq	NOUN
ejpam-6667	130	3	′	′	NUM
ejpam-6667	130	4	(	(	PUNCT
ejpam-6667	130	5	·	·	PUNCT
ejpam-6667	130	6	)	)	PUNCT
ejpam-6667	130	7	(	(	PUNCT
ejpam-6667	130	8	w−q	w−q	INTJ
ejpam-6667	130	9	′	′	NUM
ejpam-6667	130	10	(	(	PUNCT
ejpam-6667	130	11	·	·	PUNCT
ejpam-6667	130	12	)	)	PUNCT
ejpam-6667	130	13	)	)	PUNCT
ejpam-6667	130	14	.	.	PUNCT
ejpam-6667	131	1	furthermore	furthermore	ADV
ejpam-6667	131	2	,	,	PUNCT
ejpam-6667	131	3	define	define	VERB
ejpam-6667	131	4	p1	p1	PROPN
ejpam-6667	131	5	(	(	PUNCT
ejpam-6667	131	6	·	·	PUNCT
ejpam-6667	131	7	)	)	PUNCT
ejpam-6667	131	8	so	so	SCONJ
ejpam-6667	131	9	that	that	SCONJ
ejpam-6667	131	10	1	1	NUM
ejpam-6667	131	11	p1	p1	NOUN
ejpam-6667	131	12	(	(	PUNCT
ejpam-6667	131	13	·	·	PUNCT
ejpam-6667	131	14	)	)	PUNCT
ejpam-6667	131	15	=	=	SYM
ejpam-6667	132	1	α	α	PROPN
ejpam-6667	132	2	n	n	NOUN
ejpam-6667	132	3	+	+	CCONJ
ejpam-6667	132	4	1	1	NUM
ejpam-6667	132	5	p2	p2	NOUN
ejpam-6667	132	6	(	(	PUNCT
ejpam-6667	132	7	·	·	PUNCT
ejpam-6667	132	8	)	)	PUNCT
ejpam-6667	132	9	.	.	PUNCT
ejpam-6667	133	1	if	if	SCONJ
ejpam-6667	133	2	p1	p1	PROPN
ejpam-6667	133	3	(	(	PUNCT
ejpam-6667	133	4	·	·	PUNCT
ejpam-6667	133	5	)	)	PUNCT
ejpam-6667	133	6	∈	∈	PROPN
ejpam-6667	133	7	p	p	NOUN
ejpam-6667	133	8	∩lh(rn	∩lh(rn	PROPN
ejpam-6667	133	9	)	)	PUNCT
ejpam-6667	134	1	and	and	CCONJ
ejpam-6667	134	2	0	0	NUM
ejpam-6667	134	3	<	<	X
ejpam-6667	134	4	α	α	X
ejpam-6667	134	5	<	<	X
ejpam-6667	134	6	n	n	PRON
ejpam-6667	134	7	p1	p1	NOUN
ejpam-6667	134	8	,	,	PUNCT
ejpam-6667	134	9	now	now	ADV
ejpam-6667	134	10	by	by	ADP
ejpam-6667	134	11	applying	apply	VERB
ejpam-6667	134	12	the	the	DET
ejpam-6667	134	13	monotone	monotone	ADJ
ejpam-6667	134	14	property	property	NOUN
ejpam-6667	134	15	,	,	PUNCT
ejpam-6667	134	16	we	we	PRON
ejpam-6667	134	17	obtain	obtain	VERB
ejpam-6667	134	18	wp1	wp1	PROPN
ejpam-6667	134	19	(	(	PUNCT
ejpam-6667	134	20	·	·	PUNCT
ejpam-6667	134	21	)	)	PUNCT
ejpam-6667	134	22	∈	∈	PROPN
ejpam-6667	134	23	a1	a1	NOUN
ejpam-6667	134	24	⊂	⊂	NOUN
ejpam-6667	134	25	a	a	DET
ejpam-6667	134	26	1	1	NUM
ejpam-6667	134	27	+	+	NUM
ejpam-6667	134	28	p2	p2	X
ejpam-6667	134	29	(	(	PUNCT
ejpam-6667	134	30	·	·	PUNCT
ejpam-6667	134	31	)	)	PUNCT
ejpam-6667	135	1	p	p	NOUN
ejpam-6667	135	2	′	′	NUM
ejpam-6667	135	3	1	1	NUM
ejpam-6667	135	4	(	(	PUNCT
ejpam-6667	135	5	·	·	PUNCT
ejpam-6667	135	6	)	)	PUNCT
ejpam-6667	135	7	.	.	PUNCT
ejpam-6667	136	1	so	so	ADV
ejpam-6667	136	2	,	,	PUNCT
ejpam-6667	136	3	by	by	ADP
ejpam-6667	136	4	lemma	lemma	PROPN
ejpam-6667	136	5	2	2	NUM
ejpam-6667	136	6	we	we	PRON
ejpam-6667	136	7	obtain	obtain	VERB
ejpam-6667	136	8	w	w	PROPN
ejpam-6667	136	9	∈	∈	PROPN
ejpam-6667	136	10	a(p1	a(p1	NOUN
ejpam-6667	136	11	(	(	PUNCT
ejpam-6667	136	12	·	·	PUNCT
ejpam-6667	136	13	)	)	PUNCT
ejpam-6667	136	14	,	,	PUNCT
ejpam-6667	136	15	p2	p2	X
ejpam-6667	136	16	(	(	PUNCT
ejpam-6667	136	17	·	·	PUNCT
ejpam-6667	136	18	)	)	PUNCT
ejpam-6667	136	19	)	)	PUNCT
ejpam-6667	136	20	.	.	PUNCT
ejpam-6667	137	1	lemma	lemma	PROPN
ejpam-6667	137	2	7	7	NUM
ejpam-6667	137	3	.	.	PUNCT
ejpam-6667	138	1	[	[	X
ejpam-6667	138	2	48	48	NUM
ejpam-6667	138	3	]	]	PUNCT
ejpam-6667	138	4	consider	consider	VERB
ejpam-6667	138	5	a	a	DET
ejpam-6667	138	6	weight	weight	NOUN
ejpam-6667	138	7	w	w	NOUN
ejpam-6667	138	8	on	on	ADP
ejpam-6667	138	9	rn	rn	PROPN
ejpam-6667	138	10	.	.	PUNCT
ejpam-6667	138	11	there	there	PRON
ejpam-6667	138	12	exist	exist	VERB
ejpam-6667	138	13	p	p	PRON
ejpam-6667	138	14	∈	∈	PROPN
ejpam-6667	139	1	[	[	X
ejpam-6667	139	2	1,+∞	1,+∞	NUM
ejpam-6667	139	3	)	)	PUNCT
ejpam-6667	139	4	such	such	ADJ
ejpam-6667	139	5	that	that	SCONJ
ejpam-6667	139	6	w	w	PROPN
ejpam-6667	139	7	∈	∈	PROPN
ejpam-6667	139	8	ap	ap	PROPN
ejpam-6667	139	9	,	,	PUNCT
ejpam-6667	139	10	then	then	ADV
ejpam-6667	139	11	for	for	ADP
ejpam-6667	139	12	any	any	DET
ejpam-6667	139	13	measurable	measurable	ADJ
ejpam-6667	139	14	set	set	NOUN
ejpam-6667	139	15	e	e	NOUN
ejpam-6667	139	16	subset	subset	NOUN
ejpam-6667	139	17	of	of	ADP
ejpam-6667	139	18	b	b	PROPN
ejpam-6667	139	19	,	,	PUNCT
ejpam-6667	139	20	we	we	PRON
ejpam-6667	139	21	have	have	VERB
ejpam-6667	139	22	w(b	w(b	NOUN
ejpam-6667	139	23	)	)	PUNCT
ejpam-6667	139	24	w(e	w(e	NOUN
ejpam-6667	139	25	)	)	PUNCT
ejpam-6667	140	1	≤	≤	NUM
ejpam-6667	140	2	c	c	NOUN
ejpam-6667	140	3	(	(	PUNCT
ejpam-6667	140	4	|b|	|b|	PROPN
ejpam-6667	140	5	|e|	|e|	PROPN
ejpam-6667	140	6	)	)	PUNCT
ejpam-6667	140	7	p	p	NOUN
ejpam-6667	140	8	w(e	w(e	PROPN
ejpam-6667	140	9	)	)	PUNCT
ejpam-6667	140	10	w(b	w(b	NOUN
ejpam-6667	140	11	)	)	PUNCT
ejpam-6667	140	12	≤	≤	NUM
ejpam-6667	141	1	c	c	X
ejpam-6667	141	2	(	(	PUNCT
ejpam-6667	141	3	|e|	|e|	DET
ejpam-6667	141	4	|b|	|b|	PROPN
ejpam-6667	141	5	)	)	PUNCT
ejpam-6667	141	6	δ	δ	PROPN
ejpam-6667	141	7	,	,	PUNCT
ejpam-6667	141	8	where	where	SCONJ
ejpam-6667	141	9	0	0	X
ejpam-6667	141	10	<	<	X
ejpam-6667	141	11	δ	δ	X
ejpam-6667	141	12	<	<	X
ejpam-6667	141	13	1	1	NUM
ejpam-6667	141	14	represents	represent	VERB
ejpam-6667	141	15	a	a	DET
ejpam-6667	141	16	constant	constant	ADJ
ejpam-6667	141	17	independent	independent	NOUN
ejpam-6667	141	18	of	of	ADP
ejpam-6667	141	19	e	e	PROPN
ejpam-6667	141	20	and	and	CCONJ
ejpam-6667	141	21	b.	b.	PROPN
ejpam-6667	141	22	lemma	lemma	PROPN
ejpam-6667	141	23	8	8	NUM
ejpam-6667	141	24	.	.	PUNCT
ejpam-6667	142	1	[	[	X
ejpam-6667	142	2	48	48	NUM
ejpam-6667	142	3	]	]	PUNCT
ejpam-6667	142	4	let	let	VERB
ejpam-6667	142	5	us	we	PRON
ejpam-6667	142	6	consider	consider	VERB
ejpam-6667	142	7	p	p	X
ejpam-6667	142	8	(	(	PUNCT
ejpam-6667	142	9	·	·	PUNCT
ejpam-6667	142	10	)	)	PUNCT
ejpam-6667	142	11	∈	∈	PROPN
ejpam-6667	142	12	p	p	NOUN
ejpam-6667	142	13	∩	∩	NOUN
ejpam-6667	142	14	lh(rn	lh(rn	PROPN
ejpam-6667	142	15	)	)	PUNCT
ejpam-6667	142	16	.	.	PUNCT
ejpam-6667	143	1	if	if	SCONJ
ejpam-6667	143	2	wp2	wp2	PROPN
ejpam-6667	143	3	(	(	PUNCT
ejpam-6667	143	4	·	·	PUNCT
ejpam-6667	143	5	)	)	PUNCT
ejpam-6667	143	6	∈	∈	PROPN
ejpam-6667	143	7	ap2	ap2	PROPN
ejpam-6667	143	8	(	(	PUNCT
ejpam-6667	143	9	·	·	PUNCT
ejpam-6667	143	10	)	)	PUNCT
ejpam-6667	143	11	and	and	CCONJ
ejpam-6667	143	12	wp1	wp1	PROPN
ejpam-6667	143	13	(	(	PUNCT
ejpam-6667	143	14	·	·	PUNCT
ejpam-6667	143	15	)	)	PUNCT
ejpam-6667	143	16	∈	∈	PROPN
ejpam-6667	143	17	ap1	ap1	PROPN
ejpam-6667	143	18	(	(	PUNCT
ejpam-6667	143	19	·	·	PUNCT
ejpam-6667	143	20	)	)	PUNCT
ejpam-6667	143	21	imply	imply	VERB
ejpam-6667	143	22	w−p	w−p	ADJ
ejpam-6667	143	23	′	′	NUM
ejpam-6667	143	24	2	2	NUM
ejpam-6667	143	25	(	(	PUNCT
ejpam-6667	143	26	·	·	PUNCT
ejpam-6667	143	27	)	)	PUNCT
ejpam-6667	143	28	∈	∈	PROPN
ejpam-6667	143	29	a	a	DET
ejpam-6667	143	30	p	p	NOUN
ejpam-6667	143	31	′	′	NUM
ejpam-6667	143	32	2	2	NUM
ejpam-6667	143	33	(	(	PUNCT
ejpam-6667	143	34	·	·	PUNCT
ejpam-6667	143	35	)	)	PUNCT
ejpam-6667	143	36	,	,	PUNCT
ejpam-6667	143	37	w−p	w−p	PROPN
ejpam-6667	143	38	′	′	NOUN
ejpam-6667	143	39	1	1	NUM
ejpam-6667	143	40	(	(	PUNCT
ejpam-6667	143	41	·	·	PUNCT
ejpam-6667	143	42	)	)	PUNCT
ejpam-6667	143	43	∈	∈	PROPN
ejpam-6667	143	44	a	a	DET
ejpam-6667	143	45	p	p	NOUN
ejpam-6667	143	46	′	′	NUM
ejpam-6667	143	47	1	1	NUM
ejpam-6667	143	48	(	(	PUNCT
ejpam-6667	143	49	·	·	PUNCT
ejpam-6667	143	50	)	)	PUNCT
ejpam-6667	143	51	respectively	respectively	ADV
ejpam-6667	143	52	.	.	PUNCT
ejpam-6667	144	1	thus	thus	ADV
ejpam-6667	144	2	,	,	PUNCT
ejpam-6667	144	3	m	m	VERB
ejpam-6667	144	4	is	be	AUX
ejpam-6667	144	5	bounded	bound	VERB
ejpam-6667	144	6	on	on	ADP
ejpam-6667	144	7	lp	lp	NOUN
ejpam-6667	144	8	′	′	NUM
ejpam-6667	144	9	2(·)(w−p	2(·)(w−p	NUM
ejpam-6667	144	10	′	′	NUM
ejpam-6667	145	1	2	2	NUM
ejpam-6667	145	2	(	(	PUNCT
ejpam-6667	145	3	·	·	PUNCT
ejpam-6667	145	4	)	)	PUNCT
ejpam-6667	145	5	)	)	PUNCT
ejpam-6667	145	6	.	.	PUNCT
ejpam-6667	146	1	there	there	PRON
ejpam-6667	146	2	exists	exist	VERB
ejpam-6667	146	3	constants	constant	NOUN
ejpam-6667	146	4	δ1	δ1	NOUN
ejpam-6667	146	5	,	,	PUNCT
ejpam-6667	146	6	δ2	δ2	VERB
ejpam-6667	146	7	∈	∈	PROPN
ejpam-6667	146	8	(	(	PUNCT
ejpam-6667	146	9	0	0	NUM
ejpam-6667	146	10	,	,	PUNCT
ejpam-6667	146	11	1	1	NUM
ejpam-6667	146	12	)	)	PUNCT
ejpam-6667	146	13	and	and	CCONJ
ejpam-6667	146	14	e	e	X
ejpam-6667	146	15	⊂	⊂	PROPN
ejpam-6667	146	16	b	b	PROPN
ejpam-6667	146	17	such	such	ADJ
ejpam-6667	146	18	that	that	SCONJ
ejpam-6667	146	19	∥χe∥lp2(·)(wp2	∥χe∥lp2(·)(wp2	NOUN
ejpam-6667	146	20	(	(	PUNCT
ejpam-6667	146	21	·	·	PUNCT
ejpam-6667	146	22	)	)	PUNCT
ejpam-6667	146	23	)	)	PUNCT
ejpam-6667	146	24	∥χb∥lp2(·)(wp2	∥χb∥lp2(·)(wp2	PROPN
ejpam-6667	146	25	(	(	PUNCT
ejpam-6667	146	26	·	·	PUNCT
ejpam-6667	146	27	)	)	PUNCT
ejpam-6667	146	28	)	)	PUNCT
ejpam-6667	147	1	=	=	SYM
ejpam-6667	147	2	∥χe∥	∥χe∥	NOUN
ejpam-6667	147	3	(	(	PUNCT
ejpam-6667	147	4	lp	lp	NOUN
ejpam-6667	147	5	′	′	NUM
ejpam-6667	148	1	2(·)w−p	2(·)w−p	NUM
ejpam-6667	148	2	′	′	NUM
ejpam-6667	149	1	2(·))′	2(·))′	INTJ
ejpam-6667	149	2	∥χb∥	∥χb∥	NOUN
ejpam-6667	150	1	(	(	PUNCT
ejpam-6667	150	2	lp	lp	NOUN
ejpam-6667	150	3	′	′	NUM
ejpam-6667	150	4	2(·)w−p	2(·)w−p	NUM
ejpam-6667	150	5	′	′	NUM
ejpam-6667	151	1	2(·))′	2(·))′	INTJ
ejpam-6667	151	2	≲	≲	PROPN
ejpam-6667	151	3	(	(	PUNCT
ejpam-6667	151	4	|e|	|e|	DET
ejpam-6667	151	5	|b|	|b|	PROPN
ejpam-6667	151	6	)	)	PUNCT
ejpam-6667	151	7	δ1	δ1	NOUN
ejpam-6667	151	8	,	,	PUNCT
ejpam-6667	151	9	(	(	PUNCT
ejpam-6667	151	10	5	5	NUM
ejpam-6667	151	11	)	)	PUNCT
ejpam-6667	151	12	∥χe∥(lp1(·)wp1(·))′	∥χe∥(lp1(·)wp1(·))′	PROPN
ejpam-6667	151	13	∥χb∥(lp1(·)wp1(·))′	∥χb∥(lp1(·)wp1(·))′	PROPN
ejpam-6667	152	1	≲	≲	PROPN
ejpam-6667	152	2	(	(	PUNCT
ejpam-6667	152	3	|e|	|e|	DET
ejpam-6667	152	4	|b|	|b|	PROPN
ejpam-6667	152	5	)	)	PUNCT
ejpam-6667	152	6	δ2	δ2	VERB
ejpam-6667	152	7	.	.	PUNCT
ejpam-6667	153	1	(	(	PUNCT
ejpam-6667	153	2	6	6	X
ejpam-6667	153	3	)	)	PUNCT
ejpam-6667	153	4	lemma	lemma	PROPN
ejpam-6667	153	5	9	9	NUM
ejpam-6667	153	6	.	.	PUNCT
ejpam-6667	154	1	[	[	X
ejpam-6667	154	2	16	16	NUM
ejpam-6667	154	3	]	]	PUNCT
ejpam-6667	154	4	let	let	VERB
ejpam-6667	154	5	p1	p1	PROPN
ejpam-6667	154	6	(	(	PUNCT
ejpam-6667	154	7	·	·	PUNCT
ejpam-6667	154	8	)	)	PUNCT
ejpam-6667	154	9	∈	∈	PROPN
ejpam-6667	154	10	p	p	NOUN
ejpam-6667	154	11	∩	∩	X
ejpam-6667	154	12	lh(rn	lh(rn	PROPN
ejpam-6667	154	13	)	)	PUNCT
ejpam-6667	155	1	and	and	CCONJ
ejpam-6667	155	2	0	0	NUM
ejpam-6667	155	3	<	<	X
ejpam-6667	155	4	α	α	X
ejpam-6667	155	5	<	<	X
ejpam-6667	155	6	n	n	PRON
ejpam-6667	155	7	p1(.)+	p1(.)+	NOUN
ejpam-6667	155	8	,	,	PUNCT
ejpam-6667	155	9	and	and	CCONJ
ejpam-6667	155	10	1	1	NUM
ejpam-6667	155	11	p2	p2	NOUN
ejpam-6667	155	12	(	(	PUNCT
ejpam-6667	155	13	.	.	PUNCT
ejpam-6667	155	14	)	)	PUNCT
ejpam-6667	156	1	=	=	SYM
ejpam-6667	156	2	1	1	NUM
ejpam-6667	156	3	p1	p1	NOUN
ejpam-6667	156	4	(	(	PUNCT
ejpam-6667	156	5	.	.	PUNCT
ejpam-6667	156	6	)	)	PUNCT
ejpam-6667	157	1	−	−	PROPN
ejpam-6667	158	1	α	α	X
ejpam-6667	158	2	n	n	NOUN
ejpam-6667	158	3	.	.	PUNCT
ejpam-6667	159	1	if	if	SCONJ
ejpam-6667	159	2	w	w	PROPN
ejpam-6667	159	3	∈	∈	PROPN
ejpam-6667	159	4	a(p1	a(p1	NOUN
ejpam-6667	159	5	(	(	PUNCT
ejpam-6667	159	6	.	.	PUNCT
ejpam-6667	159	7	)	)	PUNCT
ejpam-6667	159	8	,	,	PUNCT
ejpam-6667	159	9	p2	p2	X
ejpam-6667	159	10	(	(	PUNCT
ejpam-6667	159	11	.	.	PUNCT
ejpam-6667	159	12	)	)	PUNCT
ejpam-6667	159	13	)	)	PUNCT
ejpam-6667	159	14	,	,	PUNCT
ejpam-6667	159	15	then	then	ADV
ejpam-6667	159	16	iα	iα	VERB
ejpam-6667	159	17	is	be	AUX
ejpam-6667	159	18	bounded	bound	VERB
ejpam-6667	159	19	from	from	ADP
ejpam-6667	159	20	lp1(.)(wp1	lp1(.)(wp1	PROPN
ejpam-6667	159	21	(	(	PUNCT
ejpam-6667	159	22	.	.	PUNCT
ejpam-6667	159	23	)	)	PUNCT
ejpam-6667	159	24	)	)	PUNCT
ejpam-6667	159	25	to	to	ADP
ejpam-6667	159	26	lp2(.)(wp2	lp2(.)(wp2	X
ejpam-6667	159	27	(	(	PUNCT
ejpam-6667	159	28	.	.	PUNCT
ejpam-6667	159	29	)	)	PUNCT
ejpam-6667	159	30	)	)	PUNCT
ejpam-6667	159	31	.	.	PUNCT
ejpam-6667	160	1	lemma	lemma	PROPN
ejpam-6667	160	2	10	10	NUM
ejpam-6667	160	3	.	.	PUNCT
ejpam-6667	161	1	[	[	X
ejpam-6667	161	2	49	49	NUM
ejpam-6667	161	3	]	]	PUNCT
ejpam-6667	161	4	if	if	SCONJ
ejpam-6667	161	5	the	the	DET
ejpam-6667	161	6	hardy	hardy	ADJ
ejpam-6667	161	7	littlewood	littlewood	NOUN
ejpam-6667	161	8	maximal	maximal	ADJ
ejpam-6667	161	9	operator	operator	NOUN
ejpam-6667	161	10	is	be	AUX
ejpam-6667	161	11	bounded	bound	VERB
ejpam-6667	161	12	on	on	ADP
ejpam-6667	161	13	the	the	DET
ejpam-6667	161	14	banach	banach	NOUN
ejpam-6667	161	15	function	function	NOUN
ejpam-6667	161	16	space	space	NOUN
ejpam-6667	161	17	y	y	PROPN
ejpam-6667	161	18	,	,	PUNCT
ejpam-6667	161	19	then	then	ADV
ejpam-6667	161	20	for	for	ADP
ejpam-6667	161	21	a	a	DET
ejpam-6667	161	22	measurable	measurable	ADJ
ejpam-6667	161	23	set	set	NOUN
ejpam-6667	161	24	e	e	PROPN
ejpam-6667	161	25	⊂	⊂	PROPN
ejpam-6667	161	26	b	b	X
ejpam-6667	161	27	we	we	PRON
ejpam-6667	161	28	have	have	VERB
ejpam-6667	161	29	the	the	DET
ejpam-6667	161	30	following	following	ADJ
ejpam-6667	161	31	result	result	NOUN
ejpam-6667	161	32	∥χb∥y	∥χb∥y	PROPN
ejpam-6667	161	33	∥χe∥y	∥χe∥y	PROPN
ejpam-6667	161	34	≲	≲	PROPN
ejpam-6667	161	35	|b|	|b|	PROPN
ejpam-6667	161	36	|e|	|e|	PROPN
ejpam-6667	161	37	.	.	PUNCT
ejpam-6667	162	1	m.	m.	PROPN
ejpam-6667	162	2	asim	asim	PROPN
ejpam-6667	162	3	,	,	PUNCT
ejpam-6667	162	4	k.	k.	PROPN
ejpam-6667	162	5	suwais	suwais	PROPN
ejpam-6667	162	6	,	,	PUNCT
ejpam-6667	162	7	n.	n.	PROPN
ejpam-6667	162	8	mlaiki	mlaiki	PROPN
ejpam-6667	162	9	/	/	SYM
ejpam-6667	162	10	eur	eur	PROPN
ejpam-6667	162	11	.	.	PUNCT
ejpam-6667	163	1	j.	j.	PROPN
ejpam-6667	163	2	pure	pure	PROPN
ejpam-6667	163	3	appl	appl	PROPN
ejpam-6667	163	4	.	.	PROPN
ejpam-6667	163	5	math	math	PROPN
ejpam-6667	163	6	,	,	PUNCT
ejpam-6667	163	7	18	18	NUM
ejpam-6667	163	8	(	(	PUNCT
ejpam-6667	163	9	4	4	NUM
ejpam-6667	163	10	)	)	PUNCT
ejpam-6667	163	11	(	(	PUNCT
ejpam-6667	163	12	2025	2025	NUM
ejpam-6667	163	13	)	)	PUNCT
ejpam-6667	163	14	,	,	PUNCT
ejpam-6667	163	15	6667	6667	NUM
ejpam-6667	163	16	7	7	NUM
ejpam-6667	163	17	of	of	ADP
ejpam-6667	163	18	20	20	NUM
ejpam-6667	163	19	4	4	NUM
ejpam-6667	163	20	.	.	PUNCT
ejpam-6667	163	21	main	main	ADJ
ejpam-6667	163	22	results	result	NOUN
ejpam-6667	163	23	and	and	CCONJ
ejpam-6667	163	24	their	their	PRON
ejpam-6667	163	25	proof	proof	NOUN
ejpam-6667	163	26	lemma	lemma	PROPN
ejpam-6667	163	27	11	11	NUM
ejpam-6667	163	28	.	.	PUNCT
ejpam-6667	164	1	if	if	SCONJ
ejpam-6667	164	2	wq1	wq1	ADJ
ejpam-6667	164	3	(	(	PUNCT
ejpam-6667	164	4	·	·	PUNCT
ejpam-6667	164	5	)	)	PUNCT
ejpam-6667	164	6	∈	∈	PROPN
ejpam-6667	164	7	a1	a1	NOUN
ejpam-6667	164	8	,	,	PUNCT
ejpam-6667	164	9	where	where	SCONJ
ejpam-6667	164	10	q1	q1	PROPN
ejpam-6667	164	11	(	(	PUNCT
ejpam-6667	164	12	·	·	PUNCT
ejpam-6667	164	13	)	)	PUNCT
ejpam-6667	164	14	∈	∈	PROPN
ejpam-6667	164	15	p(rn	p(rn	PROPN
ejpam-6667	164	16	)	)	PUNCT
ejpam-6667	164	17	⋂	⋂	PROPN
ejpam-6667	164	18	lh(rn	lh(rn	PROPN
ejpam-6667	164	19	)	)	PUNCT
ejpam-6667	164	20	,	,	PUNCT
ejpam-6667	164	21	define	define	VERB
ejpam-6667	164	22	the	the	DET
ejpam-6667	164	23	variable	variable	ADJ
ejpam-6667	164	24	exponent	exponent	NOUN
ejpam-6667	164	25	q2	q2	PROPN
ejpam-6667	164	26	(	(	PUNCT
ejpam-6667	164	27	·	·	PUNCT
ejpam-6667	164	28	)	)	PUNCT
ejpam-6667	164	29	by	by	ADP
ejpam-6667	164	30	1	1	NUM
ejpam-6667	164	31	q2(x	q2(x	NOUN
ejpam-6667	164	32	)	)	PUNCT
ejpam-6667	164	33	=	=	NOUN
ejpam-6667	164	34	1	1	NUM
ejpam-6667	164	35	q1(x	q1(x	NOUN
ejpam-6667	164	36	)	)	PUNCT
ejpam-6667	164	37	−	−	PROPN
ejpam-6667	165	1	α	α	PROPN
ejpam-6667	166	1	n	n	NOUN
ejpam-6667	166	2	,	,	PUNCT
ejpam-6667	166	3	then	then	ADV
ejpam-6667	166	4	∥χbk	∥χbk	NUM
ejpam-6667	166	5	∥lq2(·)(wq2	∥lq2(·)(wq2	PROPN
ejpam-6667	166	6	(	(	PUNCT
ejpam-6667	166	7	·	·	PUNCT
ejpam-6667	166	8	)	)	PUNCT
ejpam-6667	166	9	)	)	PUNCT
ejpam-6667	167	1	≤	≤	NUM
ejpam-6667	167	2	c2k(n−α)∥χbk	c2k(n−α)∥χbk	ADJ
ejpam-6667	167	3	∥−1	∥−1	X
ejpam-6667	167	4	(	(	PUNCT
ejpam-6667	167	5	lq1(·)(wq1(·)))′	lq1(·)(wq1(·)))′	PROPN
ejpam-6667	167	6	.	.	PUNCT
ejpam-6667	168	1	proof	proof	NOUN
ejpam-6667	168	2	.	.	PUNCT
ejpam-6667	169	1	based	base	VERB
ejpam-6667	169	2	on	on	ADP
ejpam-6667	169	3	lemmas	lemmas	PROPN
ejpam-6667	169	4	9	9	NUM
ejpam-6667	169	5	and	and	CCONJ
ejpam-6667	169	6	5	5	NUM
ejpam-6667	169	7	,	,	PUNCT
ejpam-6667	169	8	we	we	PRON
ejpam-6667	169	9	have	have	VERB
ejpam-6667	169	10	iα(χbk	iα(χbk	NOUN
ejpam-6667	169	11	)	)	PUNCT
ejpam-6667	169	12	(	(	PUNCT
ejpam-6667	169	13	x	x	X
ejpam-6667	169	14	)	)	PUNCT
ejpam-6667	169	15	≥	≥	PROPN
ejpam-6667	169	16	c2kαχbk	c2kαχbk	NOUN
ejpam-6667	169	17	(	(	PUNCT
ejpam-6667	169	18	x	x	NOUN
ejpam-6667	169	19	)	)	PUNCT
ejpam-6667	169	20	χbk	χbk	NOUN
ejpam-6667	169	21	(	(	PUNCT
ejpam-6667	169	22	x	x	NOUN
ejpam-6667	169	23	)	)	PUNCT
ejpam-6667	169	24	≤	≤	NOUN
ejpam-6667	169	25	c2−kαiα(χbk	c2−kαiα(χbk	NOUN
ejpam-6667	169	26	)	)	PUNCT
ejpam-6667	169	27	(	(	PUNCT
ejpam-6667	169	28	x	x	X
ejpam-6667	169	29	)	)	PUNCT
ejpam-6667	169	30	∥χbk	∥χbk	VERB
ejpam-6667	170	1	∥lq2(·)(wq2	∥lq2(·)(wq2	PROPN
ejpam-6667	170	2	(	(	PUNCT
ejpam-6667	170	3	·	·	PUNCT
ejpam-6667	170	4	)	)	PUNCT
ejpam-6667	170	5	)	)	PUNCT
ejpam-6667	170	6	≤	≤	NUM
ejpam-6667	170	7	c2−kα∥iα(χbk	c2−kα∥iα(χbk	NOUN
ejpam-6667	170	8	)	)	PUNCT
ejpam-6667	170	9	∥lq2(·)(wq2	∥lq2(·)(wq2	PROPN
ejpam-6667	170	10	(	(	PUNCT
ejpam-6667	170	11	·	·	PUNCT
ejpam-6667	170	12	)	)	PUNCT
ejpam-6667	170	13	)	)	PUNCT
ejpam-6667	170	14	≤	≤	NOUN
ejpam-6667	171	1	c2−kα∥χbk	c2−kα∥χbk	ADP
ejpam-6667	171	2	∥lq1(·)(wq1	∥lq1(·)(wq1	PROPN
ejpam-6667	171	3	(	(	PUNCT
ejpam-6667	171	4	·	·	PUNCT
ejpam-6667	171	5	)	)	PUNCT
ejpam-6667	171	6	)	)	PUNCT
ejpam-6667	171	7	≤	≤	NUM
ejpam-6667	172	1	c2k(n−α)∥χbk	c2k(n−α)∥χbk	ADJ
ejpam-6667	172	2	∥−1	∥−1	X
ejpam-6667	172	3	(	(	PUNCT
ejpam-6667	172	4	lq1(·)(wq1(·)))′	lq1(·)(wq1(·)))′	PROPN
ejpam-6667	172	5	.	.	PUNCT
ejpam-6667	173	1	(	(	PUNCT
ejpam-6667	173	2	7	7	X
ejpam-6667	173	3	)	)	PUNCT
ejpam-6667	173	4	4.1	4.1	NUM
ejpam-6667	173	5	.	.	PUNCT
ejpam-6667	174	1	boundedness	boundedness	NOUN
ejpam-6667	174	2	of	of	ADP
ejpam-6667	174	3	fractional	fractional	ADJ
ejpam-6667	174	4	hardy	hardy	ADJ
ejpam-6667	174	5	operators	operator	NOUN
ejpam-6667	174	6	theorem	theorem	VERB
ejpam-6667	174	7	1	1	X
ejpam-6667	174	8	.	.	PUNCT
ejpam-6667	175	1	let	let	VERB
ejpam-6667	175	2	q1	q1	PROPN
ejpam-6667	175	3	(	(	PUNCT
ejpam-6667	175	4	·	·	PUNCT
ejpam-6667	175	5	)	)	PUNCT
ejpam-6667	175	6	∈	∈	PROPN
ejpam-6667	175	7	p(rn	p(rn	PROPN
ejpam-6667	175	8	)	)	PUNCT
ejpam-6667	175	9	⋂	⋂	PROPN
ejpam-6667	175	10	lh(rn	lh(rn	PROPN
ejpam-6667	175	11	)	)	PUNCT
ejpam-6667	175	12	.	.	PUNCT
ejpam-6667	176	1	define	define	VERB
ejpam-6667	176	2	the	the	DET
ejpam-6667	176	3	variable	variable	ADJ
ejpam-6667	176	4	exponent	exponent	NOUN
ejpam-6667	176	5	q2	q2	PROPN
ejpam-6667	176	6	(	(	PUNCT
ejpam-6667	176	7	·	·	PUNCT
ejpam-6667	176	8	)	)	PUNCT
ejpam-6667	176	9	by	by	ADP
ejpam-6667	176	10	1	1	NUM
ejpam-6667	176	11	q2(x	q2(x	NOUN
ejpam-6667	176	12	)	)	PUNCT
ejpam-6667	176	13	=	=	NOUN
ejpam-6667	176	14	1	1	NUM
ejpam-6667	176	15	q1(x	q1(x	NOUN
ejpam-6667	176	16	)	)	PUNCT
ejpam-6667	176	17	−	−	PROPN
ejpam-6667	177	1	α	α	PROPN
ejpam-6667	177	2	n	n	NOUN
ejpam-6667	177	3	.	.	PUNCT
ejpam-6667	178	1	if	if	SCONJ
ejpam-6667	178	2	wq1	wq1	ADJ
ejpam-6667	178	3	(	(	PUNCT
ejpam-6667	178	4	·	·	PUNCT
ejpam-6667	178	5	)	)	PUNCT
ejpam-6667	178	6	∈	∈	PROPN
ejpam-6667	178	7	a1	a1	NOUN
ejpam-6667	178	8	,	,	PUNCT
ejpam-6667	178	9	λ2	λ2	NOUN
ejpam-6667	178	10	=	=	SYM
ejpam-6667	178	11	λ1	λ1	PROPN
ejpam-6667	178	12	+	+	CCONJ
ejpam-6667	178	13	α	α	PROPN
ejpam-6667	178	14	n	n	NOUN
ejpam-6667	178	15	,	,	PUNCT
ejpam-6667	178	16	and	and	CCONJ
ejpam-6667	178	17	δ2	δ2	VERB
ejpam-6667	178	18	+	+	CCONJ
ejpam-6667	178	19	δλ2	δλ2	NOUN
ejpam-6667	178	20	+	+	CCONJ
ejpam-6667	178	21	δ1	δ1	NOUN
ejpam-6667	178	22	>	>	X
ejpam-6667	178	23	0	0	PROPN
ejpam-6667	178	24	,	,	PUNCT
ejpam-6667	178	25	then	then	ADV
ejpam-6667	178	26	∥hαf∥ḃq2(·),λ2	∥hαf∥ḃq2(·),λ2	PROPN
ejpam-6667	178	27	(	(	PUNCT
ejpam-6667	178	28	wq2	wq2	PROPN
ejpam-6667	178	29	(	(	PUNCT
ejpam-6667	178	30	·	·	PUNCT
ejpam-6667	178	31	)	)	PUNCT
ejpam-6667	178	32	)	)	PUNCT
ejpam-6667	179	1	≤	≤	NUM
ejpam-6667	179	2	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	179	3	(	(	PUNCT
ejpam-6667	179	4	wq1	wq1	PROPN
ejpam-6667	179	5	(	(	PUNCT
ejpam-6667	179	6	·	·	PUNCT
ejpam-6667	179	7	)	)	PUNCT
ejpam-6667	179	8	)	)	PUNCT
ejpam-6667	179	9	.	.	PUNCT
ejpam-6667	180	1	proof	proof	NOUN
ejpam-6667	180	2	of	of	ADP
ejpam-6667	180	3	theorem	theorem	ADJ
ejpam-6667	180	4	1	1	NUM
ejpam-6667	180	5	using	use	VERB
ejpam-6667	180	6	generalized	generalized	ADJ
ejpam-6667	180	7	hölder	hölder	NOUN
ejpam-6667	180	8	inequality	inequality	NOUN
ejpam-6667	180	9	given	give	VERB
ejpam-6667	180	10	in	in	ADP
ejpam-6667	180	11	lemma	lemma	PROPN
ejpam-6667	180	12	3	3	NUM
ejpam-6667	180	13	.	.	PUNCT
ejpam-6667	180	14	|hαf(x	|hαf(x	NOUN
ejpam-6667	180	15	)	)	PUNCT
ejpam-6667	180	16	·	·	PUNCT
ejpam-6667	180	17	χk(x)|	χk(x)|	VERB
ejpam-6667	180	18	≤	≤	NUM
ejpam-6667	180	19	1	1	NUM
ejpam-6667	180	20	|x|n−α	|x|n−α	NOUN
ejpam-6667	180	21	∫	∫	PROPN
ejpam-6667	180	22	bk	bk	INTJ
ejpam-6667	180	23	|f(t)|dt	|f(t)|dt	X
ejpam-6667	180	24	·	·	PUNCT
ejpam-6667	180	25	χk(x	χk(x	NOUN
ejpam-6667	180	26	)	)	PUNCT
ejpam-6667	180	27	≤	≤	NUM
ejpam-6667	180	28	c2−k(n−α	c2−k(n−α	NOUN
ejpam-6667	180	29	)	)	PUNCT
ejpam-6667	180	30	k∑	k∑	NOUN
ejpam-6667	180	31	j=−∞	j=−∞	PROPN
ejpam-6667	181	1	∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1	∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1	PROPN
ejpam-6667	181	2	(	(	PUNCT
ejpam-6667	181	3	·	·	PUNCT
ejpam-6667	181	4	)	)	PUNCT
ejpam-6667	181	5	)	)	PUNCT
ejpam-6667	181	6	·	·	PUNCT
ejpam-6667	182	1	χk(x	χk(x	NOUN
ejpam-6667	182	2	)	)	PUNCT
ejpam-6667	182	3	.	.	PUNCT
ejpam-6667	183	1	∥hαf(x	∥hαf(x	NOUN
ejpam-6667	183	2	)	)	PUNCT
ejpam-6667	183	3	·	·	PUNCT
ejpam-6667	183	4	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	183	5	(	(	PUNCT
ejpam-6667	183	6	·	·	PUNCT
ejpam-6667	183	7	)	)	PUNCT
ejpam-6667	183	8	)	)	PUNCT
ejpam-6667	183	9	≤	≤	NUM
ejpam-6667	183	10	c2−k(n−α	c2−k(n−α	NOUN
ejpam-6667	183	11	)	)	PUNCT
ejpam-6667	183	12	k∑	k∑	NOUN
ejpam-6667	183	13	j=−∞	j=−∞	PROPN
ejpam-6667	184	1	∥fj∥lq1(·)(wq1(·))∥χj∥(lq1(·)(wq1(·)))′∥χk∥lq2(·)(wq2	∥fj∥lq1(·)(wq1(·))∥χj∥(lq1(·)(wq1(·)))′∥χk∥lq2(·)(wq2	PROPN
ejpam-6667	184	2	(	(	PUNCT
ejpam-6667	184	3	·	·	PUNCT
ejpam-6667	184	4	)	)	PUNCT
ejpam-6667	184	5	)	)	PUNCT
ejpam-6667	184	6	.	.	PUNCT
ejpam-6667	185	1	m.	m.	PROPN
ejpam-6667	185	2	asim	asim	PROPN
ejpam-6667	185	3	,	,	PUNCT
ejpam-6667	185	4	k.	k.	PROPN
ejpam-6667	185	5	suwais	suwais	PROPN
ejpam-6667	185	6	,	,	PUNCT
ejpam-6667	185	7	n.	n.	PROPN
ejpam-6667	185	8	mlaiki	mlaiki	PROPN
ejpam-6667	185	9	/	/	SYM
ejpam-6667	185	10	eur	eur	PROPN
ejpam-6667	185	11	.	.	PUNCT
ejpam-6667	186	1	j.	j.	PROPN
ejpam-6667	186	2	pure	pure	PROPN
ejpam-6667	186	3	appl	appl	PROPN
ejpam-6667	186	4	.	.	PROPN
ejpam-6667	186	5	math	math	PROPN
ejpam-6667	186	6	,	,	PUNCT
ejpam-6667	186	7	18	18	NUM
ejpam-6667	186	8	(	(	PUNCT
ejpam-6667	186	9	4	4	NUM
ejpam-6667	186	10	)	)	PUNCT
ejpam-6667	186	11	(	(	PUNCT
ejpam-6667	186	12	2025	2025	NUM
ejpam-6667	186	13	)	)	PUNCT
ejpam-6667	186	14	,	,	PUNCT
ejpam-6667	186	15	6667	6667	NUM
ejpam-6667	186	16	8	8	NUM
ejpam-6667	186	17	of	of	ADP
ejpam-6667	186	18	20	20	NUM
ejpam-6667	186	19	by	by	ADP
ejpam-6667	186	20	means	mean	NOUN
ejpam-6667	186	21	of	of	ADP
ejpam-6667	186	22	lemma	lemma	PROPN
ejpam-6667	186	23	5	5	NUM
ejpam-6667	186	24	,	,	PUNCT
ejpam-6667	186	25	we	we	PRON
ejpam-6667	186	26	have	have	AUX
ejpam-6667	186	27	∥hαf(x	∥hαf(x	NOUN
ejpam-6667	186	28	)	)	PUNCT
ejpam-6667	186	29	·	·	PUNCT
ejpam-6667	187	1	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	187	2	(	(	PUNCT
ejpam-6667	187	3	·	·	PUNCT
ejpam-6667	187	4	)	)	PUNCT
ejpam-6667	187	5	)	)	PUNCT
ejpam-6667	187	6	≤	≤	NOUN
ejpam-6667	187	7	c2kα	c2kα	PUNCT
ejpam-6667	187	8	k∑	k∑	VERB
ejpam-6667	187	9	j=−∞	j=−∞	NOUN
ejpam-6667	187	10	∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥−1	∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥−1	PROPN
ejpam-6667	187	11	(	(	PUNCT
ejpam-6667	187	12	lq2(·))(wq2(·)))′	lq2(·))(wq2(·)))′	PROPN
ejpam-6667	187	13	≤	≤	PROPN
ejpam-6667	187	14	c2kα	c2kα	PUNCT
ejpam-6667	187	15	k∑	k∑	PROPN
ejpam-6667	187	16	j=−∞	j=−∞	NOUN
ejpam-6667	187	17	∥fj∥lq1(·)(wq1	∥fj∥lq1(·)(wq1	PROPN
ejpam-6667	187	18	(	(	PUNCT
ejpam-6667	187	19	·	·	PUNCT
ejpam-6667	187	20	)	)	PUNCT
ejpam-6667	187	21	)	)	PUNCT
ejpam-6667	188	1	∥χj∥(lq1(·)(wq1(·)))′	∥χj∥(lq1(·)(wq1(·)))′	PROPN
ejpam-6667	188	2	∥χk∥(lq1(·)(wq1(·)))′	∥χk∥(lq1(·)(wq1(·)))′	PROPN
ejpam-6667	188	3	∥χk∥(lq1(·)(wq1(·)))′∥χk∥−1	∥χk∥(lq1(·)(wq1(·)))′∥χk∥−1	PROPN
ejpam-6667	188	4	(	(	PUNCT
ejpam-6667	188	5	lq2(·)(wq2(·)))′	lq2(·)(wq2(·)))′	PROPN
ejpam-6667	188	6	.	.	PUNCT
ejpam-6667	189	1	by	by	ADP
ejpam-6667	189	2	lemma	lemma	PROPN
ejpam-6667	189	3	8	8	NUM
ejpam-6667	189	4	and	and	CCONJ
ejpam-6667	189	5	condition	condition	NOUN
ejpam-6667	189	6	(	(	PUNCT
ejpam-6667	189	7	6	6	NUM
ejpam-6667	189	8	)	)	PUNCT
ejpam-6667	189	9	,	,	PUNCT
ejpam-6667	189	10	we	we	PRON
ejpam-6667	189	11	acquire	acquire	VERB
ejpam-6667	189	12	∥hαf(x	∥hαf(x	NOUN
ejpam-6667	189	13	)	)	PUNCT
ejpam-6667	189	14	·	·	PUNCT
ejpam-6667	190	1	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	190	2	(	(	PUNCT
ejpam-6667	190	3	·	·	PUNCT
ejpam-6667	190	4	)	)	PUNCT
ejpam-6667	190	5	)	)	PUNCT
ejpam-6667	190	6	≤	≤	NOUN
ejpam-6667	190	7	c2kα	c2kα	PUNCT
ejpam-6667	190	8	k∑	k∑	VERB
ejpam-6667	190	9	j=−∞	j=−∞	NOUN
ejpam-6667	191	1	2nδ2(j−k)∥χk∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥−1	2nδ2(j−k)∥χk∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥−1	PROPN
ejpam-6667	191	2	(	(	PUNCT
ejpam-6667	191	3	lq2(·)(wq2(·)))′	lq2(·)(wq2(·)))′	PROPN
ejpam-6667	191	4	.	.	PUNCT
ejpam-6667	192	1	(	(	PUNCT
ejpam-6667	192	2	8)	8)	NUM
ejpam-6667	192	3	using	use	VERB
ejpam-6667	192	4	inequality	inequality	NOUN
ejpam-6667	192	5	(	(	PUNCT
ejpam-6667	192	6	7	7	NUM
ejpam-6667	192	7	)	)	PUNCT
ejpam-6667	192	8	in	in	ADP
ejpam-6667	192	9	(	(	PUNCT
ejpam-6667	192	10	8)	8)	NUM
ejpam-6667	192	11	and	and	CCONJ
ejpam-6667	192	12	by	by	ADP
ejpam-6667	192	13	the	the	DET
ejpam-6667	192	14	result	result	NOUN
ejpam-6667	192	15	of	of	ADP
ejpam-6667	192	16	lemma	lemma	PROPN
ejpam-6667	192	17	5	5	NUM
ejpam-6667	192	18	∥hαf(x	∥hαf(x	NOUN
ejpam-6667	192	19	)	)	PUNCT
ejpam-6667	192	20	·	·	PUNCT
ejpam-6667	193	1	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	193	2	(	(	PUNCT
ejpam-6667	193	3	·	·	PUNCT
ejpam-6667	193	4	)	)	PUNCT
ejpam-6667	193	5	)	)	PUNCT
ejpam-6667	193	6	≤	≤	NOUN
ejpam-6667	193	7	c2kα	c2kα	PUNCT
ejpam-6667	193	8	k∑	k∑	VERB
ejpam-6667	194	1	j=−∞	j=−∞	NOUN
ejpam-6667	194	2	2nδ2(j−k)2k(n−α)∥fj∥lq1(·)(wq1(·))∥χk∥−1	2nδ2(j−k)2k(n−α)∥fj∥lq1(·)(wq1(·))∥χk∥−1	NUM
ejpam-6667	194	3	lq2(·)(wq2	lq2(·)(wq2	PROPN
ejpam-6667	194	4	(	(	PUNCT
ejpam-6667	194	5	·	·	PUNCT
ejpam-6667	194	6	)	)	PUNCT
ejpam-6667	194	7	)	)	PUNCT
ejpam-6667	195	1	∥χk∥−1	∥χk∥−1	PROPN
ejpam-6667	195	2	(	(	PUNCT
ejpam-6667	195	3	lq2(·)(wq2(·)))′	lq2(·)(wq2(·)))′	PROPN
ejpam-6667	195	4	≤	≤	PROPN
ejpam-6667	195	5	c	c	PROPN
ejpam-6667	195	6	k∑	k∑	PROPN
ejpam-6667	195	7	j=−∞	j=−∞	PROPN
ejpam-6667	195	8	2nδ2(j−k)∥fj∥lq1(·)(wq1	2nδ2(j−k)∥fj∥lq1(·)(wq1	NUM
ejpam-6667	195	9	(	(	PUNCT
ejpam-6667	195	10	·	·	PUNCT
ejpam-6667	195	11	)	)	PUNCT
ejpam-6667	195	12	)	)	PUNCT
ejpam-6667	195	13	(	(	PUNCT
ejpam-6667	195	14	2−kn∥χk∥lq2(·)(wq2(·))∥χk∥(lq2(·)(wq2(·)))′	2−kn∥χk∥lq2(·)(wq2(·))∥χk∥(lq2(·)(wq2(·)))′	X
ejpam-6667	195	15	)	)	PUNCT
ejpam-6667	195	16	−1	−1	NOUN
ejpam-6667	195	17	≤	≤	PROPN
ejpam-6667	195	18	c	c	AUX
ejpam-6667	195	19	k∑	k∑	PROPN
ejpam-6667	195	20	j=−∞	j=−∞	PROPN
ejpam-6667	195	21	2nδ2(j−k)∥fj∥lq1(·)(wq1	2nδ2(j−k)∥fj∥lq1(·)(wq1	NUM
ejpam-6667	195	22	(	(	PUNCT
ejpam-6667	195	23	·	·	PUNCT
ejpam-6667	195	24	)	)	PUNCT
ejpam-6667	195	25	)	)	PUNCT
ejpam-6667	196	1	≤	≤	NUM
ejpam-6667	196	2	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	196	3	(	(	PUNCT
ejpam-6667	196	4	wq1	wq1	PROPN
ejpam-6667	196	5	(	(	PUNCT
ejpam-6667	196	6	·	·	PUNCT
ejpam-6667	196	7	)	)	PUNCT
ejpam-6667	196	8	)	)	PUNCT
ejpam-6667	196	9	k∑	k∑	PROPN
ejpam-6667	197	1	j=−∞	j=−∞	PROPN
ejpam-6667	197	2	2nδ2(j−k)w(bj	2nδ2(j−k)w(bj	PROPN
ejpam-6667	197	3	)	)	PUNCT
ejpam-6667	198	1	λ1∥χj∥lq1(·)(wq1	λ1∥χj∥lq1(·)(wq1	PROPN
ejpam-6667	198	2	(	(	PUNCT
ejpam-6667	198	3	·	·	PUNCT
ejpam-6667	198	4	)	)	PUNCT
ejpam-6667	198	5	)	)	PUNCT
ejpam-6667	198	6	.	.	PUNCT
ejpam-6667	199	1	∥χj∥lq1(·)(wq1	∥χj∥lq1(·)(wq1	NUM
ejpam-6667	199	2	(	(	PUNCT
ejpam-6667	199	3	·	·	PUNCT
ejpam-6667	199	4	)	)	PUNCT
ejpam-6667	199	5	)	)	PUNCT
ejpam-6667	200	1	≈	≈	PROPN
ejpam-6667	200	2	w(b	w(b	PROPN
ejpam-6667	200	3	)	)	PUNCT
ejpam-6667	200	4	1	1	NUM
ejpam-6667	200	5	q1	q1	PROPN
ejpam-6667	200	6	(	(	PUNCT
ejpam-6667	200	7	·	·	PUNCT
ejpam-6667	200	8	)	)	PUNCT
ejpam-6667	201	1	≈	≈	PROPN
ejpam-6667	201	2	w(b	w(b	PROPN
ejpam-6667	201	3	)	)	PUNCT
ejpam-6667	201	4	1	1	NUM
ejpam-6667	201	5	q2	q2	NOUN
ejpam-6667	201	6	(	(	PUNCT
ejpam-6667	201	7	·	·	PUNCT
ejpam-6667	201	8	)	)	PUNCT
ejpam-6667	202	1	+	+	NOUN
ejpam-6667	202	2	α	α	PROPN
ejpam-6667	202	3	n	n	X
ejpam-6667	202	4	≈	≈	PROPN
ejpam-6667	202	5	w(b	w(b	PROPN
ejpam-6667	202	6	)	)	PUNCT
ejpam-6667	202	7	α	α	PROPN
ejpam-6667	202	8	n	n	X
ejpam-6667	202	9	∥χj∥lq2(·)(wq2	∥χj∥lq2(·)(wq2	PROPN
ejpam-6667	202	10	(	(	PUNCT
ejpam-6667	202	11	·	·	PUNCT
ejpam-6667	202	12	)	)	PUNCT
ejpam-6667	202	13	)	)	PUNCT
ejpam-6667	202	14	.	.	PUNCT
ejpam-6667	203	1	∥hαf(x	∥hαf(x	X
ejpam-6667	203	2	)	)	PUNCT
ejpam-6667	203	3	·	·	PUNCT
ejpam-6667	204	1	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	204	2	(	(	PUNCT
ejpam-6667	204	3	·	·	PUNCT
ejpam-6667	204	4	)	)	PUNCT
ejpam-6667	204	5	)	)	PUNCT
ejpam-6667	204	6	≤	≤	NUM
ejpam-6667	204	7	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	204	8	(	(	PUNCT
ejpam-6667	204	9	wq1	wq1	PROPN
ejpam-6667	204	10	(	(	PUNCT
ejpam-6667	204	11	·	·	PUNCT
ejpam-6667	204	12	)	)	PUNCT
ejpam-6667	204	13	)	)	PUNCT
ejpam-6667	204	14	k∑	k∑	PROPN
ejpam-6667	205	1	j=−∞	j=−∞	PROPN
ejpam-6667	205	2	2nδ2(j−k)w(bj	2nδ2(j−k)w(bj	PROPN
ejpam-6667	205	3	)	)	PUNCT
ejpam-6667	205	4	λ1	λ1	PROPN
ejpam-6667	205	5	+	+	X
ejpam-6667	205	6	α	α	PROPN
ejpam-6667	205	7	n	n	X
ejpam-6667	205	8	∥χj∥lq2(·)(wq2	∥χj∥lq2(·)(wq2	PROPN
ejpam-6667	205	9	(	(	PUNCT
ejpam-6667	205	10	·	·	PUNCT
ejpam-6667	205	11	)	)	PUNCT
ejpam-6667	205	12	)	)	PUNCT
ejpam-6667	206	1	=	=	SYM
ejpam-6667	206	2	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	X
ejpam-6667	206	3	(	(	PUNCT
ejpam-6667	206	4	wq1	wq1	PROPN
ejpam-6667	206	5	(	(	PUNCT
ejpam-6667	206	6	·	·	PUNCT
ejpam-6667	206	7	)	)	PUNCT
ejpam-6667	206	8	)	)	PUNCT
ejpam-6667	206	9	k∑	k∑	VERB
ejpam-6667	207	1	j=−∞	j=−∞	NOUN
ejpam-6667	207	2	2nδ2(j−k)w(bk	2nδ2(j−k)w(bk	X
ejpam-6667	207	3	)	)	PUNCT
ejpam-6667	207	4	λ2	λ2	NOUN
ejpam-6667	207	5	w(bj	w(bj	NOUN
ejpam-6667	207	6	)	)	PUNCT
ejpam-6667	207	7	λ2	λ2	NOUN
ejpam-6667	207	8	w(bk)λ2	w(bk)λ2	PROPN
ejpam-6667	207	9	∥χk∥lq2(·)(wq2	∥χk∥lq2(·)(wq2	X
ejpam-6667	207	10	(	(	PUNCT
ejpam-6667	207	11	·	·	PUNCT
ejpam-6667	207	12	)	)	PUNCT
ejpam-6667	207	13	)	)	PUNCT
ejpam-6667	208	1	∥χj∥lq2(·)(wq2	∥χj∥lq2(·)(wq2	PROPN
ejpam-6667	208	2	(	(	PUNCT
ejpam-6667	208	3	·	·	PUNCT
ejpam-6667	208	4	)	)	PUNCT
ejpam-6667	208	5	)	)	PUNCT
ejpam-6667	209	1	∥χk∥lq2(·)(wq2	∥χk∥lq2(·)(wq2	PROPN
ejpam-6667	209	2	(	(	PUNCT
ejpam-6667	209	3	·	·	PUNCT
ejpam-6667	209	4	)	)	PUNCT
ejpam-6667	209	5	)	)	PUNCT
ejpam-6667	209	6	.	.	PUNCT
ejpam-6667	210	1	m.	m.	PROPN
ejpam-6667	210	2	asim	asim	PROPN
ejpam-6667	210	3	,	,	PUNCT
ejpam-6667	210	4	k.	k.	PROPN
ejpam-6667	210	5	suwais	suwais	PROPN
ejpam-6667	210	6	,	,	PUNCT
ejpam-6667	210	7	n.	n.	PROPN
ejpam-6667	210	8	mlaiki	mlaiki	PROPN
ejpam-6667	210	9	/	/	SYM
ejpam-6667	210	10	eur	eur	PROPN
ejpam-6667	210	11	.	.	PUNCT
ejpam-6667	211	1	j.	j.	PROPN
ejpam-6667	211	2	pure	pure	PROPN
ejpam-6667	211	3	appl	appl	PROPN
ejpam-6667	211	4	.	.	PROPN
ejpam-6667	211	5	math	math	PROPN
ejpam-6667	211	6	,	,	PUNCT
ejpam-6667	211	7	18	18	NUM
ejpam-6667	211	8	(	(	PUNCT
ejpam-6667	211	9	4	4	NUM
ejpam-6667	211	10	)	)	PUNCT
ejpam-6667	211	11	(	(	PUNCT
ejpam-6667	211	12	2025	2025	NUM
ejpam-6667	211	13	)	)	PUNCT
ejpam-6667	211	14	,	,	PUNCT
ejpam-6667	211	15	6667	6667	NUM
ejpam-6667	211	16	9	9	NUM
ejpam-6667	211	17	of	of	ADP
ejpam-6667	211	18	20	20	NUM
ejpam-6667	211	19	applying	apply	VERB
ejpam-6667	211	20	lemmas	lemmas	PROPN
ejpam-6667	211	21	8	8	NUM
ejpam-6667	211	22	and	and	CCONJ
ejpam-6667	211	23	7	7	NUM
ejpam-6667	211	24	∥hαf(x	∥hαf(x	NOUN
ejpam-6667	211	25	)	)	PUNCT
ejpam-6667	211	26	·	·	PUNCT
ejpam-6667	212	1	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	212	2	(	(	PUNCT
ejpam-6667	212	3	·	·	PUNCT
ejpam-6667	212	4	)	)	PUNCT
ejpam-6667	212	5	)	)	PUNCT
ejpam-6667	212	6	≤	≤	NUM
ejpam-6667	212	7	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	212	8	(	(	PUNCT
ejpam-6667	212	9	wq1	wq1	PROPN
ejpam-6667	212	10	(	(	PUNCT
ejpam-6667	212	11	·	·	PUNCT
ejpam-6667	212	12	)	)	PUNCT
ejpam-6667	212	13	)	)	PUNCT
ejpam-6667	212	14	k∑	k∑	NOUN
ejpam-6667	213	1	j=−∞	j=−∞	NOUN
ejpam-6667	214	1	2nδ2(j−k)|bk|λ2	2nδ2(j−k)|bk|λ2	NUM
ejpam-6667	214	2	(	(	PUNCT
ejpam-6667	214	3	|bj	|bj	NOUN
ejpam-6667	214	4	|	|	ADV
ejpam-6667	214	5	|bk|	|bk|	PROPN
ejpam-6667	214	6	)	)	PUNCT
ejpam-6667	214	7	δλ2	δλ2	PROPN
ejpam-6667	214	8	∥χk∥lq2(·)(wq2	∥χk∥lq2(·)(wq2	PROPN
ejpam-6667	214	9	(	(	PUNCT
ejpam-6667	214	10	·	·	PUNCT
ejpam-6667	214	11	)	)	PUNCT
ejpam-6667	214	12	)	)	PUNCT
ejpam-6667	215	1	∥χj∥lq2(·)(wq2	∥χj∥lq2(·)(wq2	PROPN
ejpam-6667	215	2	(	(	PUNCT
ejpam-6667	215	3	·	·	PUNCT
ejpam-6667	215	4	)	)	PUNCT
ejpam-6667	215	5	)	)	PUNCT
ejpam-6667	216	1	∥χk∥lq2(·)(wq2	∥χk∥lq2(·)(wq2	PROPN
ejpam-6667	216	2	(	(	PUNCT
ejpam-6667	216	3	·	·	PUNCT
ejpam-6667	216	4	)	)	PUNCT
ejpam-6667	216	5	)	)	PUNCT
ejpam-6667	216	6	≤	≤	NUM
ejpam-6667	216	7	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	216	8	(	(	PUNCT
ejpam-6667	216	9	wq1(·))|bk|λ2∥χk∥lq2(·)(wq2	wq1(·))|bk|λ2∥χk∥lq2(·)(wq2	X
ejpam-6667	216	10	(	(	PUNCT
ejpam-6667	216	11	·	·	PUNCT
ejpam-6667	216	12	)	)	PUNCT
ejpam-6667	216	13	)	)	PUNCT
ejpam-6667	216	14	k∑	k∑	VERB
ejpam-6667	216	15	j=−∞	j=−∞	NOUN
ejpam-6667	217	1	2(j−k)(nδ3+nδ1+nδλ2	2(j−k)(nδ3+nδ1+nδλ2	NUM
ejpam-6667	217	2	)	)	PUNCT
ejpam-6667	217	3	,	,	PUNCT
ejpam-6667	217	4	∥hαf(x	∥hαf(x	NOUN
ejpam-6667	217	5	)	)	PUNCT
ejpam-6667	217	6	·	·	PUNCT
ejpam-6667	218	1	χk∥ḃq2(·),λ2	χk∥ḃq2(·),λ2	ADJ
ejpam-6667	218	2	(	(	PUNCT
ejpam-6667	218	3	wq2	wq2	PROPN
ejpam-6667	218	4	(	(	PUNCT
ejpam-6667	218	5	·	·	PUNCT
ejpam-6667	218	6	)	)	PUNCT
ejpam-6667	218	7	)	)	PUNCT
ejpam-6667	218	8	≤	≤	NUM
ejpam-6667	218	9	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	218	10	(	(	PUNCT
ejpam-6667	218	11	wq1	wq1	PROPN
ejpam-6667	218	12	(	(	PUNCT
ejpam-6667	218	13	·	·	PUNCT
ejpam-6667	218	14	)	)	PUNCT
ejpam-6667	218	15	)	)	PUNCT
ejpam-6667	218	16	k∑	k∑	PROPN
ejpam-6667	218	17	j=−∞	j=−∞	PROPN
ejpam-6667	219	1	2n(j−k)(δ2+δ1+δλ2	2n(j−k)(δ2+δ1+δλ2	NUM
ejpam-6667	219	2	)	)	PUNCT
ejpam-6667	219	3	.	.	PUNCT
ejpam-6667	220	1	since	since	SCONJ
ejpam-6667	220	2	it	it	PRON
ejpam-6667	220	3	is	be	AUX
ejpam-6667	220	4	given	give	VERB
ejpam-6667	220	5	that	that	SCONJ
ejpam-6667	220	6	δ2	δ2	VERB
ejpam-6667	220	7	+	+	NOUN
ejpam-6667	220	8	δ1	δ1	NOUN
ejpam-6667	220	9	+	+	CCONJ
ejpam-6667	220	10	δλ2	δλ2	PROPN
ejpam-6667	220	11	>	>	X
ejpam-6667	220	12	0	0	PROPN
ejpam-6667	220	13	,	,	PUNCT
ejpam-6667	220	14	which	which	PRON
ejpam-6667	220	15	gives	give	VERB
ejpam-6667	220	16	the	the	DET
ejpam-6667	220	17	required	require	VERB
ejpam-6667	220	18	result	result	NOUN
ejpam-6667	220	19	:	:	PUNCT
ejpam-6667	220	20	∥hαf(x	∥hαf(x	NUM
ejpam-6667	220	21	)	)	PUNCT
ejpam-6667	220	22	·	·	PUNCT
ejpam-6667	221	1	χk∥ḃq2(·),λ2	χk∥ḃq2(·),λ2	ADJ
ejpam-6667	221	2	(	(	PUNCT
ejpam-6667	221	3	wq2	wq2	PROPN
ejpam-6667	221	4	(	(	PUNCT
ejpam-6667	221	5	·	·	PUNCT
ejpam-6667	221	6	)	)	PUNCT
ejpam-6667	221	7	)	)	PUNCT
ejpam-6667	221	8	≤	≤	NUM
ejpam-6667	221	9	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	221	10	(	(	PUNCT
ejpam-6667	221	11	wq1	wq1	PROPN
ejpam-6667	221	12	(	(	PUNCT
ejpam-6667	221	13	·	·	PUNCT
ejpam-6667	221	14	)	)	PUNCT
ejpam-6667	221	15	)	)	PUNCT
ejpam-6667	221	16	.	.	PUNCT
ejpam-6667	221	17	□	□	PUNCT
ejpam-6667	221	18	theorem	theorem	ADJ
ejpam-6667	221	19	2	2	X
ejpam-6667	221	20	.	.	PUNCT
ejpam-6667	221	21	let	let	VERB
ejpam-6667	221	22	q1	q1	PROPN
ejpam-6667	221	23	(	(	PUNCT
ejpam-6667	221	24	·	·	PUNCT
ejpam-6667	221	25	)	)	PUNCT
ejpam-6667	221	26	,	,	PUNCT
ejpam-6667	221	27	q2	q2	NOUN
ejpam-6667	221	28	(	(	PUNCT
ejpam-6667	221	29	·	·	PUNCT
ejpam-6667	221	30	)	)	PUNCT
ejpam-6667	221	31	and	and	CCONJ
ejpam-6667	221	32	α	α	PRON
ejpam-6667	221	33	be	be	AUX
ejpam-6667	221	34	the	the	DET
ejpam-6667	221	35	same	same	ADJ
ejpam-6667	221	36	as	as	ADP
ejpam-6667	221	37	in	in	ADP
ejpam-6667	221	38	theorem	theorem	NOUN
ejpam-6667	221	39	1	1	NUM
ejpam-6667	221	40	.	.	PUNCT
ejpam-6667	222	1	if	if	SCONJ
ejpam-6667	222	2	λ2	λ2	PRON
ejpam-6667	222	3	=	=	SYM
ejpam-6667	222	4	λ1	λ1	PROPN
ejpam-6667	222	5	+	+	CCONJ
ejpam-6667	222	6	α	α	PROPN
ejpam-6667	222	7	n	n	NOUN
ejpam-6667	222	8	,	,	PUNCT
ejpam-6667	222	9	wq1	wq1	ADJ
ejpam-6667	222	10	(	(	PUNCT
ejpam-6667	222	11	·	·	PUNCT
ejpam-6667	222	12	)	)	PUNCT
ejpam-6667	222	13	∈	∈	NOUN
ejpam-6667	222	14	a1	a1	NOUN
ejpam-6667	222	15	and	and	CCONJ
ejpam-6667	222	16	α	α	NOUN
ejpam-6667	222	17	<	<	X
ejpam-6667	222	18	−n(1	−n(1	PROPN
ejpam-6667	222	19	+	+	SYM
ejpam-6667	222	20	λ2	λ2	NOUN
ejpam-6667	222	21	)	)	PUNCT
ejpam-6667	222	22	,	,	PUNCT
ejpam-6667	222	23	then	then	ADV
ejpam-6667	222	24	∥h∗	∥h∗	PUNCT
ejpam-6667	222	25	αf∥ḃq2(·),λ2	αf∥ḃq2(·),λ2	X
ejpam-6667	222	26	(	(	PUNCT
ejpam-6667	222	27	wq2	wq2	PROPN
ejpam-6667	222	28	(	(	PUNCT
ejpam-6667	222	29	·	·	PUNCT
ejpam-6667	222	30	)	)	PUNCT
ejpam-6667	222	31	)	)	PUNCT
ejpam-6667	223	1	≤	≤	NUM
ejpam-6667	223	2	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	223	3	(	(	PUNCT
ejpam-6667	223	4	wq1	wq1	PROPN
ejpam-6667	223	5	(	(	PUNCT
ejpam-6667	223	6	·	·	PUNCT
ejpam-6667	223	7	)	)	PUNCT
ejpam-6667	223	8	)	)	PUNCT
ejpam-6667	223	9	.	.	PUNCT
ejpam-6667	224	1	proof	proof	NOUN
ejpam-6667	224	2	of	of	ADP
ejpam-6667	224	3	theorem	theorem	ADJ
ejpam-6667	224	4	2	2	NUM
ejpam-6667	224	5	|h∗	|h∗	PROPN
ejpam-6667	224	6	αf(x	αf(x	NUM
ejpam-6667	224	7	)	)	PUNCT
ejpam-6667	224	8	·	·	PUNCT
ejpam-6667	224	9	χk(x)|	χk(x)|	VERB
ejpam-6667	224	10	≤	≤	NUM
ejpam-6667	224	11	∫	∫	PROPN
ejpam-6667	224	12	rn\bk	rn\bk	PROPN
ejpam-6667	224	13	|f(t)||t|α−ndt	|f(t)||t|α−ndt	X
ejpam-6667	224	14	·	·	PUNCT
ejpam-6667	224	15	χk(x	χk(x	NOUN
ejpam-6667	224	16	)	)	PUNCT
ejpam-6667	224	17	≤	≤	NUM
ejpam-6667	224	18	c	c	VERB
ejpam-6667	225	1	∞∑	∞∑	NUM
ejpam-6667	225	2	j	j	X
ejpam-6667	225	3	=	=	PRON
ejpam-6667	225	4	k+1	k+1	X
ejpam-6667	225	5	2j(α−n)∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))χk(x	2j(α−n)∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))χk(x	NUM
ejpam-6667	225	6	)	)	PUNCT
ejpam-6667	225	7	.	.	PUNCT
ejpam-6667	226	1	∥h∗	∥h∗	PROPN
ejpam-6667	226	2	αf(x	αf(x	NUM
ejpam-6667	226	3	)	)	PUNCT
ejpam-6667	226	4	·	·	PUNCT
ejpam-6667	227	1	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	227	2	(	(	PUNCT
ejpam-6667	227	3	·	·	PUNCT
ejpam-6667	227	4	)	)	PUNCT
ejpam-6667	227	5	)	)	PUNCT
ejpam-6667	227	6	≤	≤	NUM
ejpam-6667	227	7	c	c	X
ejpam-6667	227	8	∞∑	∞∑	NUM
ejpam-6667	227	9	j	j	X
ejpam-6667	227	10	=	=	NOUN
ejpam-6667	227	11	k+1	k+1	X
ejpam-6667	227	12	2j(α−n)∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥lq2(·)(wq2	2j(α−n)∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥lq2(·)(wq2	NUM
ejpam-6667	227	13	(	(	PUNCT
ejpam-6667	227	14	·	·	PUNCT
ejpam-6667	227	15	)	)	PUNCT
ejpam-6667	227	16	)	)	PUNCT
ejpam-6667	227	17	.	.	PUNCT
ejpam-6667	228	1	≤	≤	NUM
ejpam-6667	229	1	c	c	X
ejpam-6667	230	1	∞∑	∞∑	NUM
ejpam-6667	230	2	j	j	X
ejpam-6667	230	3	=	=	NOUN
ejpam-6667	230	4	k+1	k+1	X
ejpam-6667	230	5	2j(α−n	2j(α−n	NUM
ejpam-6667	230	6	)	)	PUNCT
ejpam-6667	230	7	∥χj∥(lq1(·)(wq1(·)))′	∥χj∥(lq1(·)(wq1(·)))′	PROPN
ejpam-6667	230	8	∥χk∥(lq1(·)(wq1(·)))′	∥χk∥(lq1(·)(wq1(·)))′	PROPN
ejpam-6667	230	9	∥χk∥(lq1(·)(wq1(·)))′∥χk∥lq2(·)(wq2(·))∥fj∥lq1(·)(wq1	∥χk∥(lq1(·)(wq1(·)))′∥χk∥lq2(·)(wq2(·))∥fj∥lq1(·)(wq1	PROPN
ejpam-6667	230	10	(	(	PUNCT
ejpam-6667	230	11	·	·	PUNCT
ejpam-6667	230	12	)	)	PUNCT
ejpam-6667	230	13	)	)	PUNCT
ejpam-6667	230	14	.	.	PUNCT
ejpam-6667	231	1	by	by	ADP
ejpam-6667	231	2	virtue	virtue	NOUN
ejpam-6667	231	3	of	of	ADP
ejpam-6667	231	4	lemmas	lemmas	PROPN
ejpam-6667	231	5	2	2	NUM
ejpam-6667	231	6	,	,	PUNCT
ejpam-6667	231	7	10	10	NUM
ejpam-6667	231	8	,	,	PUNCT
ejpam-6667	231	9	6	6	NUM
ejpam-6667	231	10	and	and	CCONJ
ejpam-6667	231	11	by	by	ADP
ejpam-6667	231	12	the	the	DET
ejpam-6667	231	13	definition	definition	NOUN
ejpam-6667	231	14	of	of	ADP
ejpam-6667	231	15	a(q2	a(q2	NOUN
ejpam-6667	231	16	(	(	PUNCT
ejpam-6667	231	17	·	·	PUNCT
ejpam-6667	231	18	)	)	PUNCT
ejpam-6667	231	19	,	,	PUNCT
ejpam-6667	231	20	q1	q1	PROPN
ejpam-6667	231	21	(	(	PUNCT
ejpam-6667	231	22	·	·	PUNCT
ejpam-6667	231	23	)	)	PUNCT
ejpam-6667	231	24	)	)	PUNCT
ejpam-6667	232	1	we	we	PRON
ejpam-6667	232	2	obtain	obtain	VERB
ejpam-6667	232	3	the	the	DET
ejpam-6667	232	4	following	follow	VERB
ejpam-6667	232	5	inequalities	inequality	NOUN
ejpam-6667	232	6	:	:	PUNCT
ejpam-6667	232	7	∥h∗	∥h∗	PROPN
ejpam-6667	232	8	αf(x	αf(x	NUM
ejpam-6667	232	9	)	)	PUNCT
ejpam-6667	232	10	·	·	PUNCT
ejpam-6667	233	1	χk∥lq2(·)(wq2	χk∥lq2(·)(wq2	X
ejpam-6667	233	2	(	(	PUNCT
ejpam-6667	233	3	·	·	PUNCT
ejpam-6667	233	4	)	)	PUNCT
ejpam-6667	233	5	)	)	PUNCT
ejpam-6667	233	6	≤	≤	NUM
ejpam-6667	233	7	c	c	X
ejpam-6667	233	8	∞∑	∞∑	NUM
ejpam-6667	233	9	j	j	X
ejpam-6667	233	10	=	=	NOUN
ejpam-6667	233	11	k+1	k+1	X
ejpam-6667	233	12	2j(α−n)2n(j−k)∥χk∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥lq2(·)(wq2	2j(α−n)2n(j−k)∥χk∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥lq2(·)(wq2	PROPN
ejpam-6667	233	13	(	(	PUNCT
ejpam-6667	233	14	·	·	PUNCT
ejpam-6667	233	15	)	)	PUNCT
ejpam-6667	233	16	)	)	PUNCT
ejpam-6667	233	17	.	.	PUNCT
ejpam-6667	234	1	≤	≤	NUM
ejpam-6667	235	1	c	c	X
ejpam-6667	236	1	∞∑	∞∑	NUM
ejpam-6667	236	2	j	j	X
ejpam-6667	236	3	=	=	PRON
ejpam-6667	236	4	k+1	k+1	PRON
ejpam-6667	236	5	2(j−k)(α−n)2n(j−k)∥fj∥lq1(·)(wq1	2(j−k)(α−n)2n(j−k)∥fj∥lq1(·)(wq1	NUM
ejpam-6667	236	6	(	(	PUNCT
ejpam-6667	236	7	·	·	PUNCT
ejpam-6667	236	8	)	)	PUNCT
ejpam-6667	236	9	)	)	PUNCT
ejpam-6667	236	10	.	.	PUNCT
ejpam-6667	237	1	m.	m.	PROPN
ejpam-6667	237	2	asim	asim	PROPN
ejpam-6667	237	3	,	,	PUNCT
ejpam-6667	237	4	k.	k.	PROPN
ejpam-6667	237	5	suwais	suwais	PROPN
ejpam-6667	237	6	,	,	PUNCT
ejpam-6667	237	7	n.	n.	PROPN
ejpam-6667	237	8	mlaiki	mlaiki	PROPN
ejpam-6667	237	9	/	/	SYM
ejpam-6667	237	10	eur	eur	PROPN
ejpam-6667	237	11	.	.	PUNCT
ejpam-6667	238	1	j.	j.	PROPN
ejpam-6667	238	2	pure	pure	PROPN
ejpam-6667	238	3	appl	appl	PROPN
ejpam-6667	238	4	.	.	PROPN
ejpam-6667	238	5	math	math	PROPN
ejpam-6667	238	6	,	,	PUNCT
ejpam-6667	238	7	18	18	NUM
ejpam-6667	238	8	(	(	PUNCT
ejpam-6667	238	9	4	4	NUM
ejpam-6667	238	10	)	)	PUNCT
ejpam-6667	238	11	(	(	PUNCT
ejpam-6667	238	12	2025	2025	NUM
ejpam-6667	238	13	)	)	PUNCT
ejpam-6667	238	14	,	,	PUNCT
ejpam-6667	238	15	6667	6667	NUM
ejpam-6667	238	16	10	10	NUM
ejpam-6667	238	17	of	of	ADP
ejpam-6667	238	18	20	20	NUM
ejpam-6667	238	19	∥h∗	∥h∗	PROPN
ejpam-6667	238	20	αf(x	αf(x	NUM
ejpam-6667	238	21	)	)	PUNCT
ejpam-6667	238	22	·	·	PUNCT
ejpam-6667	239	1	χk∥ḃq2(·),λ2	χk∥ḃq2(·),λ2	ADJ
ejpam-6667	239	2	(	(	PUNCT
ejpam-6667	239	3	wq2	wq2	PROPN
ejpam-6667	239	4	(	(	PUNCT
ejpam-6667	239	5	·	·	PUNCT
ejpam-6667	239	6	)	)	PUNCT
ejpam-6667	239	7	)	)	PUNCT
ejpam-6667	239	8	≤	≤	NUM
ejpam-6667	239	9	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	239	10	(	(	PUNCT
ejpam-6667	239	11	wq1	wq1	PROPN
ejpam-6667	239	12	(	(	PUNCT
ejpam-6667	239	13	·	·	PUNCT
ejpam-6667	239	14	)	)	PUNCT
ejpam-6667	239	15	)	)	PUNCT
ejpam-6667	240	1	∞∑	∞∑	PRON
ejpam-6667	240	2	j	j	X
ejpam-6667	240	3	=	=	PRON
ejpam-6667	240	4	k+1	k+1	NOUN
ejpam-6667	240	5	2(j−k)(α+n+nλ2	2(j−k)(α+n+nλ2	NUM
ejpam-6667	240	6	)	)	PUNCT
ejpam-6667	240	7	.	.	PUNCT
ejpam-6667	241	1	by	by	ADP
ejpam-6667	241	2	using	use	VERB
ejpam-6667	241	3	α	α	PRON
ejpam-6667	241	4	<	<	X
ejpam-6667	241	5	−n(1	−n(1	ADJ
ejpam-6667	241	6	+	+	SYM
ejpam-6667	241	7	λ2	λ2	NOUN
ejpam-6667	241	8	)	)	PUNCT
ejpam-6667	241	9	,	,	PUNCT
ejpam-6667	241	10	we	we	PRON
ejpam-6667	241	11	get	get	VERB
ejpam-6667	241	12	the	the	DET
ejpam-6667	241	13	final	final	ADJ
ejpam-6667	241	14	result	result	NOUN
ejpam-6667	241	15	:	:	PUNCT
ejpam-6667	241	16	∥h∗	∥h∗	PUNCT
ejpam-6667	241	17	αf∥ḃq2(·),λ2	αf∥ḃq2(·),λ2	X
ejpam-6667	241	18	(	(	PUNCT
ejpam-6667	241	19	wq2	wq2	PROPN
ejpam-6667	241	20	(	(	PUNCT
ejpam-6667	241	21	·	·	PUNCT
ejpam-6667	241	22	)	)	PUNCT
ejpam-6667	241	23	)	)	PUNCT
ejpam-6667	241	24	≤	≤	NUM
ejpam-6667	241	25	c∥f∥ḃq1(·),λ1	c∥f∥ḃq1(·),λ1	NOUN
ejpam-6667	241	26	(	(	PUNCT
ejpam-6667	241	27	wq1	wq1	PROPN
ejpam-6667	241	28	(	(	PUNCT
ejpam-6667	241	29	·	·	PUNCT
ejpam-6667	241	30	)	)	PUNCT
ejpam-6667	241	31	)	)	PUNCT
ejpam-6667	241	32	.	.	PUNCT
ejpam-6667	242	1	□	□	PUNCT
ejpam-6667	242	2	4.2	4.2	NUM
ejpam-6667	242	3	.	.	PUNCT
ejpam-6667	243	1	commutators	commutator	NOUN
ejpam-6667	243	2	of	of	ADP
ejpam-6667	243	3	fractional	fractional	ADJ
ejpam-6667	243	4	hardy	hardy	ADJ
ejpam-6667	243	5	operators	operator	NOUN
ejpam-6667	243	6	theorem	theorem	VERB
ejpam-6667	243	7	3	3	X
ejpam-6667	243	8	.	.	PUNCT
ejpam-6667	244	1	let	let	VERB
ejpam-6667	244	2	0	0	NUM
ejpam-6667	244	3	<	<	X
ejpam-6667	244	4	α	α	X
ejpam-6667	244	5	<	<	X
ejpam-6667	244	6	n	n	CCONJ
ejpam-6667	244	7	,	,	PUNCT
ejpam-6667	244	8	and	and	CCONJ
ejpam-6667	244	9	p1	p1	PROPN
ejpam-6667	244	10	(	(	PUNCT
ejpam-6667	244	11	·	·	PUNCT
ejpam-6667	244	12	)	)	PUNCT
ejpam-6667	244	13	,	,	PUNCT
ejpam-6667	244	14	p	p	X
ejpam-6667	244	15	(	(	PUNCT
ejpam-6667	244	16	·	·	PUNCT
ejpam-6667	244	17	)	)	PUNCT
ejpam-6667	244	18	∈	∈	PROPN
ejpam-6667	244	19	p(rn	p(rn	PROPN
ejpam-6667	244	20	)	)	PUNCT
ejpam-6667	244	21	⋂	⋂	PROPN
ejpam-6667	244	22	lh(rn	lh(rn	PROPN
ejpam-6667	244	23	)	)	PUNCT
ejpam-6667	244	24	.	.	PUNCT
ejpam-6667	245	1	define	define	VERB
ejpam-6667	245	2	the	the	DET
ejpam-6667	245	3	variable	variable	ADJ
ejpam-6667	245	4	exponent	exponent	NOUN
ejpam-6667	245	5	p2	p2	PROPN
ejpam-6667	245	6	(	(	PUNCT
ejpam-6667	245	7	·	·	PUNCT
ejpam-6667	245	8	)	)	PUNCT
ejpam-6667	245	9	by	by	ADP
ejpam-6667	245	10	1	1	NUM
ejpam-6667	245	11	p2(x	p2(x	NOUN
ejpam-6667	245	12	)	)	PUNCT
ejpam-6667	245	13	=	=	SYM
ejpam-6667	245	14	1	1	NUM
ejpam-6667	245	15	p(x	p(x	NOUN
ejpam-6667	245	16	)	)	PUNCT
ejpam-6667	245	17	+	+	CCONJ
ejpam-6667	245	18	1	1	NUM
ejpam-6667	245	19	p1(x	p1(x	NOUN
ejpam-6667	245	20	)	)	PUNCT
ejpam-6667	245	21	−	−	PROPN
ejpam-6667	246	1	α	α	PRON
ejpam-6667	246	2	n	n	NOUN
ejpam-6667	246	3	.	.	PUNCT
ejpam-6667	247	1	if	if	SCONJ
ejpam-6667	247	2	wp1	wp1	PROPN
ejpam-6667	247	3	(	(	PUNCT
ejpam-6667	247	4	·	·	PUNCT
ejpam-6667	247	5	)	)	PUNCT
ejpam-6667	247	6	∈	∈	PROPN
ejpam-6667	247	7	a1	a1	NOUN
ejpam-6667	247	8	,	,	PUNCT
ejpam-6667	247	9	b	b	PROPN
ejpam-6667	247	10	∈	∈	PROPN
ejpam-6667	247	11	∥b∥cbmop(·),λ(wp	∥b∥cbmop(·),λ(wp	X
ejpam-6667	247	12	(	(	PUNCT
ejpam-6667	247	13	·	·	PUNCT
ejpam-6667	247	14	)	)	PUNCT
ejpam-6667	247	15	)	)	PUNCT
ejpam-6667	247	16	,	,	PUNCT
ejpam-6667	247	17	µ	µ	X
ejpam-6667	247	18	=	=	SYM
ejpam-6667	247	19	λ1	λ1	PROPN
ejpam-6667	247	20	+	+	CCONJ
ejpam-6667	247	21	α	α	PROPN
ejpam-6667	247	22	n	n	NOUN
ejpam-6667	247	23	and	and	CCONJ
ejpam-6667	247	24	λ2	λ2	NOUN
ejpam-6667	247	25	=	=	PUNCT
ejpam-6667	247	26	λ+	λ+	PUNCT
ejpam-6667	247	27	λ1	λ1	VERB
ejpam-6667	247	28	+	+	CCONJ
ejpam-6667	247	29	α	α	PROPN
ejpam-6667	247	30	n	n	NOUN
ejpam-6667	247	31	,	,	PUNCT
ejpam-6667	247	32	then	then	ADV
ejpam-6667	247	33	∥[b	∥[b	PROPN
ejpam-6667	247	34	,	,	PUNCT
ejpam-6667	247	35	hα]f∥ḃp2(·),λ2	hα]f∥ḃp2(·),λ2	PROPN
ejpam-6667	247	36	(	(	PUNCT
ejpam-6667	247	37	wp2	wp2	PROPN
ejpam-6667	247	38	(	(	PUNCT
ejpam-6667	247	39	·	·	PUNCT
ejpam-6667	247	40	)	)	PUNCT
ejpam-6667	247	41	)	)	PUNCT
ejpam-6667	247	42	≤	≤	PROPN
ejpam-6667	248	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	248	2	(	(	PUNCT
ejpam-6667	248	3	wp1	wp1	PROPN
ejpam-6667	248	4	(	(	PUNCT
ejpam-6667	248	5	·	·	PUNCT
ejpam-6667	248	6	)	)	PUNCT
ejpam-6667	248	7	)	)	PUNCT
ejpam-6667	248	8	.	.	PUNCT
ejpam-6667	249	1	proof	proof	NOUN
ejpam-6667	249	2	of	of	ADP
ejpam-6667	249	3	theorem	theorem	ADJ
ejpam-6667	249	4	3	3	NUM
ejpam-6667	249	5	|[b	|[b	PROPN
ejpam-6667	249	6	,	,	PUNCT
ejpam-6667	249	7	hα]f(x	hα]f(x	PROPN
ejpam-6667	249	8	)	)	PUNCT
ejpam-6667	249	9	·	·	PUNCT
ejpam-6667	249	10	χb(x)|	χb(x)|	VERB
ejpam-6667	249	11	≤	≤	NUM
ejpam-6667	249	12	1	1	NUM
ejpam-6667	249	13	|x|n−α	|x|n−α	NOUN
ejpam-6667	249	14	∫	∫	PROPN
ejpam-6667	249	15	b(0,|x|	b(0,|x|	X
ejpam-6667	249	16	)	)	PUNCT
ejpam-6667	249	17	|(b(x)−	|(b(x)−	PROPN
ejpam-6667	249	18	b(v))f(v)|dv	b(v))f(v)|dv	PROPN
ejpam-6667	249	19	·	·	PUNCT
ejpam-6667	249	20	χb(x	χb(x	PUNCT
ejpam-6667	249	21	)	)	PUNCT
ejpam-6667	249	22	≤	≤	NUM
ejpam-6667	249	23	1	1	NUM
ejpam-6667	249	24	|x|n−α	|x|n−α	NOUN
ejpam-6667	249	25	∫	∫	PROPN
ejpam-6667	249	26	b(0,|x|	b(0,|x|	X
ejpam-6667	249	27	)	)	PUNCT
ejpam-6667	249	28	|(b(x)−	|(b(x)−	PROPN
ejpam-6667	249	29	bb)f(v)|dv	bb)f(v)|dv	PROPN
ejpam-6667	249	30	·	·	PUNCT
ejpam-6667	249	31	χb(x	χb(x	PUNCT
ejpam-6667	249	32	)	)	PUNCT
ejpam-6667	250	1	+	+	CCONJ
ejpam-6667	250	2	1	1	NUM
ejpam-6667	250	3	|x|n−α	|x|n−α	NOUN
ejpam-6667	250	4	∫	∫	PROPN
ejpam-6667	250	5	b(0,|x|	b(0,|x|	X
ejpam-6667	250	6	)	)	PUNCT
ejpam-6667	250	7	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	250	8	bb)f(v)|dv	bb)f(v)|dv	PROPN
ejpam-6667	250	9	·	·	PUNCT
ejpam-6667	250	10	χb(x	χb(x	PUNCT
ejpam-6667	250	11	)	)	PUNCT
ejpam-6667	250	12	=	=	SYM
ejpam-6667	250	13	a1	a1	PROPN
ejpam-6667	250	14	+	+	PROPN
ejpam-6667	250	15	a2	a2	PROPN
ejpam-6667	250	16	.	.	PUNCT
ejpam-6667	251	1	first	first	ADV
ejpam-6667	251	2	,	,	PUNCT
ejpam-6667	251	3	we	we	PRON
ejpam-6667	251	4	estimate	estimate	VERB
ejpam-6667	251	5	a1	a1	PROPN
ejpam-6667	251	6	.	.	PROPN
ejpam-6667	251	7	denote	denote	VERB
ejpam-6667	251	8	1	1	NUM
ejpam-6667	251	9	s(x	s(x	PROPN
ejpam-6667	251	10	)	)	PUNCT
ejpam-6667	251	11	=	=	SYM
ejpam-6667	251	12	1	1	NUM
ejpam-6667	251	13	p1(x	p1(x	NOUN
ejpam-6667	251	14	)	)	PUNCT
ejpam-6667	251	15	−	−	PROPN
ejpam-6667	252	1	α	α	PROPN
ejpam-6667	253	1	n	n	NOUN
ejpam-6667	253	2	,	,	PUNCT
ejpam-6667	253	3	then	then	ADV
ejpam-6667	253	4	1	1	NUM
ejpam-6667	253	5	p2(x	p2(x	NOUN
ejpam-6667	253	6	)	)	PUNCT
ejpam-6667	253	7	=	=	SYM
ejpam-6667	253	8	1	1	NUM
ejpam-6667	253	9	s(x	s(x	PROPN
ejpam-6667	253	10	)	)	PUNCT
ejpam-6667	254	1	+	+	CCONJ
ejpam-6667	254	2	1	1	NUM
ejpam-6667	254	3	p(x	p(x	NOUN
ejpam-6667	254	4	)	)	PUNCT
ejpam-6667	254	5	.	.	PUNCT
ejpam-6667	255	1	a1	a1	NOUN
ejpam-6667	255	2	=	=	SYM
ejpam-6667	255	3	1	1	NUM
ejpam-6667	255	4	|x|n−α	|x|n−α	NOUN
ejpam-6667	255	5	∫	∫	PROPN
ejpam-6667	255	6	b(0,|x|	b(0,|x|	X
ejpam-6667	255	7	)	)	PUNCT
ejpam-6667	255	8	|(b(x)−	|(b(x)−	PROPN
ejpam-6667	255	9	bb)f(v)|dv	bb)f(v)|dv	PROPN
ejpam-6667	255	10	·	·	PUNCT
ejpam-6667	255	11	χb(x	χb(x	PUNCT
ejpam-6667	255	12	)	)	PUNCT
ejpam-6667	256	1	=	=	SYM
ejpam-6667	256	2	|(b(x)−	|(b(x)−	NOUN
ejpam-6667	256	3	bb)χb(x)||hαf(x)|	bb)χb(x)||hαf(x)|	NOUN
ejpam-6667	256	4	,	,	PUNCT
ejpam-6667	256	5	∥a1∥lp2(·)(wp2	∥a1∥lp2(·)(wp2	X
ejpam-6667	256	6	(	(	PUNCT
ejpam-6667	256	7	·	·	PUNCT
ejpam-6667	256	8	)	)	PUNCT
ejpam-6667	256	9	)	)	PUNCT
ejpam-6667	257	1	=	=	SYM
ejpam-6667	257	2	∥(b(x)−	∥(b(x)−	PROPN
ejpam-6667	257	3	bb)χb(x)hαf(x)∥lp2(·)(wp2	bb)χb(x)hαf(x)∥lp2(·)(wp2	NOUN
ejpam-6667	257	4	(	(	PUNCT
ejpam-6667	257	5	·	·	PUNCT
ejpam-6667	257	6	)	)	PUNCT
ejpam-6667	257	7	)	)	PUNCT
ejpam-6667	257	8	.	.	PUNCT
ejpam-6667	258	1	using	use	VERB
ejpam-6667	258	2	hölder	hölder	NOUN
ejpam-6667	258	3	inequality	inequality	NOUN
ejpam-6667	258	4	(	(	PUNCT
ejpam-6667	258	5	1	1	NUM
ejpam-6667	258	6	p2	p2	NOUN
ejpam-6667	258	7	(	(	PUNCT
ejpam-6667	258	8	·	·	PUNCT
ejpam-6667	258	9	)	)	PUNCT
ejpam-6667	258	10	=	=	SYM
ejpam-6667	258	11	1	1	NUM
ejpam-6667	258	12	s	s	PROPN
ejpam-6667	258	13	(	(	PUNCT
ejpam-6667	258	14	·	·	PUNCT
ejpam-6667	258	15	)	)	PUNCT
ejpam-6667	259	1	+	+	CCONJ
ejpam-6667	259	2	1	1	NUM
ejpam-6667	259	3	p	p	X
ejpam-6667	259	4	(	(	PUNCT
ejpam-6667	259	5	·	·	PUNCT
ejpam-6667	259	6	)	)	PUNCT
ejpam-6667	259	7	)	)	PUNCT
ejpam-6667	259	8	∥a1∥lp2(·)(wp2	∥a1∥lp2(·)(wp2	PUNCT
ejpam-6667	259	9	(	(	PUNCT
ejpam-6667	259	10	·	·	PUNCT
ejpam-6667	259	11	)	)	PUNCT
ejpam-6667	259	12	)	)	PUNCT
ejpam-6667	260	1	≤	≤	NUM
ejpam-6667	260	2	∥(b(x)−	∥(b(x)−	NOUN
ejpam-6667	260	3	bb)χb(x)∥lp(·)(wp(·))∥hαf(x)χb∥ls(·)(ws	bb)χb(x)∥lp(·)(wp(·))∥hαf(x)χb∥ls(·)(ws	NOUN
ejpam-6667	260	4	(	(	PUNCT
ejpam-6667	260	5	·	·	PUNCT
ejpam-6667	260	6	)	)	PUNCT
ejpam-6667	260	7	)	)	PUNCT
ejpam-6667	261	1	=	=	SYM
ejpam-6667	261	2	c∥b∥cbmop(·),λ(wp(·))|b|λ∥χb∥lp(·)(wp(·))|b|µ∥χb∥ls(·)(ws(·))∥hαf∥ḃµ,s(·)(ws	c∥b∥cbmop(·),λ(wp(·))|b|λ∥χb∥lp(·)(wp(·))|b|µ∥χb∥ls(·)(ws(·))∥hαf∥ḃµ,s(·)(ws	X
ejpam-6667	261	3	(	(	PUNCT
ejpam-6667	261	4	·	·	PUNCT
ejpam-6667	261	5	)	)	PUNCT
ejpam-6667	261	6	)	)	PUNCT
ejpam-6667	261	7	,	,	PUNCT
ejpam-6667	261	8	∥a1∥lp2(·)(wp2	∥a1∥lp2(·)(wp2	X
ejpam-6667	261	9	(	(	PUNCT
ejpam-6667	261	10	·	·	PUNCT
ejpam-6667	261	11	)	)	PUNCT
ejpam-6667	261	12	)	)	PUNCT
ejpam-6667	261	13	≤	≤	NUM
ejpam-6667	261	14	c∥b∥cbmop(·),λ(wp(·))|b|λ∥χb∥lp(·)(wp(·))|b|µ∥χb∥ls(·)(ws(·))∥hαf∥ḃµ,s(·)(ws	c∥b∥cbmop(·),λ(wp(·))|b|λ∥χb∥lp(·)(wp(·))|b|µ∥χb∥ls(·)(ws(·))∥hαf∥ḃµ,s(·)(w	NOUN
ejpam-6667	261	15	(	(	PUNCT
ejpam-6667	261	16	·	·	PUNCT
ejpam-6667	261	17	)	)	PUNCT
ejpam-6667	261	18	)	)	PUNCT
ejpam-6667	261	19	.	.	PUNCT
ejpam-6667	262	1	m.	m.	PROPN
ejpam-6667	262	2	asim	asim	PROPN
ejpam-6667	262	3	,	,	PUNCT
ejpam-6667	262	4	k.	k.	PROPN
ejpam-6667	262	5	suwais	suwais	PROPN
ejpam-6667	262	6	,	,	PUNCT
ejpam-6667	262	7	n.	n.	PROPN
ejpam-6667	262	8	mlaiki	mlaiki	PROPN
ejpam-6667	262	9	/	/	SYM
ejpam-6667	262	10	eur	eur	PROPN
ejpam-6667	262	11	.	.	PUNCT
ejpam-6667	263	1	j.	j.	PROPN
ejpam-6667	263	2	pure	pure	PROPN
ejpam-6667	263	3	appl	appl	PROPN
ejpam-6667	263	4	.	.	PROPN
ejpam-6667	263	5	math	math	PROPN
ejpam-6667	263	6	,	,	PUNCT
ejpam-6667	263	7	18	18	NUM
ejpam-6667	263	8	(	(	PUNCT
ejpam-6667	263	9	4	4	NUM
ejpam-6667	263	10	)	)	PUNCT
ejpam-6667	263	11	(	(	PUNCT
ejpam-6667	263	12	2025	2025	NUM
ejpam-6667	263	13	)	)	PUNCT
ejpam-6667	263	14	,	,	PUNCT
ejpam-6667	263	15	6667	6667	NUM
ejpam-6667	263	16	11	11	NUM
ejpam-6667	263	17	of	of	ADP
ejpam-6667	263	18	20	20	NUM
ejpam-6667	263	19	∥χb∥lp2(·)(wp2	∥χb∥lp2(·)(wp2	NOUN
ejpam-6667	263	20	(	(	PUNCT
ejpam-6667	263	21	·	·	PUNCT
ejpam-6667	263	22	)	)	PUNCT
ejpam-6667	263	23	)	)	PUNCT
ejpam-6667	264	1	≈	≈	PROPN
ejpam-6667	264	2	w(b	w(b	NOUN
ejpam-6667	264	3	)	)	PUNCT
ejpam-6667	264	4	1	1	NUM
ejpam-6667	264	5	p2	p2	NOUN
ejpam-6667	264	6	(	(	PUNCT
ejpam-6667	264	7	·	·	PUNCT
ejpam-6667	264	8	)	)	PUNCT
ejpam-6667	265	1	≈	≈	PROPN
ejpam-6667	265	2	w(b	w(b	PROPN
ejpam-6667	265	3	)	)	PUNCT
ejpam-6667	265	4	1	1	NUM
ejpam-6667	265	5	s(·)+	s(·)+	ADP
ejpam-6667	265	6	1	1	NUM
ejpam-6667	265	7	p	p	X
ejpam-6667	265	8	(	(	PUNCT
ejpam-6667	265	9	·	·	PUNCT
ejpam-6667	265	10	)	)	PUNCT
ejpam-6667	266	1	≈	≈	PROPN
ejpam-6667	266	2	∥χb∥lp(·)(wp(·))∥χb∥ls(·)(ws	∥χb∥lp(·)(wp(·))∥χb∥ls(·)(ws	PROPN
ejpam-6667	266	3	(	(	PUNCT
ejpam-6667	266	4	·	·	PUNCT
ejpam-6667	266	5	)	)	PUNCT
ejpam-6667	266	6	)	)	PUNCT
ejpam-6667	266	7	given	give	VERB
ejpam-6667	266	8	that	that	DET
ejpam-6667	266	9	µ	µ	NOUN
ejpam-6667	266	10	=	=	SYM
ejpam-6667	266	11	λ1	λ1	PROPN
ejpam-6667	266	12	+	+	CCONJ
ejpam-6667	266	13	α	α	PROPN
ejpam-6667	266	14	n	n	NOUN
ejpam-6667	266	15	,	,	PUNCT
ejpam-6667	266	16	using	use	VERB
ejpam-6667	266	17	the	the	DET
ejpam-6667	266	18	result	result	NOUN
ejpam-6667	266	19	of	of	ADP
ejpam-6667	266	20	theorem	theorem	ADJ
ejpam-6667	266	21	1	1	NUM
ejpam-6667	266	22	∥a1∥lp2(·)(wp2	∥a1∥lp2(·)(wp2	PROPN
ejpam-6667	266	23	(	(	PUNCT
ejpam-6667	266	24	·	·	PUNCT
ejpam-6667	266	25	)	)	PUNCT
ejpam-6667	266	26	)	)	PUNCT
ejpam-6667	267	1	≤	≤	NUM
ejpam-6667	267	2	c∥b∥cbmop(·),λ(wp(·))|b|λ2∥χb∥lp2(·)(wp2(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))|b|λ2∥χb∥lp2(·)(wp2(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	267	3	(	(	PUNCT
ejpam-6667	267	4	wp1	wp1	PROPN
ejpam-6667	267	5	(	(	PUNCT
ejpam-6667	267	6	·	·	PUNCT
ejpam-6667	267	7	)	)	PUNCT
ejpam-6667	267	8	)	)	PUNCT
ejpam-6667	267	9	,	,	PUNCT
ejpam-6667	267	10	a2	a2	PROPN
ejpam-6667	267	11	=	=	SYM
ejpam-6667	267	12	1	1	NUM
ejpam-6667	267	13	|x|n−α	|x|n−α	NOUN
ejpam-6667	267	14	∫	∫	PROPN
ejpam-6667	267	15	b(0,|x|	b(0,|x|	X
ejpam-6667	267	16	)	)	PUNCT
ejpam-6667	267	17	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	267	18	bb)f(v)|dv	bb)f(v)|dv	PROPN
ejpam-6667	267	19	·	·	PUNCT
ejpam-6667	267	20	χb(x	χb(x	NUM
ejpam-6667	267	21	)	)	PUNCT
ejpam-6667	267	22	.	.	PUNCT
ejpam-6667	268	1	a2	a2	PROPN
ejpam-6667	268	2	=	=	SYM
ejpam-6667	269	1	0∑	0∑	NOUN
ejpam-6667	269	2	k=−∞	k=−∞	NOUN
ejpam-6667	270	1	1	1	NUM
ejpam-6667	270	2	|x|n−α	|x|n−α	NOUN
ejpam-6667	270	3	k∑	k∑	VERB
ejpam-6667	270	4	l=−∞	l=−∞	INTJ
ejpam-6667	270	5	∫	∫	PROPN
ejpam-6667	270	6	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	270	7	|(b(v)−	|(b(v)−	NUM
ejpam-6667	270	8	bb)f(v)|dv	bb)f(v)|dv	PROPN
ejpam-6667	270	9	·	·	PUNCT
ejpam-6667	270	10	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	270	11	)	)	PUNCT
ejpam-6667	270	12	≤	≤	NUM
ejpam-6667	270	13	0∑	0∑	NOUN
ejpam-6667	270	14	k=−∞	k=−∞	NOUN
ejpam-6667	270	15	1	1	NUM
ejpam-6667	270	16	|x|n−α	|x|n−α	NOUN
ejpam-6667	270	17	k∑	k∑	VERB
ejpam-6667	270	18	l=−∞	l=−∞	INTJ
ejpam-6667	271	1	∫	∫	PROPN
ejpam-6667	271	2	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	271	3	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	271	4	b2lb)f(v)|dv	b2lb)f(v)|dv	NOUN
ejpam-6667	271	5	·	·	PUNCT
ejpam-6667	271	6	χ2kb\2k−1b(x	χ2kb\2k−1b(x	NUM
ejpam-6667	271	7	)	)	PUNCT
ejpam-6667	272	1	+	+	NUM
ejpam-6667	272	2	0∑	0∑	NOUN
ejpam-6667	272	3	k=−∞	k=−∞	NOUN
ejpam-6667	272	4	1	1	NUM
ejpam-6667	272	5	|x|n−α	|x|n−α	NOUN
ejpam-6667	272	6	k∑	k∑	VERB
ejpam-6667	272	7	l=−∞	l=−∞	INTJ
ejpam-6667	272	8	∫	∫	PROPN
ejpam-6667	272	9	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	273	1	|(bb	|(bb	PUNCT
ejpam-6667	273	2	−	−	PROPN
ejpam-6667	273	3	b2lb)f(v)|dv	b2lb)f(v)|dv	NOUN
ejpam-6667	273	4	·	·	PUNCT
ejpam-6667	273	5	χ2kb\2k−1b(x	χ2kb\2k−1b(x	NUM
ejpam-6667	273	6	)	)	PUNCT
ejpam-6667	273	7	=	=	SYM
ejpam-6667	273	8	a21	a21	PROPN
ejpam-6667	274	1	+	+	NUM
ejpam-6667	274	2	a22	a22	NOUN
ejpam-6667	274	3	a21	a21	NOUN
ejpam-6667	275	1	=	=	SYM
ejpam-6667	275	2	0∑	0∑	NUM
ejpam-6667	275	3	k=−∞	k=−∞	NOUN
ejpam-6667	276	1	|2kb|	|2kb|	NOUN
ejpam-6667	276	2	α	α	PROPN
ejpam-6667	276	3	n	n	VERB
ejpam-6667	276	4	−1	−1	NOUN
ejpam-6667	276	5	k∑	k∑	NOUN
ejpam-6667	276	6	l=−∞	l=−∞	INTJ
ejpam-6667	277	1	∫	∫	PROPN
ejpam-6667	277	2	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	277	3	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	277	4	b2lb)f(v)|dv	b2lb)f(v)|dv	NOUN
ejpam-6667	277	5	·	·	PUNCT
ejpam-6667	277	6	χ2kb\2k−1b(x	χ2kb\2k−1b(x	NUM
ejpam-6667	277	7	)	)	PUNCT
ejpam-6667	277	8	.	.	PUNCT
ejpam-6667	278	1	using	use	VERB
ejpam-6667	278	2	hölder	hölder	NOUN
ejpam-6667	278	3	inequality	inequality	NOUN
ejpam-6667	278	4	(	(	PUNCT
ejpam-6667	278	5	1	1	NUM
ejpam-6667	278	6	p1	p1	NOUN
ejpam-6667	278	7	(	(	PUNCT
ejpam-6667	278	8	·	·	PUNCT
ejpam-6667	278	9	)	)	PUNCT
ejpam-6667	279	1	+	+	CCONJ
ejpam-6667	279	2	1	1	NUM
ejpam-6667	279	3	t	t	PROPN
ejpam-6667	279	4	(	(	PUNCT
ejpam-6667	279	5	·	·	PUNCT
ejpam-6667	279	6	)	)	PUNCT
ejpam-6667	280	1	+	+	CCONJ
ejpam-6667	280	2	1	1	NUM
ejpam-6667	280	3	p	p	X
ejpam-6667	280	4	(	(	PUNCT
ejpam-6667	280	5	·	·	PUNCT
ejpam-6667	280	6	)	)	PUNCT
ejpam-6667	280	7	=	=	SYM
ejpam-6667	280	8	1	1	NUM
ejpam-6667	280	9	)	)	PUNCT
ejpam-6667	280	10	.	.	PUNCT
ejpam-6667	281	1	a21	a21	PROPN
ejpam-6667	281	2	≤	≤	PROPN
ejpam-6667	282	1	c	c	NOUN
ejpam-6667	282	2	0∑	0∑	NOUN
ejpam-6667	282	3	k=−∞	k=−∞	INTJ
ejpam-6667	283	1	|2kb|	|2kb|	VERB
ejpam-6667	283	2	α	α	PROPN
ejpam-6667	283	3	n	n	X
ejpam-6667	283	4	−1χ2kb\2k−1b(x	−1χ2kb\2k−1b(x	PROPN
ejpam-6667	283	5	)	)	PUNCT
ejpam-6667	283	6	k∑	k∑	NOUN
ejpam-6667	283	7	l=−∞	l=−∞	PUNCT
ejpam-6667	284	1	∥(b(v)−	∥(b(v)−	PROPN
ejpam-6667	284	2	b2lb)χ2lb∥lp(·)(wp(·))∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	b2lb)χ2lb∥lp(·)(wp(·))∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	NOUN
ejpam-6667	284	3	(	(	PUNCT
ejpam-6667	284	4	·	·	PUNCT
ejpam-6667	284	5	)	)	PUNCT
ejpam-6667	284	6	)	)	PUNCT
ejpam-6667	285	1	=	=	PUNCT
ejpam-6667	286	1	c	c	NOUN
ejpam-6667	286	2	0∑	0∑	NOUN
ejpam-6667	286	3	k=−∞	k=−∞	INTJ
ejpam-6667	287	1	|2kb|	|2kb|	VERB
ejpam-6667	287	2	α	α	PROPN
ejpam-6667	287	3	n	n	X
ejpam-6667	287	4	−1χ2kb\2k−1b(x	−1χ2kb\2k−1b(x	PROPN
ejpam-6667	287	5	)	)	PUNCT
ejpam-6667	287	6	k∑	k∑	NOUN
ejpam-6667	287	7	l=−∞	l=−∞	PRON
ejpam-6667	287	8	∥b∥cbmop(·),λ(wp(·))|2	∥b∥cbmop(·),λ(wp(·))|2	VERB
ejpam-6667	287	9	lb|λ∥χ2lb∥lp(·)(wp	lb|λ∥χ2lb∥lp(·)(wp	PROPN
ejpam-6667	287	10	(	(	PUNCT
ejpam-6667	287	11	·	·	PUNCT
ejpam-6667	287	12	)	)	PUNCT
ejpam-6667	287	13	)	)	PUNCT
ejpam-6667	288	1	∥f∥ḃp1(·),λ1	∥f∥ḃp1(·),λ1	NUM
ejpam-6667	288	2	(	(	PUNCT
ejpam-6667	288	3	wp1(·))|2	wp1(·))|2	PROPN
ejpam-6667	288	4	lb|λ1∥χ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	lb|λ1∥χ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	PROPN
ejpam-6667	288	5	(	(	PUNCT
ejpam-6667	288	6	·	·	PUNCT
ejpam-6667	288	7	)	)	PUNCT
ejpam-6667	288	8	)	)	PUNCT
ejpam-6667	288	9	∥χ2lb∥	∥χ2lb∥	NOUN
ejpam-6667	288	10	(	(	PUNCT
ejpam-6667	288	11	lp	lp	NOUN
ejpam-6667	288	12	′	′	NUM
ejpam-6667	288	13	1(·)(wp1(·)))′	1(·)(wp1(·)))′	NUM
ejpam-6667	289	1	≈	≈	PROPN
ejpam-6667	289	2	w(2	w(2	NOUN
ejpam-6667	289	3	lb	lb	NOUN
ejpam-6667	289	4	)	)	PUNCT
ejpam-6667	289	5	1	1	NUM
ejpam-6667	289	6	p	p	NOUN
ejpam-6667	289	7	′	′	NUM
ejpam-6667	289	8	1	1	NUM
ejpam-6667	289	9	(	(	PUNCT
ejpam-6667	289	10	·	·	PUNCT
ejpam-6667	289	11	)	)	PUNCT
ejpam-6667	290	1	≈	≈	PROPN
ejpam-6667	290	2	w(2	w(2	NOUN
ejpam-6667	290	3	lb	lb	NOUN
ejpam-6667	290	4	)	)	PUNCT
ejpam-6667	290	5	1	1	NUM
ejpam-6667	290	6	p(·)+	p(·)+	NUM
ejpam-6667	290	7	1	1	NUM
ejpam-6667	290	8	t	t	PROPN
ejpam-6667	290	9	(	(	PUNCT
ejpam-6667	290	10	·	·	PUNCT
ejpam-6667	290	11	)	)	PUNCT
ejpam-6667	291	1	≈	≈	PROPN
ejpam-6667	291	2	∥χ2lb∥lp(·)(wp(·))∥χ2lb∥lt(·)(wt	∥χ2lb∥lp(·)(wp(·))∥χ2lb∥lt(·)(wt	PROPN
ejpam-6667	291	3	(	(	PUNCT
ejpam-6667	291	4	·	·	PUNCT
ejpam-6667	291	5	)	)	PUNCT
ejpam-6667	291	6	)	)	PUNCT
ejpam-6667	291	7	a21	a21	NOUN
ejpam-6667	291	8	=	=	SYM
ejpam-6667	292	1	c	c	NOUN
ejpam-6667	292	2	0∑	0∑	NOUN
ejpam-6667	292	3	k=−∞	k=−∞	INTJ
ejpam-6667	293	1	|2kb|	|2kb|	VERB
ejpam-6667	293	2	α	α	PROPN
ejpam-6667	293	3	n	n	PRON
ejpam-6667	293	4	−1χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	−1χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	NOUN
ejpam-6667	293	5	(	(	PUNCT
ejpam-6667	293	6	wp1	wp1	PROPN
ejpam-6667	293	7	(	(	PUNCT
ejpam-6667	293	8	·	·	PUNCT
ejpam-6667	293	9	)	)	PUNCT
ejpam-6667	293	10	)	)	PUNCT
ejpam-6667	294	1	k∑	k∑	VERB
ejpam-6667	294	2	l=−∞	l=−∞	PRON
ejpam-6667	294	3	|2lb|λ+λ1∥χ2lb∥	|2lb|λ+λ1∥χ2lb∥	VERB
ejpam-6667	294	4	(	(	PUNCT
ejpam-6667	294	5	lp	lp	NOUN
ejpam-6667	294	6	′	′	NUM
ejpam-6667	294	7	1(·)(wp1(·)))′	1(·)(wp1(·)))′	NUM
ejpam-6667	294	8	∥χ2lb∥lp1(·)(wp1	∥χ2lb∥lp1(·)(wp1	NOUN
ejpam-6667	294	9	(	(	PUNCT
ejpam-6667	294	10	·	·	PUNCT
ejpam-6667	294	11	)	)	PUNCT
ejpam-6667	294	12	)	)	PUNCT
ejpam-6667	294	13	.	.	PUNCT
ejpam-6667	295	1	m.	m.	PROPN
ejpam-6667	295	2	asim	asim	PROPN
ejpam-6667	295	3	,	,	PUNCT
ejpam-6667	295	4	k.	k.	PROPN
ejpam-6667	295	5	suwais	suwais	PROPN
ejpam-6667	295	6	,	,	PUNCT
ejpam-6667	295	7	n.	n.	PROPN
ejpam-6667	295	8	mlaiki	mlaiki	PROPN
ejpam-6667	295	9	/	/	SYM
ejpam-6667	295	10	eur	eur	PROPN
ejpam-6667	295	11	.	.	PUNCT
ejpam-6667	296	1	j.	j.	PROPN
ejpam-6667	296	2	pure	pure	PROPN
ejpam-6667	296	3	appl	appl	PROPN
ejpam-6667	296	4	.	.	PROPN
ejpam-6667	296	5	math	math	PROPN
ejpam-6667	296	6	,	,	PUNCT
ejpam-6667	296	7	18	18	NUM
ejpam-6667	296	8	(	(	PUNCT
ejpam-6667	296	9	4	4	NUM
ejpam-6667	296	10	)	)	PUNCT
ejpam-6667	296	11	(	(	PUNCT
ejpam-6667	296	12	2025	2025	NUM
ejpam-6667	296	13	)	)	PUNCT
ejpam-6667	296	14	,	,	PUNCT
ejpam-6667	296	15	6667	6667	NUM
ejpam-6667	296	16	12	12	NUM
ejpam-6667	296	17	of	of	ADP
ejpam-6667	296	18	20	20	NUM
ejpam-6667	296	19	by	by	ADP
ejpam-6667	296	20	using	use	VERB
ejpam-6667	296	21	the	the	DET
ejpam-6667	296	22	result	result	NOUN
ejpam-6667	296	23	of	of	ADP
ejpam-6667	296	24	lemma	lemma	PROPN
ejpam-6667	296	25	5	5	NUM
ejpam-6667	296	26	,	,	PUNCT
ejpam-6667	296	27	we	we	PRON
ejpam-6667	296	28	will	will	AUX
ejpam-6667	296	29	have	have	VERB
ejpam-6667	296	30	a21	a21	NOUN
ejpam-6667	296	31	=	=	SYM
ejpam-6667	296	32	c	c	NOUN
ejpam-6667	296	33	0∑	0∑	NOUN
ejpam-6667	296	34	k=−∞	k=−∞	INTJ
ejpam-6667	297	1	|2kb|	|2kb|	VERB
ejpam-6667	297	2	α	α	PROPN
ejpam-6667	297	3	n	n	PRON
ejpam-6667	297	4	−1χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	−1χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	NOUN
ejpam-6667	297	5	(	(	PUNCT
ejpam-6667	297	6	wp1	wp1	PROPN
ejpam-6667	297	7	(	(	PUNCT
ejpam-6667	297	8	·	·	PUNCT
ejpam-6667	297	9	)	)	PUNCT
ejpam-6667	297	10	)	)	PUNCT
ejpam-6667	298	1	k∑	k∑	VERB
ejpam-6667	298	2	l=−∞	l=−∞	PUNCT
ejpam-6667	299	1	|2l|λ+λ1	|2l|λ+λ1	X
ejpam-6667	299	2	+	+	NOUN
ejpam-6667	299	3	1|b|λ+λ1	1|b|λ+λ1	NUM
ejpam-6667	299	4	+	+	SYM
ejpam-6667	299	5	1	1	NUM
ejpam-6667	299	6	=	=	SYM
ejpam-6667	299	7	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	299	8	(	(	PUNCT
ejpam-6667	299	9	wp1	wp1	PROPN
ejpam-6667	299	10	(	(	PUNCT
ejpam-6667	299	11	·	·	PUNCT
ejpam-6667	299	12	)	)	PUNCT
ejpam-6667	299	13	)	)	PUNCT
ejpam-6667	300	1	0∑	0∑	NOUN
ejpam-6667	300	2	k=−∞	k=−∞	PROPN
ejpam-6667	301	1	|2k|	|2k|	PROPN
ejpam-6667	301	2	α	α	PROPN
ejpam-6667	301	3	n	n	PROPN
ejpam-6667	302	1	+	+	NOUN
ejpam-6667	302	2	λ+λ1χ2kb\2k−1b(x)|b|λ+λ1	λ+λ1χ2kb\2k−1b(x)|b|λ+λ1	PROPN
ejpam-6667	302	3	+	+	NOUN
ejpam-6667	302	4	α	α	PROPN
ejpam-6667	302	5	n	n	PRON
ejpam-6667	302	6	∥a21∥lp2(·)(wp2	∥a21∥lp2(·)(wp2	NOUN
ejpam-6667	302	7	(	(	PUNCT
ejpam-6667	302	8	·	·	PUNCT
ejpam-6667	302	9	)	)	PUNCT
ejpam-6667	302	10	)	)	PUNCT
ejpam-6667	303	1	≤	≤	PROPN
ejpam-6667	303	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	303	3	(	(	PUNCT
ejpam-6667	303	4	wp1	wp1	PROPN
ejpam-6667	303	5	(	(	PUNCT
ejpam-6667	303	6	·	·	PUNCT
ejpam-6667	303	7	)	)	PUNCT
ejpam-6667	303	8	)	)	PUNCT
ejpam-6667	304	1	0∑	0∑	NOUN
ejpam-6667	304	2	k=−∞	k=−∞	PROPN
ejpam-6667	305	1	|2k|	|2k|	PROPN
ejpam-6667	305	2	α	α	PROPN
ejpam-6667	305	3	n	n	PROPN
ejpam-6667	305	4	+	+	ADJ
ejpam-6667	305	5	λ+λ1∥χ2kb∥lp2(·)(wp2(·))|b|λ+λ1	λ+λ1∥χ2kb∥lp2(·)(wp2(·))|b|λ+λ1	PROPN
ejpam-6667	305	6	+	+	NOUN
ejpam-6667	305	7	α	α	PROPN
ejpam-6667	305	8	n	n	NOUN
ejpam-6667	305	9	=	=	SYM
ejpam-6667	305	10	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	305	11	(	(	PUNCT
ejpam-6667	305	12	wp1	wp1	PROPN
ejpam-6667	305	13	(	(	PUNCT
ejpam-6667	305	14	·	·	PUNCT
ejpam-6667	305	15	)	)	PUNCT
ejpam-6667	305	16	)	)	PUNCT
ejpam-6667	306	1	0∑	0∑	NOUN
ejpam-6667	306	2	k=−∞	k=−∞	PROPN
ejpam-6667	307	1	|2k|	|2k|	PROPN
ejpam-6667	307	2	α	α	PROPN
ejpam-6667	307	3	n	n	PROPN
ejpam-6667	307	4	+	+	ADJ
ejpam-6667	307	5	λ+λ1w(2	λ+λ1w(2	PROPN
ejpam-6667	307	6	kb	kb	X
ejpam-6667	307	7	)	)	PUNCT
ejpam-6667	307	8	1	1	NUM
ejpam-6667	307	9	p2	p2	NOUN
ejpam-6667	307	10	(	(	PUNCT
ejpam-6667	307	11	·	·	PUNCT
ejpam-6667	307	12	)	)	PUNCT
ejpam-6667	307	13	|b|λ+λ1	|b|λ+λ1	NOUN
ejpam-6667	307	14	+	+	CCONJ
ejpam-6667	307	15	α	α	PROPN
ejpam-6667	307	16	n	n	NOUN
ejpam-6667	307	17	=	=	SYM
ejpam-6667	307	18	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	307	19	(	(	PUNCT
ejpam-6667	307	20	wp1(·))w(b	wp1(·))w(b	NOUN
ejpam-6667	307	21	)	)	PUNCT
ejpam-6667	307	22	1	1	NUM
ejpam-6667	307	23	p2	p2	NOUN
ejpam-6667	307	24	(	(	PUNCT
ejpam-6667	307	25	·	·	PUNCT
ejpam-6667	307	26	)	)	PUNCT
ejpam-6667	307	27	|b|λ2	|b|λ2	NOUN
ejpam-6667	308	1	0∑	0∑	NOUN
ejpam-6667	308	2	k=−∞	k=−∞	PROPN
ejpam-6667	308	3	|2|k(λ2	|2|k(λ2	NOUN
ejpam-6667	308	4	+	+	CCONJ
ejpam-6667	308	5	1	1	NUM
ejpam-6667	308	6	p2	p2	NOUN
ejpam-6667	308	7	(	(	PUNCT
ejpam-6667	308	8	·	·	PUNCT
ejpam-6667	308	9	)	)	PUNCT
ejpam-6667	308	10	)	)	PUNCT
ejpam-6667	308	11	∥a21∥lp2(·)(wp2	∥a21∥lp2(·)(wp2	NOUN
ejpam-6667	308	12	(	(	PUNCT
ejpam-6667	308	13	·	·	PUNCT
ejpam-6667	308	14	)	)	PUNCT
ejpam-6667	308	15	)	)	PUNCT
ejpam-6667	309	1	≤	≤	PROPN
ejpam-6667	309	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	309	3	(	(	PUNCT
ejpam-6667	309	4	wp1(·))∥χb∥lp2(·)(wp2(·))|b|λ2	wp1(·))∥χb∥lp2(·)(wp2(·))|b|λ2	NOUN
ejpam-6667	309	5	a22	a22	PROPN
ejpam-6667	309	6	=	=	PUNCT
ejpam-6667	309	7	0∑	0∑	NUM
ejpam-6667	309	8	k=−∞	k=−∞	NOUN
ejpam-6667	309	9	|2kb|	|2kb|	NOUN
ejpam-6667	309	10	α	α	PROPN
ejpam-6667	309	11	n	n	VERB
ejpam-6667	309	12	−1	−1	NOUN
ejpam-6667	309	13	k∑	k∑	NOUN
ejpam-6667	309	14	l=−∞	l=−∞	INTJ
ejpam-6667	309	15	∫	∫	PROPN
ejpam-6667	309	16	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	309	17	|(bb	|(bb	PUNCT
ejpam-6667	309	18	−	−	PROPN
ejpam-6667	309	19	b2lb)f(y)|dy	b2lb)f(y)|dy	X
ejpam-6667	309	20	·	·	PUNCT
ejpam-6667	309	21	χ2kb\2k−1b(x	χ2kb\2k−1b(x	NUM
ejpam-6667	309	22	)	)	PUNCT
ejpam-6667	309	23	|(bb	|(bb	NUM
ejpam-6667	309	24	−	−	PROPN
ejpam-6667	309	25	b2lb)|	b2lb)|	PROPN
ejpam-6667	309	26	=	=	SYM
ejpam-6667	309	27	−1∑	−1∑	PROPN
ejpam-6667	309	28	i	i	PROPN
ejpam-6667	309	29	=	=	PROPN
ejpam-6667	309	30	l	l	NOUN
ejpam-6667	309	31	|(b2i+1b	|(b2i+1b	PROPN
ejpam-6667	309	32	−	−	NOUN
ejpam-6667	309	33	b2ib	b2ib	PUNCT
ejpam-6667	309	34	)	)	PUNCT
ejpam-6667	309	35	=	=	SYM
ejpam-6667	310	1	−1∑	−1∑	PROPN
ejpam-6667	310	2	i	i	NOUN
ejpam-6667	310	3	=	=	NOUN
ejpam-6667	310	4	l	l	NOUN
ejpam-6667	310	5	1	1	NUM
ejpam-6667	310	6	|2ib|	|2ib|	NOUN
ejpam-6667	310	7	∫	∫	PROPN
ejpam-6667	310	8	2ib	2ib	PROPN
ejpam-6667	310	9	|b(y)−	|b(y)−	VERB
ejpam-6667	310	10	b2i+1b|dy	b2i+1b|dy	PUNCT
ejpam-6667	310	11	≤	≤	NUM
ejpam-6667	310	12	c	c	X
ejpam-6667	311	1	−1∑	−1∑	PROPN
ejpam-6667	311	2	i	i	PROPN
ejpam-6667	311	3	=	=	NOUN
ejpam-6667	311	4	l	l	NOUN
ejpam-6667	311	5	1	1	NUM
ejpam-6667	311	6	|2ib|	|2ib|	NOUN
ejpam-6667	311	7	∥(b−	∥(b−	NOUN
ejpam-6667	311	8	b2i+1b)χ2i+1b∥lp(·)(wp(·))∥χ2i+1b∥(lp(·)(wp1(·)))′	b2i+1b)χ2i+1b∥lp(·)(wp(·))∥χ2i+1b∥(lp(·)(wp1(·)))′	NOUN
ejpam-6667	311	9	by	by	ADP
ejpam-6667	311	10	virtue	virtue	NOUN
ejpam-6667	311	11	of	of	ADP
ejpam-6667	311	12	lemma	lemma	PROPN
ejpam-6667	311	13	5	5	NUM
ejpam-6667	311	14	,	,	PUNCT
ejpam-6667	311	15	we	we	PRON
ejpam-6667	311	16	have	have	VERB
ejpam-6667	311	17	|(bb	|(bb	VERB
ejpam-6667	311	18	−	−	PROPN
ejpam-6667	311	19	b2lb)|	b2lb)|	PROPN
ejpam-6667	311	20	≤	≤	NOUN
ejpam-6667	311	21	c	c	PUNCT
ejpam-6667	312	1	−1∑	−1∑	PROPN
ejpam-6667	312	2	i	i	PROPN
ejpam-6667	312	3	=	=	NOUN
ejpam-6667	312	4	l	l	NOUN
ejpam-6667	312	5	1	1	NUM
ejpam-6667	312	6	|2ib|	|2ib|	NOUN
ejpam-6667	312	7	∥(b−	∥(b−	NOUN
ejpam-6667	312	8	b2i+1b)χ2i+1b∥lp(·)(wp	b2i+1b)χ2i+1b∥lp(·)(wp	NOUN
ejpam-6667	312	9	(	(	PUNCT
ejpam-6667	312	10	·	·	PUNCT
ejpam-6667	312	11	)	)	PUNCT
ejpam-6667	312	12	)	)	PUNCT
ejpam-6667	312	13	|2i+1b|	|2i+1b|	NOUN
ejpam-6667	312	14	∥χ2i+1b∥lp(·)(wp	∥χ2i+1b∥lp(·)(wp	X
ejpam-6667	312	15	(	(	PUNCT
ejpam-6667	312	16	·	·	PUNCT
ejpam-6667	312	17	)	)	PUNCT
ejpam-6667	312	18	)	)	PUNCT
ejpam-6667	312	19	≤	≤	NUM
ejpam-6667	313	1	c	c	AUX
ejpam-6667	313	2	−1∑	−1∑	PROPN
ejpam-6667	313	3	i	i	PROPN
ejpam-6667	313	4	=	=	NOUN
ejpam-6667	313	5	l	l	NOUN
ejpam-6667	313	6	∥b∥cbmop(·),λ(wp(·))|2	∥b∥cbmop(·),λ(wp(·))|2	NOUN
ejpam-6667	313	7	i+1b|λ	i+1b|λ	VERB
ejpam-6667	313	8	≤	≤	NUM
ejpam-6667	313	9	c∥b∥cbmop(·),λ(wp	c∥b∥cbmop(·),λ(wp	PROPN
ejpam-6667	313	10	(	(	PUNCT
ejpam-6667	313	11	·	·	PUNCT
ejpam-6667	313	12	)	)	PUNCT
ejpam-6667	313	13	)	)	PUNCT
ejpam-6667	314	1	−1∑	−1∑	PROPN
ejpam-6667	314	2	i	i	PROPN
ejpam-6667	314	3	=	=	PROPN
ejpam-6667	314	4	l	l	NOUN
ejpam-6667	314	5	|2i+1b|λ	|2i+1b|λ	PROPN
ejpam-6667	314	6	≤	≤	PROPN
ejpam-6667	314	7	c∥b∥cbmop(·),λ(wp(·))|2	c∥b∥cbmop(·),λ(wp(·))|2	PROPN
ejpam-6667	314	8	l+1b|λ|l|	l+1b|λ|l|	NOUN
ejpam-6667	314	9	(	(	PUNCT
ejpam-6667	314	10	9	9	NUM
ejpam-6667	314	11	)	)	PUNCT
ejpam-6667	314	12	m.	m.	NOUN
ejpam-6667	314	13	asim	asim	PROPN
ejpam-6667	314	14	,	,	PUNCT
ejpam-6667	314	15	k.	k.	PROPN
ejpam-6667	314	16	suwais	suwais	PROPN
ejpam-6667	314	17	,	,	PUNCT
ejpam-6667	314	18	n.	n.	PROPN
ejpam-6667	314	19	mlaiki	mlaiki	PROPN
ejpam-6667	314	20	/	/	SYM
ejpam-6667	314	21	eur	eur	PROPN
ejpam-6667	314	22	.	.	PUNCT
ejpam-6667	315	1	j.	j.	PROPN
ejpam-6667	315	2	pure	pure	PROPN
ejpam-6667	315	3	appl	appl	PROPN
ejpam-6667	315	4	.	.	PROPN
ejpam-6667	315	5	math	math	PROPN
ejpam-6667	315	6	,	,	PUNCT
ejpam-6667	315	7	18	18	NUM
ejpam-6667	315	8	(	(	PUNCT
ejpam-6667	315	9	4	4	NUM
ejpam-6667	315	10	)	)	PUNCT
ejpam-6667	315	11	(	(	PUNCT
ejpam-6667	315	12	2025	2025	NUM
ejpam-6667	315	13	)	)	PUNCT
ejpam-6667	315	14	,	,	PUNCT
ejpam-6667	315	15	6667	6667	NUM
ejpam-6667	315	16	13	13	NUM
ejpam-6667	315	17	of	of	ADP
ejpam-6667	315	18	20	20	NUM
ejpam-6667	315	19	a22	a22	PROPN
ejpam-6667	315	20	≤	≤	NUM
ejpam-6667	316	1	c	c	NOUN
ejpam-6667	316	2	0∑	0∑	NOUN
ejpam-6667	316	3	k=−∞	k=−∞	NOUN
ejpam-6667	317	1	χ2kb\2k−1b(x)|2kb|	χ2kb\2k−1b(x)|2kb|	NOUN
ejpam-6667	317	2	α	α	PROPN
ejpam-6667	317	3	n	n	VERB
ejpam-6667	317	4	−1	−1	NOUN
ejpam-6667	317	5	k∑	k∑	NOUN
ejpam-6667	317	6	l=−∞	l=−∞	PRON
ejpam-6667	317	7	∥b∥cbmop(·),λ(wp(·))|2	∥b∥cbmop(·),λ(wp(·))|2	VERB
ejpam-6667	317	8	l+1b|λ|l|	l+1b|λ|l|	NOUN
ejpam-6667	317	9	∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp1(·)(wp1(·)))′	∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp1(·)(wp1(·)))′	PROPN
ejpam-6667	317	10	≤	≤	PROPN
ejpam-6667	317	11	c∥b∥cbmop(·),λ(wp	c∥b∥cbmop(·),λ(wp	PROPN
ejpam-6667	317	12	(	(	PUNCT
ejpam-6667	317	13	·	·	PUNCT
ejpam-6667	317	14	)	)	PUNCT
ejpam-6667	317	15	)	)	PUNCT
ejpam-6667	318	1	0∑	0∑	NOUN
ejpam-6667	318	2	k=−∞	k=−∞	NOUN
ejpam-6667	319	1	χ2kb\2k−1b(x)|2kb|	χ2kb\2k−1b(x)|2kb|	NOUN
ejpam-6667	319	2	α	α	PROPN
ejpam-6667	319	3	n	n	VERB
ejpam-6667	319	4	−1	−1	NOUN
ejpam-6667	319	5	k∑	k∑	NOUN
ejpam-6667	319	6	l=−∞	l=−∞	NOUN
ejpam-6667	319	7	|2l+1b|λ|l|	|2l+1b|λ|l|	NOUN
ejpam-6667	319	8	∥fχ2lb∥lp1(·)(wp1	∥fχ2lb∥lp1(·)(wp1	PROPN
ejpam-6667	319	9	(	(	PUNCT
ejpam-6667	319	10	·	·	PUNCT
ejpam-6667	319	11	)	)	PUNCT
ejpam-6667	319	12	)	)	PUNCT
ejpam-6667	319	13	|2lb|	|2lb|	CCONJ
ejpam-6667	319	14	∥χ2lb∥lp1(·)(wp1	∥χ2lb∥lp1(·)(wp1	NOUN
ejpam-6667	319	15	(	(	PUNCT
ejpam-6667	319	16	·	·	PUNCT
ejpam-6667	319	17	)	)	PUNCT
ejpam-6667	319	18	)	)	PUNCT
ejpam-6667	319	19	≤	≤	NUM
ejpam-6667	319	20	c∥b∥cbmop(·),λ(wp	c∥b∥cbmop(·),λ(wp	PROPN
ejpam-6667	319	21	(	(	PUNCT
ejpam-6667	319	22	·	·	PUNCT
ejpam-6667	319	23	)	)	PUNCT
ejpam-6667	319	24	)	)	PUNCT
ejpam-6667	320	1	0∑	0∑	NOUN
ejpam-6667	320	2	k=−∞	k=−∞	NOUN
ejpam-6667	321	1	χ2kb\2k−1b(x)|2kb|	χ2kb\2k−1b(x)|2kb|	NOUN
ejpam-6667	321	2	α	α	PROPN
ejpam-6667	321	3	n	n	VERB
ejpam-6667	321	4	−1	−1	NOUN
ejpam-6667	321	5	k∑	k∑	ADJ
ejpam-6667	321	6	l=−∞	l=−∞	NOUN
ejpam-6667	321	7	|2lb|λ+1|l|∥f∥ḃp1(·),λ1	|2lb|λ+1|l|∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	321	8	(	(	PUNCT
ejpam-6667	321	9	wp1(·))|2	wp1(·))|2	PROPN
ejpam-6667	321	10	lb|λ1	lb|λ1	VERB
ejpam-6667	321	11	≤	≤	PROPN
ejpam-6667	321	12	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	321	13	(	(	PUNCT
ejpam-6667	321	14	wp1	wp1	PROPN
ejpam-6667	321	15	(	(	PUNCT
ejpam-6667	321	16	·	·	PUNCT
ejpam-6667	321	17	)	)	PUNCT
ejpam-6667	321	18	)	)	PUNCT
ejpam-6667	322	1	0∑	0∑	NOUN
ejpam-6667	322	2	k=−∞	k=−∞	NOUN
ejpam-6667	323	1	χ2kb\2k−1b(x)|2kb|	χ2kb\2k−1b(x)|2kb|	NOUN
ejpam-6667	323	2	α	α	PROPN
ejpam-6667	323	3	n	n	VERB
ejpam-6667	323	4	−1	−1	NOUN
ejpam-6667	323	5	k∑	k∑	ADJ
ejpam-6667	323	6	l=−∞	l=−∞	X
ejpam-6667	324	1	|2lb|λ+λ1	|2lb|λ+λ1	NOUN
ejpam-6667	324	2	+	+	NOUN
ejpam-6667	324	3	1|l|	1|l|	NOUN
ejpam-6667	324	4	≤	≤	PUNCT
ejpam-6667	325	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	325	2	(	(	PUNCT
ejpam-6667	325	3	wp1	wp1	PROPN
ejpam-6667	325	4	(	(	PUNCT
ejpam-6667	325	5	·	·	PUNCT
ejpam-6667	325	6	)	)	PUNCT
ejpam-6667	325	7	)	)	PUNCT
ejpam-6667	326	1	0∑	0∑	NOUN
ejpam-6667	326	2	k=−∞	k=−∞	NOUN
ejpam-6667	327	1	χ2kb\2k−1b(x)|2kb|	χ2kb\2k−1b(x)|2kb|	NOUN
ejpam-6667	327	2	α	α	NOUN
ejpam-6667	327	3	n	n	PRON
ejpam-6667	327	4	−1|2kb|λ+λ1	−1|2kb|λ+λ1	NOUN
ejpam-6667	327	5	+	+	NOUN
ejpam-6667	327	6	1|k|	1|k|	NUM
ejpam-6667	327	7	≤	≤	NUM
ejpam-6667	327	8	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	327	9	(	(	PUNCT
ejpam-6667	327	10	wp1	wp1	PROPN
ejpam-6667	327	11	(	(	PUNCT
ejpam-6667	327	12	·	·	PUNCT
ejpam-6667	327	13	)	)	PUNCT
ejpam-6667	327	14	)	)	PUNCT
ejpam-6667	328	1	0∑	0∑	NOUN
ejpam-6667	328	2	k=−∞	k=−∞	PROPN
ejpam-6667	329	1	|k||2kb|λ+λ1	|k||2kb|λ+λ1	ADP
ejpam-6667	329	2	+	+	PROPN
ejpam-6667	329	3	α	α	PROPN
ejpam-6667	329	4	nχ2kb\2k−1b(x	nχ2kb\2k−1b(x	PROPN
ejpam-6667	329	5	)	)	PUNCT
ejpam-6667	329	6	∥a22∥lp2(·)(wp2	∥a22∥lp2(·)(wp2	NOUN
ejpam-6667	329	7	(	(	PUNCT
ejpam-6667	329	8	·	·	PUNCT
ejpam-6667	329	9	)	)	PUNCT
ejpam-6667	329	10	)	)	PUNCT
ejpam-6667	330	1	≤	≤	PROPN
ejpam-6667	330	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	330	3	(	(	PUNCT
ejpam-6667	330	4	wp1	wp1	PROPN
ejpam-6667	330	5	(	(	PUNCT
ejpam-6667	330	6	·	·	PUNCT
ejpam-6667	330	7	)	)	PUNCT
ejpam-6667	330	8	)	)	PUNCT
ejpam-6667	331	1	0∑	0∑	NOUN
ejpam-6667	331	2	k=−∞	k=−∞	PROPN
ejpam-6667	332	1	|k||2kb|λ+λ1	|k||2kb|λ+λ1	ADP
ejpam-6667	332	2	+	+	ADP
ejpam-6667	332	3	α	α	PROPN
ejpam-6667	332	4	n	n	PRON
ejpam-6667	332	5	∥χ2kb∥lp2	∥χ2kb∥lp2	NOUN
ejpam-6667	332	6	(	(	PUNCT
ejpam-6667	332	7	·	·	PUNCT
ejpam-6667	332	8	)	)	PUNCT
ejpam-6667	332	9	≤	≤	PROPN
ejpam-6667	333	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	333	2	(	(	PUNCT
ejpam-6667	333	3	wp1	wp1	PROPN
ejpam-6667	333	4	(	(	PUNCT
ejpam-6667	333	5	·	·	PUNCT
ejpam-6667	333	6	)	)	PUNCT
ejpam-6667	333	7	)	)	PUNCT
ejpam-6667	334	1	0∑	0∑	NOUN
ejpam-6667	334	2	k=−∞	k=−∞	PROPN
ejpam-6667	335	1	|k||2kb|λ+λ1	|k||2kb|λ+λ1	ADP
ejpam-6667	335	2	+	+	CCONJ
ejpam-6667	335	3	α	α	PROPN
ejpam-6667	335	4	nw(2	nw(2	NOUN
ejpam-6667	335	5	kb	kb	PROPN
ejpam-6667	335	6	)	)	PUNCT
ejpam-6667	335	7	1	1	NUM
ejpam-6667	335	8	p2	p2	NOUN
ejpam-6667	335	9	(	(	PUNCT
ejpam-6667	335	10	·	·	PUNCT
ejpam-6667	335	11	)	)	PUNCT
ejpam-6667	335	12	≤	≤	PROPN
ejpam-6667	336	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	336	2	(	(	PUNCT
ejpam-6667	336	3	wp1	wp1	PROPN
ejpam-6667	336	4	(	(	PUNCT
ejpam-6667	336	5	·	·	PUNCT
ejpam-6667	336	6	)	)	PUNCT
ejpam-6667	336	7	)	)	PUNCT
ejpam-6667	337	1	0∑	0∑	NOUN
ejpam-6667	337	2	k=−∞	k=−∞	NOUN
ejpam-6667	337	3	|k||2k|λ2	|k||2k|λ2	PUNCT
ejpam-6667	338	1	+	+	SYM
ejpam-6667	338	2	1	1	NUM
ejpam-6667	338	3	p2	p2	NOUN
ejpam-6667	338	4	(	(	PUNCT
ejpam-6667	338	5	·	·	PUNCT
ejpam-6667	338	6	)	)	PUNCT
ejpam-6667	338	7	|b|λ2w(b	|b|λ2w(b	NOUN
ejpam-6667	338	8	)	)	PUNCT
ejpam-6667	338	9	1	1	NUM
ejpam-6667	338	10	p2	p2	NOUN
ejpam-6667	338	11	(	(	PUNCT
ejpam-6667	338	12	·	·	PUNCT
ejpam-6667	338	13	)	)	PUNCT
ejpam-6667	338	14	≤	≤	PROPN
ejpam-6667	338	15	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	338	16	(	(	PUNCT
ejpam-6667	338	17	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	PROPN
ejpam-6667	338	18	(	(	PUNCT
ejpam-6667	338	19	·	·	PUNCT
ejpam-6667	338	20	)	)	PUNCT
ejpam-6667	338	21	)	)	PUNCT
ejpam-6667	338	22	combine	combine	VERB
ejpam-6667	338	23	all	all	DET
ejpam-6667	338	24	the	the	DET
ejpam-6667	338	25	results	result	NOUN
ejpam-6667	338	26	of	of	ADP
ejpam-6667	338	27	a1	a1	NOUN
ejpam-6667	338	28	,	,	PUNCT
ejpam-6667	338	29	a2	a2	PROPN
ejpam-6667	338	30	,	,	PUNCT
ejpam-6667	338	31	a21	a21	PROPN
ejpam-6667	338	32	,	,	PUNCT
ejpam-6667	338	33	a22	a22	PROPN
ejpam-6667	338	34	,	,	PUNCT
ejpam-6667	338	35	we	we	PRON
ejpam-6667	338	36	obtain	obtain	VERB
ejpam-6667	338	37	the	the	DET
ejpam-6667	338	38	required	require	VERB
ejpam-6667	338	39	result	result	NOUN
ejpam-6667	338	40	∥[b	∥[b	PROPN
ejpam-6667	338	41	,	,	PUNCT
ejpam-6667	338	42	hα]f∥lp2(·)(wp2	hα]f∥lp2(·)(wp2	X
ejpam-6667	338	43	(	(	PUNCT
ejpam-6667	338	44	·	·	PUNCT
ejpam-6667	338	45	)	)	PUNCT
ejpam-6667	338	46	)	)	PUNCT
ejpam-6667	339	1	≤	≤	PROPN
ejpam-6667	339	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	339	3	(	(	PUNCT
ejpam-6667	339	4	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	PROPN
ejpam-6667	339	5	(	(	PUNCT
ejpam-6667	339	6	·	·	PUNCT
ejpam-6667	339	7	)	)	PUNCT
ejpam-6667	339	8	)	)	PUNCT
ejpam-6667	340	1	∥[b	∥[b	PROPN
ejpam-6667	340	2	,	,	PUNCT
ejpam-6667	340	3	hα]f∥ḃp2(·),λ2	hα]f∥ḃp2(·),λ2	PROPN
ejpam-6667	340	4	(	(	PUNCT
ejpam-6667	340	5	wp2	wp2	PROPN
ejpam-6667	340	6	(	(	PUNCT
ejpam-6667	340	7	·	·	PUNCT
ejpam-6667	340	8	)	)	PUNCT
ejpam-6667	340	9	)	)	PUNCT
ejpam-6667	340	10	≤	≤	PROPN
ejpam-6667	341	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	341	2	(	(	PUNCT
ejpam-6667	341	3	wp1	wp1	PROPN
ejpam-6667	341	4	(	(	PUNCT
ejpam-6667	341	5	·	·	PUNCT
ejpam-6667	341	6	)	)	PUNCT
ejpam-6667	341	7	)	)	PUNCT
ejpam-6667	341	8	.	.	PUNCT
ejpam-6667	342	1	□	□	PUNCT
ejpam-6667	342	2	theorem	theorem	ADJ
ejpam-6667	342	3	4	4	NUM
ejpam-6667	342	4	.	.	PUNCT
ejpam-6667	343	1	let	let	VERB
ejpam-6667	343	2	p1	p1	PROPN
ejpam-6667	343	3	(	(	PUNCT
ejpam-6667	343	4	·	·	PUNCT
ejpam-6667	343	5	)	)	PUNCT
ejpam-6667	343	6	,	,	PUNCT
ejpam-6667	343	7	p2	p2	X
ejpam-6667	343	8	(	(	PUNCT
ejpam-6667	343	9	·	·	PUNCT
ejpam-6667	343	10	)	)	PUNCT
ejpam-6667	343	11	,	,	PUNCT
ejpam-6667	343	12	p	p	X
ejpam-6667	343	13	(	(	PUNCT
ejpam-6667	343	14	·	·	PUNCT
ejpam-6667	343	15	)	)	PUNCT
ejpam-6667	343	16	,	,	PUNCT
ejpam-6667	343	17	and	and	CCONJ
ejpam-6667	343	18	α	α	PRON
ejpam-6667	343	19	be	be	AUX
ejpam-6667	343	20	defined	define	VERB
ejpam-6667	343	21	the	the	DET
ejpam-6667	343	22	same	same	ADJ
ejpam-6667	343	23	way	way	NOUN
ejpam-6667	343	24	as	as	ADP
ejpam-6667	343	25	in	in	ADP
ejpam-6667	343	26	theorem	theorem	NOUN
ejpam-6667	343	27	3	3	X
ejpam-6667	343	28	.	.	PUNCT
ejpam-6667	344	1	if	if	SCONJ
ejpam-6667	344	2	b	b	PROPN
ejpam-6667	344	3	∈	∈	PROPN
ejpam-6667	344	4	∥b∥cbmop(·),λ(wp	∥b∥cbmop(·),λ(wp	X
ejpam-6667	344	5	(	(	PUNCT
ejpam-6667	344	6	·	·	PUNCT
ejpam-6667	344	7	)	)	PUNCT
ejpam-6667	344	8	)	)	PUNCT
ejpam-6667	344	9	,	,	PUNCT
ejpam-6667	344	10	µ	µ	X
ejpam-6667	344	11	=	=	SYM
ejpam-6667	344	12	λ1	λ1	PROPN
ejpam-6667	344	13	+	+	CCONJ
ejpam-6667	344	14	α	α	PROPN
ejpam-6667	344	15	n	n	NOUN
ejpam-6667	344	16	and	and	CCONJ
ejpam-6667	344	17	λ2	λ2	NOUN
ejpam-6667	344	18	=	=	PUNCT
ejpam-6667	344	19	λ+	λ+	PUNCT
ejpam-6667	344	20	λ1	λ1	VERB
ejpam-6667	344	21	+	+	CCONJ
ejpam-6667	344	22	α	α	PROPN
ejpam-6667	344	23	n	n	NOUN
ejpam-6667	344	24	,	,	PUNCT
ejpam-6667	344	25	then	then	ADV
ejpam-6667	344	26	∥[b	∥[b	PROPN
ejpam-6667	344	27	,	,	PUNCT
ejpam-6667	344	28	h∗	h∗	PROPN
ejpam-6667	344	29	α]f∥ḃp2(·),λ2	α]f∥ḃp2(·),λ2	PROPN
ejpam-6667	344	30	(	(	PUNCT
ejpam-6667	344	31	wp2	wp2	PROPN
ejpam-6667	344	32	(	(	PUNCT
ejpam-6667	344	33	·	·	PUNCT
ejpam-6667	344	34	)	)	PUNCT
ejpam-6667	344	35	)	)	PUNCT
ejpam-6667	344	36	≤	≤	PROPN
ejpam-6667	345	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	345	2	(	(	PUNCT
ejpam-6667	345	3	wp1	wp1	PROPN
ejpam-6667	345	4	(	(	PUNCT
ejpam-6667	345	5	·	·	PUNCT
ejpam-6667	345	6	)	)	PUNCT
ejpam-6667	345	7	)	)	PUNCT
ejpam-6667	345	8	.	.	PUNCT
ejpam-6667	346	1	m.	m.	PROPN
ejpam-6667	346	2	asim	asim	PROPN
ejpam-6667	346	3	,	,	PUNCT
ejpam-6667	346	4	k.	k.	PROPN
ejpam-6667	346	5	suwais	suwais	PROPN
ejpam-6667	346	6	,	,	PUNCT
ejpam-6667	346	7	n.	n.	PROPN
ejpam-6667	346	8	mlaiki	mlaiki	PROPN
ejpam-6667	346	9	/	/	SYM
ejpam-6667	346	10	eur	eur	PROPN
ejpam-6667	346	11	.	.	PUNCT
ejpam-6667	347	1	j.	j.	PROPN
ejpam-6667	347	2	pure	pure	PROPN
ejpam-6667	347	3	appl	appl	PROPN
ejpam-6667	347	4	.	.	PROPN
ejpam-6667	347	5	math	math	PROPN
ejpam-6667	347	6	,	,	PUNCT
ejpam-6667	347	7	18	18	NUM
ejpam-6667	347	8	(	(	PUNCT
ejpam-6667	347	9	4	4	NUM
ejpam-6667	347	10	)	)	PUNCT
ejpam-6667	347	11	(	(	PUNCT
ejpam-6667	347	12	2025	2025	NUM
ejpam-6667	347	13	)	)	PUNCT
ejpam-6667	347	14	,	,	PUNCT
ejpam-6667	347	15	6667	6667	NUM
ejpam-6667	347	16	14	14	NUM
ejpam-6667	347	17	of	of	ADP
ejpam-6667	347	18	20	20	NUM
ejpam-6667	347	19	proof	proof	NOUN
ejpam-6667	347	20	of	of	ADP
ejpam-6667	347	21	theorem	theorem	ADJ
ejpam-6667	347	22	4	4	NUM
ejpam-6667	347	23	|[b	|[b	PROPN
ejpam-6667	347	24	,	,	PUNCT
ejpam-6667	347	25	h∗	h∗	PROPN
ejpam-6667	347	26	α]f(x	α]f(x	PROPN
ejpam-6667	347	27	)	)	PUNCT
ejpam-6667	347	28	·	·	PUNCT
ejpam-6667	347	29	χb(x)|	χb(x)|	VERB
ejpam-6667	347	30	≤	≤	NUM
ejpam-6667	347	31	∫	∫	PROPN
ejpam-6667	347	32	b(0,|x|)c	b(0,|x|)c	PROPN
ejpam-6667	347	33	|(b(x)−	|(b(x)−	PROPN
ejpam-6667	347	34	b(v))f(v)|	b(v))f(v)|	PROPN
ejpam-6667	347	35	|v|n−α	|v|n−α	VERB
ejpam-6667	347	36	dv	dv	PROPN
ejpam-6667	347	37	·	·	PUNCT
ejpam-6667	347	38	χb(x	χb(x	ADJ
ejpam-6667	347	39	)	)	PUNCT
ejpam-6667	347	40	≤	≤	NUM
ejpam-6667	347	41	∫	∫	NOUN
ejpam-6667	347	42	b(0,|x|)c	b(0,|x|)c	PROPN
ejpam-6667	347	43	|(b(x)−	|(b(x)−	PROPN
ejpam-6667	347	44	bb)f(v)|	bb)f(v)|	PROPN
ejpam-6667	347	45	|v|n−α	|v|n−α	AUX
ejpam-6667	347	46	dv	dv	PROPN
ejpam-6667	347	47	·	·	PUNCT
ejpam-6667	347	48	χb(x	χb(x	PUNCT
ejpam-6667	347	49	)	)	PUNCT
ejpam-6667	348	1	+	+	CCONJ
ejpam-6667	348	2	∫	∫	PROPN
ejpam-6667	348	3	b(0,|x|)c	b(0,|x|)c	PROPN
ejpam-6667	348	4	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	348	5	bb)f(v)|	bb)f(v)|	NOUN
ejpam-6667	348	6	|v|n−α	|v|n−α	AUX
ejpam-6667	348	7	dv	dv	PROPN
ejpam-6667	348	8	·	·	PUNCT
ejpam-6667	348	9	χb(x	χb(x	PUNCT
ejpam-6667	348	10	)	)	PUNCT
ejpam-6667	349	1	=	=	SYM
ejpam-6667	349	2	d1	d1	PROPN
ejpam-6667	349	3	+	+	SYM
ejpam-6667	349	4	d2	d2	NOUN
ejpam-6667	349	5	.	.	PUNCT
ejpam-6667	349	6	d1	d1	PROPN
ejpam-6667	349	7	=	=	SYM
ejpam-6667	349	8	∫	∫	PROPN
ejpam-6667	349	9	b(0,|x|)c	b(0,|x|)c	PROPN
ejpam-6667	349	10	|(b(x)−	|(b(x)−	PROPN
ejpam-6667	349	11	bb)f(v)|	bb)f(v)|	PROPN
ejpam-6667	349	12	|v|n−α	|v|n−α	AUX
ejpam-6667	349	13	dv	dv	PROPN
ejpam-6667	349	14	·	·	PUNCT
ejpam-6667	349	15	χb(x	χb(x	PUNCT
ejpam-6667	349	16	)	)	PUNCT
ejpam-6667	349	17	=	=	SYM
ejpam-6667	349	18	|(b(x)−	|(b(x)−	PROPN
ejpam-6667	349	19	bb)χb(x)||h∗	bb)χb(x)||h∗	NUM
ejpam-6667	349	20	αf(x)|	αf(x)|	NOUN
ejpam-6667	349	21	,	,	PUNCT
ejpam-6667	349	22	∥d1∥lp2(·)(wp2	∥d1∥lp2(·)(wp2	PUNCT
ejpam-6667	349	23	(	(	PUNCT
ejpam-6667	349	24	·	·	PUNCT
ejpam-6667	349	25	)	)	PUNCT
ejpam-6667	349	26	)	)	PUNCT
ejpam-6667	350	1	=	=	SYM
ejpam-6667	350	2	∥(b(x)−	∥(b(x)−	PROPN
ejpam-6667	350	3	bb)χbh	bb)χbh	PROPN
ejpam-6667	350	4	∗	∗	NOUN
ejpam-6667	350	5	αf∥lp2(·)(wp2	αf∥lp2(·)(wp2	NOUN
ejpam-6667	350	6	(	(	PUNCT
ejpam-6667	350	7	·	·	PUNCT
ejpam-6667	350	8	)	)	PUNCT
ejpam-6667	350	9	)	)	PUNCT
ejpam-6667	350	10	.	.	PUNCT
ejpam-6667	351	1	using	use	VERB
ejpam-6667	351	2	hölder	hölder	NOUN
ejpam-6667	351	3	inequality	inequality	NOUN
ejpam-6667	351	4	(	(	PUNCT
ejpam-6667	351	5	1	1	NUM
ejpam-6667	351	6	p2	p2	NOUN
ejpam-6667	351	7	(	(	PUNCT
ejpam-6667	351	8	·	·	PUNCT
ejpam-6667	351	9	)	)	PUNCT
ejpam-6667	351	10	=	=	SYM
ejpam-6667	351	11	1	1	NUM
ejpam-6667	351	12	s	s	PROPN
ejpam-6667	351	13	(	(	PUNCT
ejpam-6667	351	14	·	·	PUNCT
ejpam-6667	351	15	)	)	PUNCT
ejpam-6667	352	1	+	+	CCONJ
ejpam-6667	352	2	1	1	NUM
ejpam-6667	352	3	p	p	X
ejpam-6667	352	4	(	(	PUNCT
ejpam-6667	352	5	·	·	PUNCT
ejpam-6667	352	6	)	)	PUNCT
ejpam-6667	352	7	)	)	PUNCT
ejpam-6667	352	8	∥d1∥lp2(·)(wp2	∥d1∥lp2(·)(wp2	PUNCT
ejpam-6667	352	9	(	(	PUNCT
ejpam-6667	352	10	·	·	PUNCT
ejpam-6667	352	11	)	)	PUNCT
ejpam-6667	352	12	)	)	PUNCT
ejpam-6667	352	13	≤	≤	NOUN
ejpam-6667	353	1	c∥(b(x)−	c∥(b(x)−	PROPN
ejpam-6667	353	2	bb)χb∥lp(·)(wp(·))∥h	bb)χb∥lp(·)(wp(·))∥h	PROPN
ejpam-6667	353	3	∗	∗	NOUN
ejpam-6667	353	4	αfχb∥ls(·)(ws	αfχb∥ls(·)(ws	PROPN
ejpam-6667	353	5	(	(	PUNCT
ejpam-6667	353	6	·	·	PUNCT
ejpam-6667	353	7	)	)	PUNCT
ejpam-6667	353	8	)	)	PUNCT
ejpam-6667	354	1	=	=	PUNCT
ejpam-6667	354	2	c∥b∥cbmop(·),λ(wp(·))|b|λ∥χb∥lp(·)(wp(·))|b|µ∥χb∥ls(·)(ws(·))∥h	c∥b∥cbmop(·),λ(wp(·))|b|λ∥χb∥lp(·)(wp(·))|b|µ∥χb∥ls(·)(ws(·))∥h	ADJ
ejpam-6667	354	3	∗	∗	NOUN
ejpam-6667	354	4	αf∥ḃµ,s(·)(ws	αf∥ḃµ,s(·)(ws	NOUN
ejpam-6667	354	5	(	(	PUNCT
ejpam-6667	354	6	·	·	PUNCT
ejpam-6667	354	7	)	)	PUNCT
ejpam-6667	354	8	)	)	PUNCT
ejpam-6667	354	9	,	,	PUNCT
ejpam-6667	354	10	given	give	VERB
ejpam-6667	354	11	that	that	DET
ejpam-6667	354	12	µ	µ	NOUN
ejpam-6667	354	13	=	=	SYM
ejpam-6667	354	14	λ1	λ1	PROPN
ejpam-6667	354	15	+	+	CCONJ
ejpam-6667	354	16	α	α	PROPN
ejpam-6667	354	17	n	n	NOUN
ejpam-6667	354	18	,	,	PUNCT
ejpam-6667	354	19	using	use	VERB
ejpam-6667	354	20	the	the	DET
ejpam-6667	354	21	result	result	NOUN
ejpam-6667	354	22	of	of	ADP
ejpam-6667	354	23	theorem	theorem	ADJ
ejpam-6667	354	24	2	2	NUM
ejpam-6667	354	25	∥d1∥lp2(·)(wp2	∥d1∥lp2(·)(wp2	X
ejpam-6667	354	26	(	(	PUNCT
ejpam-6667	354	27	·	·	PUNCT
ejpam-6667	354	28	)	)	PUNCT
ejpam-6667	354	29	)	)	PUNCT
ejpam-6667	354	30	≤	≤	NUM
ejpam-6667	354	31	c∥b∥cbmop(·),λ(wp(·))|b|λ2∥χb∥lp(·)(wp(·))∥χb∥ls(·)(ws(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))|b|λ2∥χb∥lp(·)(wp(·))∥χb∥ls(·)(ws(·))∥f∥ḃp1(·),λ1	X
ejpam-6667	354	32	(	(	PUNCT
ejpam-6667	354	33	wp1	wp1	PROPN
ejpam-6667	354	34	(	(	PUNCT
ejpam-6667	354	35	·	·	PUNCT
ejpam-6667	354	36	)	)	PUNCT
ejpam-6667	354	37	)	)	PUNCT
ejpam-6667	354	38	,	,	PUNCT
ejpam-6667	354	39	≤	≤	X
ejpam-6667	354	40	c∥b∥cbmop(·),λ(wp(·))|b|λ2∥χb∥lp2(·)(wp2(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))|b|λ2∥χb∥lp2(·)(wp2(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	354	41	(	(	PUNCT
ejpam-6667	354	42	wp1	wp1	PROPN
ejpam-6667	354	43	(	(	PUNCT
ejpam-6667	354	44	·	·	PUNCT
ejpam-6667	354	45	)	)	PUNCT
ejpam-6667	354	46	)	)	PUNCT
ejpam-6667	354	47	,	,	PUNCT
ejpam-6667	354	48	d2	d2	PROPN
ejpam-6667	354	49	=	=	SYM
ejpam-6667	354	50	∫	∫	PROPN
ejpam-6667	354	51	b(0,|x|)c	b(0,|x|)c	PROPN
ejpam-6667	354	52	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	354	53	bb)f(v)|	bb)f(v)|	NOUN
ejpam-6667	354	54	|v|n−α	|v|n−α	AUX
ejpam-6667	354	55	dv	dv	PROPN
ejpam-6667	354	56	·	·	PUNCT
ejpam-6667	354	57	χb(x	χb(x	ADJ
ejpam-6667	354	58	)	)	PUNCT
ejpam-6667	354	59	.	.	PUNCT
ejpam-6667	355	1	d2	d2	PROPN
ejpam-6667	355	2	=	=	SYM
ejpam-6667	355	3	0∑	0∑	PROPN
ejpam-6667	355	4	k=−∞	k=−∞	PROPN
ejpam-6667	355	5	∫	∫	PROPN
ejpam-6667	355	6	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	355	7	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	355	8	bb)f(v)|	bb)f(v)|	PROPN
ejpam-6667	355	9	|v|n−α	|v|n−α	AUX
ejpam-6667	355	10	dv	dv	PROPN
ejpam-6667	355	11	·	·	PUNCT
ejpam-6667	355	12	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	355	13	)	)	PUNCT
ejpam-6667	355	14	≤	≤	NUM
ejpam-6667	355	15	0∑	0∑	NOUN
ejpam-6667	355	16	k=−∞	k=−∞	PROPN
ejpam-6667	355	17	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	355	18	)	)	PUNCT
ejpam-6667	356	1	∞∑	∞∑	NUM
ejpam-6667	356	2	l	l	NOUN
ejpam-6667	356	3	=	=	X
ejpam-6667	356	4	k+1	k+1	X
ejpam-6667	356	5	|2lb|	|2lb|	PUNCT
ejpam-6667	356	6	α	α	NOUN
ejpam-6667	356	7	n	n	ADP
ejpam-6667	356	8	−1	−1	NOUN
ejpam-6667	356	9	∫	∫	PROPN
ejpam-6667	356	10	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	356	11	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	356	12	b2lb)f(v)|dv	b2lb)f(v)|dv	NOUN
ejpam-6667	356	13	+	+	CCONJ
ejpam-6667	356	14	0∑	0∑	NOUN
ejpam-6667	356	15	k=−∞	k=−∞	PROPN
ejpam-6667	356	16	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	356	17	)	)	PUNCT
ejpam-6667	356	18	∞∑	∞∑	NUM
ejpam-6667	356	19	l	l	NOUN
ejpam-6667	356	20	=	=	X
ejpam-6667	356	21	k+1	k+1	X
ejpam-6667	356	22	|2lb|	|2lb|	PUNCT
ejpam-6667	356	23	α	α	NOUN
ejpam-6667	356	24	n	n	CCONJ
ejpam-6667	356	25	−1	−1	NOUN
ejpam-6667	356	26	∫	∫	NOUN
ejpam-6667	356	27	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	356	28	|(bb	|(bb	PUNCT
ejpam-6667	356	29	−	−	PROPN
ejpam-6667	356	30	b2lb)f(v)|dv	b2lb)f(v)|dv	NOUN
ejpam-6667	356	31	=	=	PROPN
ejpam-6667	356	32	d21	d21	PROPN
ejpam-6667	356	33	+	+	PROPN
ejpam-6667	356	34	d22	d22	PROPN
ejpam-6667	356	35	d21	d21	NOUN
ejpam-6667	356	36	=	=	PROPN
ejpam-6667	356	37	0∑	0∑	PROPN
ejpam-6667	356	38	k=−∞	k=−∞	PROPN
ejpam-6667	356	39	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	356	40	)	)	PUNCT
ejpam-6667	356	41	∞∑	∞∑	NUM
ejpam-6667	356	42	l	l	NOUN
ejpam-6667	356	43	=	=	X
ejpam-6667	356	44	k+1	k+1	X
ejpam-6667	356	45	|2lb|	|2lb|	PUNCT
ejpam-6667	356	46	α	α	NOUN
ejpam-6667	356	47	n	n	ADP
ejpam-6667	356	48	−1	−1	NOUN
ejpam-6667	356	49	∫	∫	PROPN
ejpam-6667	356	50	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	356	51	|(b(v)−	|(b(v)−	PROPN
ejpam-6667	356	52	b2lb)f(v)|dv	b2lb)f(v)|dv	NOUN
ejpam-6667	356	53	.	.	PUNCT
ejpam-6667	356	54	m.	m.	PROPN
ejpam-6667	356	55	asim	asim	PROPN
ejpam-6667	356	56	,	,	PUNCT
ejpam-6667	356	57	k.	k.	PROPN
ejpam-6667	356	58	suwais	suwais	PROPN
ejpam-6667	356	59	,	,	PUNCT
ejpam-6667	356	60	n.	n.	PROPN
ejpam-6667	356	61	mlaiki	mlaiki	PROPN
ejpam-6667	356	62	/	/	SYM
ejpam-6667	356	63	eur	eur	PROPN
ejpam-6667	356	64	.	.	PUNCT
ejpam-6667	357	1	j.	j.	PROPN
ejpam-6667	357	2	pure	pure	PROPN
ejpam-6667	357	3	appl	appl	PROPN
ejpam-6667	357	4	.	.	PROPN
ejpam-6667	357	5	math	math	PROPN
ejpam-6667	357	6	,	,	PUNCT
ejpam-6667	357	7	18	18	NUM
ejpam-6667	357	8	(	(	PUNCT
ejpam-6667	357	9	4	4	NUM
ejpam-6667	357	10	)	)	PUNCT
ejpam-6667	357	11	(	(	PUNCT
ejpam-6667	357	12	2025	2025	NUM
ejpam-6667	357	13	)	)	PUNCT
ejpam-6667	357	14	,	,	PUNCT
ejpam-6667	357	15	6667	6667	NUM
ejpam-6667	357	16	15	15	NUM
ejpam-6667	357	17	of	of	ADP
ejpam-6667	357	18	20	20	NUM
ejpam-6667	357	19	using	use	VERB
ejpam-6667	357	20	hölder	hölder	NOUN
ejpam-6667	357	21	inequality	inequality	NOUN
ejpam-6667	357	22	(	(	PUNCT
ejpam-6667	357	23	1	1	NUM
ejpam-6667	357	24	t	t	PROPN
ejpam-6667	357	25	(	(	PUNCT
ejpam-6667	357	26	·	·	PUNCT
ejpam-6667	357	27	)	)	PUNCT
ejpam-6667	358	1	+	+	CCONJ
ejpam-6667	358	2	1	1	NUM
ejpam-6667	358	3	p1	p1	NOUN
ejpam-6667	358	4	(	(	PUNCT
ejpam-6667	358	5	·	·	PUNCT
ejpam-6667	358	6	)	)	PUNCT
ejpam-6667	359	1	+	+	CCONJ
ejpam-6667	359	2	1	1	NUM
ejpam-6667	359	3	p	p	X
ejpam-6667	359	4	(	(	PUNCT
ejpam-6667	359	5	·	·	PUNCT
ejpam-6667	359	6	)	)	PUNCT
ejpam-6667	359	7	=	=	SYM
ejpam-6667	359	8	1	1	NUM
ejpam-6667	359	9	)	)	PUNCT
ejpam-6667	359	10	.	.	PUNCT
ejpam-6667	360	1	d21	d21	PROPN
ejpam-6667	360	2	≤	≤	PROPN
ejpam-6667	361	1	c	c	PROPN
ejpam-6667	361	2	0∑	0∑	PROPN
ejpam-6667	361	3	k=−∞	k=−∞	PROPN
ejpam-6667	361	4	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	361	5	)	)	PUNCT
ejpam-6667	362	1	∞∑	∞∑	NUM
ejpam-6667	362	2	l	l	NOUN
ejpam-6667	362	3	=	=	X
ejpam-6667	362	4	k+1	k+1	X
ejpam-6667	362	5	|2lb|	|2lb|	PUNCT
ejpam-6667	362	6	α	α	NOUN
ejpam-6667	362	7	n	n	CCONJ
ejpam-6667	362	8	−1∥(b(v)−	−1∥(b(v)−	PROPN
ejpam-6667	362	9	b2lb)χ2lb∥lp(·)(wp(·))∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	b2lb)χ2lb∥lp(·)(wp(·))∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	NOUN
ejpam-6667	362	10	(	(	PUNCT
ejpam-6667	362	11	·	·	PUNCT
ejpam-6667	362	12	)	)	PUNCT
ejpam-6667	362	13	)	)	PUNCT
ejpam-6667	363	1	=	=	PUNCT
ejpam-6667	364	1	c	c	NOUN
ejpam-6667	364	2	0∑	0∑	PROPN
ejpam-6667	364	3	k=−∞	k=−∞	PROPN
ejpam-6667	364	4	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	364	5	)	)	PUNCT
ejpam-6667	365	1	∞∑	∞∑	NUM
ejpam-6667	365	2	l	l	NOUN
ejpam-6667	365	3	=	=	X
ejpam-6667	365	4	k+1	k+1	X
ejpam-6667	365	5	|2lb|	|2lb|	PUNCT
ejpam-6667	365	6	α	α	NOUN
ejpam-6667	365	7	n	n	PRON
ejpam-6667	365	8	−1∥b∥cbmop(·),λ(wp(·))|2	−1∥b∥cbmop(·),λ(wp(·))|2	NOUN
ejpam-6667	365	9	lb|λ∥χ2lb∥lp(·)(wp	lb|λ∥χ2lb∥lp(·)(wp	NOUN
ejpam-6667	365	10	(	(	PUNCT
ejpam-6667	365	11	·	·	PUNCT
ejpam-6667	365	12	)	)	PUNCT
ejpam-6667	365	13	)	)	PUNCT
ejpam-6667	365	14	∥f∥ḃp1(·),λ1	∥f∥ḃp1(·),λ1	NUM
ejpam-6667	365	15	(	(	PUNCT
ejpam-6667	365	16	wp1(·))|2	wp1(·))|2	PROPN
ejpam-6667	365	17	lb|λ1∥χ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	lb|λ1∥χ2lb∥lp1(·)(wp1(·))∥χ2lb∥lt(·)(wt	PROPN
ejpam-6667	365	18	(	(	PUNCT
ejpam-6667	365	19	·	·	PUNCT
ejpam-6667	365	20	)	)	PUNCT
ejpam-6667	365	21	)	)	PUNCT
ejpam-6667	365	22	≤	≤	NUM
ejpam-6667	366	1	c	c	X
ejpam-6667	366	2	0∑	0∑	PROPN
ejpam-6667	366	3	k=−∞	k=−∞	PROPN
ejpam-6667	366	4	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	366	5	)	)	PUNCT
ejpam-6667	367	1	∞∑	∞∑	NUM
ejpam-6667	367	2	l	l	NOUN
ejpam-6667	367	3	=	=	X
ejpam-6667	367	4	k+1	k+1	X
ejpam-6667	367	5	|2lb|	|2lb|	PUNCT
ejpam-6667	367	6	α	α	NOUN
ejpam-6667	367	7	n	n	ADV
ejpam-6667	367	8	−1∥b∥cbmop(·),λ(wp(·))|2	−1∥b∥cbmop(·),λ(wp(·))|2	PROPN
ejpam-6667	367	9	lb|λ	lb|λ	NOUN
ejpam-6667	367	10	∥f∥ḃp1(·),λ1	∥f∥ḃp1(·),λ1	NUM
ejpam-6667	367	11	(	(	PUNCT
ejpam-6667	367	12	wp1(·))|2	wp1(·))|2	PROPN
ejpam-6667	367	13	lb|λ1∥χ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp(·)(wp(·)))′	lb|λ1∥χ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp(·)(wp(·)))′	PROPN
ejpam-6667	367	14	=	=	PUNCT
ejpam-6667	367	15	c	c	PROPN
ejpam-6667	367	16	0∑	0∑	NOUN
ejpam-6667	367	17	k=−∞	k=−∞	PROPN
ejpam-6667	367	18	χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	367	19	(	(	PUNCT
ejpam-6667	367	20	wp1	wp1	PROPN
ejpam-6667	367	21	(	(	PUNCT
ejpam-6667	367	22	·	·	PUNCT
ejpam-6667	367	23	)	)	PUNCT
ejpam-6667	367	24	)	)	PUNCT
ejpam-6667	368	1	∞∑	∞∑	NUM
ejpam-6667	368	2	l	l	NOUN
ejpam-6667	368	3	=	=	X
ejpam-6667	368	4	k+1	k+1	X
ejpam-6667	368	5	|2lb|	|2lb|	PUNCT
ejpam-6667	368	6	α	α	NOUN
ejpam-6667	368	7	n	n	NOUN
ejpam-6667	368	8	−1|2lb|λ+λ1	−1|2lb|λ+λ1	X
ejpam-6667	368	9	+	+	NOUN
ejpam-6667	368	10	1	1	NUM
ejpam-6667	368	11	=	=	SYM
ejpam-6667	368	12	c	c	NOUN
ejpam-6667	368	13	0∑	0∑	NOUN
ejpam-6667	368	14	k=−∞	k=−∞	PROPN
ejpam-6667	368	15	χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	368	16	(	(	PUNCT
ejpam-6667	368	17	wp1	wp1	PROPN
ejpam-6667	368	18	(	(	PUNCT
ejpam-6667	368	19	·	·	PUNCT
ejpam-6667	368	20	)	)	PUNCT
ejpam-6667	368	21	)	)	PUNCT
ejpam-6667	369	1	∞∑	∞∑	NUM
ejpam-6667	369	2	l	l	NOUN
ejpam-6667	369	3	=	=	NOUN
ejpam-6667	369	4	k+1	k+1	X
ejpam-6667	369	5	|2lb|λ2	|2lb|λ2	NOUN
ejpam-6667	369	6	=	=	SYM
ejpam-6667	369	7	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	369	8	(	(	PUNCT
ejpam-6667	369	9	wp1	wp1	PROPN
ejpam-6667	369	10	(	(	PUNCT
ejpam-6667	369	11	·	·	PUNCT
ejpam-6667	369	12	)	)	PUNCT
ejpam-6667	369	13	)	)	PUNCT
ejpam-6667	369	14	0∑	0∑	NOUN
ejpam-6667	369	15	k=−∞	k=−∞	PROPN
ejpam-6667	369	16	|2(k+1)b|λ2χ2kb\2k−1b(x	|2(k+1)b|λ2χ2kb\2k−1b(x	VERB
ejpam-6667	369	17	)	)	PUNCT
ejpam-6667	369	18	∥d21∥lp2(·)(wp2	∥d21∥lp2(·)(wp2	NOUN
ejpam-6667	369	19	(	(	PUNCT
ejpam-6667	369	20	·	·	PUNCT
ejpam-6667	369	21	)	)	PUNCT
ejpam-6667	369	22	)	)	PUNCT
ejpam-6667	369	23	≤	≤	PROPN
ejpam-6667	370	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	370	2	(	(	PUNCT
ejpam-6667	370	3	wp1	wp1	PROPN
ejpam-6667	370	4	(	(	PUNCT
ejpam-6667	370	5	·	·	PUNCT
ejpam-6667	370	6	)	)	PUNCT
ejpam-6667	370	7	)	)	PUNCT
ejpam-6667	371	1	0∑	0∑	NOUN
ejpam-6667	371	2	k=−∞	k=−∞	PROPN
ejpam-6667	371	3	|2(k+1)b|λ2∥χ2kb∥lp2(·)(wp2	|2(k+1)b|λ2∥χ2kb∥lp2(·)(wp2	PROPN
ejpam-6667	371	4	(	(	PUNCT
ejpam-6667	371	5	·	·	PUNCT
ejpam-6667	371	6	)	)	PUNCT
ejpam-6667	371	7	)	)	PUNCT
ejpam-6667	372	1	≤	≤	PROPN
ejpam-6667	372	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	372	3	(	(	PUNCT
ejpam-6667	372	4	wp1	wp1	PROPN
ejpam-6667	372	5	(	(	PUNCT
ejpam-6667	372	6	·	·	PUNCT
ejpam-6667	372	7	)	)	PUNCT
ejpam-6667	372	8	)	)	PUNCT
ejpam-6667	373	1	0∑	0∑	NOUN
ejpam-6667	373	2	k=−∞	k=−∞	PROPN
ejpam-6667	373	3	|2(k+1)b|λ2w(2	|2(k+1)b|λ2w(2	PROPN
ejpam-6667	373	4	kb	kb	PROPN
ejpam-6667	373	5	)	)	PUNCT
ejpam-6667	373	6	1	1	NUM
ejpam-6667	373	7	p2	p2	NOUN
ejpam-6667	373	8	(	(	PUNCT
ejpam-6667	373	9	·	·	PUNCT
ejpam-6667	373	10	)	)	PUNCT
ejpam-6667	373	11	≤	≤	PROPN
ejpam-6667	374	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	374	2	(	(	PUNCT
ejpam-6667	374	3	wp1(·))|b|λ2w(b	wp1(·))|b|λ2w(b	NOUN
ejpam-6667	374	4	)	)	PUNCT
ejpam-6667	374	5	1	1	NUM
ejpam-6667	374	6	p2	p2	NOUN
ejpam-6667	374	7	(	(	PUNCT
ejpam-6667	374	8	·	·	PUNCT
ejpam-6667	374	9	)	)	PUNCT
ejpam-6667	374	10	0∑	0∑	NOUN
ejpam-6667	374	11	k=−∞	k=−∞	PROPN
ejpam-6667	374	12	|2(k+1)|λ2	|2(k+1)|λ2	PROPN
ejpam-6667	374	13	+	+	NOUN
ejpam-6667	374	14	1	1	NUM
ejpam-6667	374	15	p2	p2	NOUN
ejpam-6667	374	16	(	(	PUNCT
ejpam-6667	374	17	·	·	PUNCT
ejpam-6667	374	18	)	)	PUNCT
ejpam-6667	374	19	≤	≤	PROPN
ejpam-6667	374	20	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	374	21	(	(	PUNCT
ejpam-6667	374	22	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	PROPN
ejpam-6667	374	23	(	(	PUNCT
ejpam-6667	374	24	·	·	PUNCT
ejpam-6667	374	25	)	)	PUNCT
ejpam-6667	374	26	)	)	PUNCT
ejpam-6667	374	27	d22	d22	NOUN
ejpam-6667	374	28	=	=	SYM
ejpam-6667	374	29	0∑	0∑	PROPN
ejpam-6667	374	30	k=−∞	k=−∞	PROPN
ejpam-6667	374	31	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	374	32	)	)	PUNCT
ejpam-6667	374	33	k∑	k∑	NOUN
ejpam-6667	374	34	l=−∞	l=−∞	INTJ
ejpam-6667	375	1	|2lb|	|2lb|	INTJ
ejpam-6667	375	2	α	α	NOUN
ejpam-6667	375	3	n	n	VERB
ejpam-6667	375	4	−1	−1	NOUN
ejpam-6667	375	5	∫	∫	NOUN
ejpam-6667	375	6	2lb\2l−1b	2lb\2l−1b	NUM
ejpam-6667	375	7	|(bb	|(bb	NOUN
ejpam-6667	375	8	−	−	PROPN
ejpam-6667	375	9	b2lb)f(v)|dv	b2lb)f(v)|dv	NOUN
ejpam-6667	375	10	.	.	PUNCT
ejpam-6667	376	1	m.	m.	PROPN
ejpam-6667	376	2	asim	asim	PROPN
ejpam-6667	376	3	,	,	PUNCT
ejpam-6667	376	4	k.	k.	PROPN
ejpam-6667	376	5	suwais	suwais	PROPN
ejpam-6667	376	6	,	,	PUNCT
ejpam-6667	376	7	n.	n.	PROPN
ejpam-6667	376	8	mlaiki	mlaiki	PROPN
ejpam-6667	376	9	/	/	SYM
ejpam-6667	376	10	eur	eur	PROPN
ejpam-6667	376	11	.	.	PUNCT
ejpam-6667	377	1	j.	j.	PROPN
ejpam-6667	377	2	pure	pure	PROPN
ejpam-6667	377	3	appl	appl	PROPN
ejpam-6667	377	4	.	.	PROPN
ejpam-6667	377	5	math	math	PROPN
ejpam-6667	377	6	,	,	PUNCT
ejpam-6667	377	7	18	18	NUM
ejpam-6667	377	8	(	(	PUNCT
ejpam-6667	377	9	4	4	NUM
ejpam-6667	377	10	)	)	PUNCT
ejpam-6667	377	11	(	(	PUNCT
ejpam-6667	377	12	2025	2025	NUM
ejpam-6667	377	13	)	)	PUNCT
ejpam-6667	377	14	,	,	PUNCT
ejpam-6667	377	15	6667	6667	NUM
ejpam-6667	377	16	16	16	NUM
ejpam-6667	377	17	of	of	ADP
ejpam-6667	377	18	20	20	NUM
ejpam-6667	377	19	here	here	ADV
ejpam-6667	377	20	we	we	PRON
ejpam-6667	377	21	use	use	VERB
ejpam-6667	377	22	inequality	inequality	NOUN
ejpam-6667	377	23	(	(	PUNCT
ejpam-6667	377	24	9	9	NUM
ejpam-6667	377	25	)	)	PUNCT
ejpam-6667	377	26	d22	d22	NOUN
ejpam-6667	377	27	≤	≤	NUM
ejpam-6667	378	1	c	c	NOUN
ejpam-6667	378	2	0∑	0∑	PROPN
ejpam-6667	378	3	k=−∞	k=−∞	PROPN
ejpam-6667	378	4	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	378	5	)	)	PUNCT
ejpam-6667	378	6	∞∑	∞∑	NUM
ejpam-6667	378	7	l	l	NOUN
ejpam-6667	378	8	=	=	X
ejpam-6667	378	9	k+1	k+1	X
ejpam-6667	378	10	|2lb|	|2lb|	PUNCT
ejpam-6667	378	11	α	α	NOUN
ejpam-6667	378	12	n	n	NOUN
ejpam-6667	378	13	−1∥b∥cbmop(·),λ(wp(·))|2	−1∥b∥cbmop(·),λ(wp(·))|2	NOUN
ejpam-6667	378	14	l+1b|λ|l|	l+1b|λ|l|	NOUN
ejpam-6667	378	15	∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp1(·)(wp1(·)))′	∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp1(·)(wp1(·)))′	PROPN
ejpam-6667	378	16	≤	≤	PROPN
ejpam-6667	378	17	c∥b∥cbmop(·),λ(wp	c∥b∥cbmop(·),λ(wp	PROPN
ejpam-6667	378	18	(	(	PUNCT
ejpam-6667	378	19	·	·	PUNCT
ejpam-6667	378	20	)	)	PUNCT
ejpam-6667	378	21	)	)	PUNCT
ejpam-6667	379	1	0∑	0∑	PROPN
ejpam-6667	379	2	k=−∞	k=−∞	PROPN
ejpam-6667	379	3	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	379	4	)	)	PUNCT
ejpam-6667	379	5	∞∑	∞∑	NUM
ejpam-6667	379	6	l	l	NOUN
ejpam-6667	379	7	=	=	X
ejpam-6667	379	8	k+1	k+1	X
ejpam-6667	379	9	|2lb|	|2lb|	PUNCT
ejpam-6667	379	10	α	α	NOUN
ejpam-6667	379	11	n	n	NOUN
ejpam-6667	379	12	−1|2l+1b|λ|l|	−1|2l+1b|λ|l|	NOUN
ejpam-6667	379	13	∥fχ2lb∥lp1(·)(wp1	∥fχ2lb∥lp1(·)(wp1	PROPN
ejpam-6667	379	14	(	(	PUNCT
ejpam-6667	379	15	·	·	PUNCT
ejpam-6667	379	16	)	)	PUNCT
ejpam-6667	379	17	)	)	PUNCT
ejpam-6667	379	18	|2lb|	|2lb|	CCONJ
ejpam-6667	379	19	∥χ2lb∥lp1(·)(wp1	∥χ2lb∥lp1(·)(wp1	NOUN
ejpam-6667	379	20	(	(	PUNCT
ejpam-6667	379	21	·	·	PUNCT
ejpam-6667	379	22	)	)	PUNCT
ejpam-6667	379	23	)	)	PUNCT
ejpam-6667	379	24	≤	≤	NUM
ejpam-6667	379	25	c∥b∥cbmop(·),λ(wp	c∥b∥cbmop(·),λ(wp	PROPN
ejpam-6667	379	26	(	(	PUNCT
ejpam-6667	379	27	·	·	PUNCT
ejpam-6667	379	28	)	)	PUNCT
ejpam-6667	379	29	)	)	PUNCT
ejpam-6667	380	1	0∑	0∑	PROPN
ejpam-6667	380	2	k=−∞	k=−∞	PROPN
ejpam-6667	380	3	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	380	4	)	)	PUNCT
ejpam-6667	380	5	∞∑	∞∑	NUM
ejpam-6667	380	6	l	l	NOUN
ejpam-6667	380	7	=	=	X
ejpam-6667	380	8	k+1	k+1	X
ejpam-6667	380	9	|2lb|	|2lb|	PUNCT
ejpam-6667	380	10	α	α	NOUN
ejpam-6667	380	11	n	n	ADV
ejpam-6667	380	12	−1|2lb|λ+1|l|∥f∥ḃp1(·),λ1	−1|2lb|λ+1|l|∥f∥ḃp1(·),λ1	ADP
ejpam-6667	380	13	(	(	PUNCT
ejpam-6667	380	14	wp1(·))|2	wp1(·))|2	PROPN
ejpam-6667	380	15	lb|λ1	lb|λ1	VERB
ejpam-6667	380	16	≤	≤	PROPN
ejpam-6667	380	17	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	380	18	(	(	PUNCT
ejpam-6667	380	19	wp1	wp1	PROPN
ejpam-6667	380	20	(	(	PUNCT
ejpam-6667	380	21	·	·	PUNCT
ejpam-6667	380	22	)	)	PUNCT
ejpam-6667	380	23	)	)	PUNCT
ejpam-6667	381	1	0∑	0∑	PROPN
ejpam-6667	381	2	k=−∞	k=−∞	PROPN
ejpam-6667	381	3	χ2kb\2k−1b(x	χ2kb\2k−1b(x	PROPN
ejpam-6667	381	4	)	)	PUNCT
ejpam-6667	381	5	∞∑	∞∑	NUM
ejpam-6667	381	6	l	l	NOUN
ejpam-6667	381	7	=	=	NOUN
ejpam-6667	381	8	k+1	k+1	NOUN
ejpam-6667	381	9	|2lb|λ+λ1	|2lb|λ+λ1	NOUN
ejpam-6667	381	10	+	+	CCONJ
ejpam-6667	381	11	α	α	PROPN
ejpam-6667	381	12	n	n	NOUN
ejpam-6667	381	13	|l|	|l|	VERB
ejpam-6667	381	14	≤	≤	PUNCT
ejpam-6667	381	15	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	381	16	(	(	PUNCT
ejpam-6667	381	17	wp1	wp1	PROPN
ejpam-6667	381	18	(	(	PUNCT
ejpam-6667	381	19	·	·	PUNCT
ejpam-6667	381	20	)	)	PUNCT
ejpam-6667	381	21	)	)	PUNCT
ejpam-6667	382	1	0∑	0∑	PROPN
ejpam-6667	382	2	k=−∞	k=−∞	PROPN
ejpam-6667	382	3	χ2kb\2k−1b(x)|2k+1b|λ2	χ2kb\2k−1b(x)|2k+1b|λ2	VERB
ejpam-6667	382	4	|k	|k	NOUN
ejpam-6667	383	1	+	+	CCONJ
ejpam-6667	383	2	1|	1|	NUM
ejpam-6667	383	3	≤	≤	PROPN
ejpam-6667	383	4	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	383	5	(	(	PUNCT
ejpam-6667	383	6	wp1	wp1	PROPN
ejpam-6667	383	7	(	(	PUNCT
ejpam-6667	383	8	·	·	PUNCT
ejpam-6667	383	9	)	)	PUNCT
ejpam-6667	383	10	)	)	PUNCT
ejpam-6667	384	1	0∑	0∑	NOUN
ejpam-6667	384	2	k=−∞	k=−∞	PROPN
ejpam-6667	385	1	|k	|k	NOUN
ejpam-6667	386	1	+	+	CCONJ
ejpam-6667	386	2	1||2k+1b|λ2χ2kb\2k−1b(x	1||2k+1b|λ2χ2kb\2k−1b(x	NUM
ejpam-6667	387	1	)	)	PUNCT
ejpam-6667	387	2	∥d22∥lp2(·)(wp2	∥d22∥lp2(·)(wp2	NOUN
ejpam-6667	387	3	(	(	PUNCT
ejpam-6667	387	4	·	·	PUNCT
ejpam-6667	387	5	)	)	PUNCT
ejpam-6667	387	6	)	)	PUNCT
ejpam-6667	388	1	≤	≤	PROPN
ejpam-6667	388	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	388	3	(	(	PUNCT
ejpam-6667	388	4	wp1	wp1	PROPN
ejpam-6667	388	5	(	(	PUNCT
ejpam-6667	388	6	·	·	PUNCT
ejpam-6667	388	7	)	)	PUNCT
ejpam-6667	388	8	)	)	PUNCT
ejpam-6667	389	1	0∑	0∑	NOUN
ejpam-6667	389	2	k=−∞	k=−∞	PROPN
ejpam-6667	390	1	|k	|k	NOUN
ejpam-6667	390	2	+	+	CCONJ
ejpam-6667	390	3	1||2k+1b|λ2∥χ2kb∥lp2(·)(wp2	1||2k+1b|λ2∥χ2kb∥lp2(·)(wp2	NUM
ejpam-6667	390	4	(	(	PUNCT
ejpam-6667	390	5	·	·	PUNCT
ejpam-6667	390	6	)	)	PUNCT
ejpam-6667	390	7	)	)	PUNCT
ejpam-6667	391	1	≤	≤	PROPN
ejpam-6667	391	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	391	3	(	(	PUNCT
ejpam-6667	391	4	wp1	wp1	PROPN
ejpam-6667	391	5	(	(	PUNCT
ejpam-6667	391	6	·	·	PUNCT
ejpam-6667	391	7	)	)	PUNCT
ejpam-6667	391	8	)	)	PUNCT
ejpam-6667	392	1	0∑	0∑	NOUN
ejpam-6667	392	2	k=−∞	k=−∞	PROPN
ejpam-6667	393	1	|k	|k	X
ejpam-6667	393	2	+	+	CCONJ
ejpam-6667	393	3	1||2k+1b|λ2w(2	1||2k+1b|λ2w(2	NUM
ejpam-6667	393	4	kb	kb	NOUN
ejpam-6667	393	5	)	)	PUNCT
ejpam-6667	393	6	1	1	NUM
ejpam-6667	393	7	p2	p2	NOUN
ejpam-6667	393	8	(	(	PUNCT
ejpam-6667	393	9	·	·	PUNCT
ejpam-6667	393	10	)	)	PUNCT
ejpam-6667	393	11	≤	≤	PROPN
ejpam-6667	394	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	394	2	(	(	PUNCT
ejpam-6667	394	3	wp1	wp1	PROPN
ejpam-6667	394	4	(	(	PUNCT
ejpam-6667	394	5	·	·	PUNCT
ejpam-6667	394	6	)	)	PUNCT
ejpam-6667	394	7	)	)	PUNCT
ejpam-6667	395	1	0∑	0∑	NOUN
ejpam-6667	395	2	k=−∞	k=−∞	PROPN
ejpam-6667	396	1	|k	|k	NOUN
ejpam-6667	397	1	+	+	CCONJ
ejpam-6667	397	2	1||2k+1|λ2	1||2k+1|λ2	NUM
ejpam-6667	397	3	+	+	SYM
ejpam-6667	397	4	1	1	NUM
ejpam-6667	397	5	p2	p2	NOUN
ejpam-6667	397	6	(	(	PUNCT
ejpam-6667	397	7	·	·	PUNCT
ejpam-6667	397	8	)	)	PUNCT
ejpam-6667	397	9	|b|λ2w(b	|b|λ2w(b	NOUN
ejpam-6667	397	10	)	)	PUNCT
ejpam-6667	397	11	1	1	NUM
ejpam-6667	397	12	p2	p2	NOUN
ejpam-6667	397	13	(	(	PUNCT
ejpam-6667	397	14	·	·	PUNCT
ejpam-6667	397	15	)	)	PUNCT
ejpam-6667	397	16	≤	≤	PROPN
ejpam-6667	398	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	398	2	(	(	PUNCT
ejpam-6667	398	3	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	PROPN
ejpam-6667	398	4	(	(	PUNCT
ejpam-6667	398	5	·	·	PUNCT
ejpam-6667	398	6	)	)	PUNCT
ejpam-6667	398	7	)	)	PUNCT
ejpam-6667	398	8	combine	combine	VERB
ejpam-6667	398	9	all	all	DET
ejpam-6667	398	10	results	result	NOUN
ejpam-6667	398	11	of	of	ADP
ejpam-6667	398	12	d1	d1	NOUN
ejpam-6667	398	13	,	,	PUNCT
ejpam-6667	398	14	d2	d2	PROPN
ejpam-6667	398	15	,	,	PUNCT
ejpam-6667	398	16	d21	d21	NOUN
ejpam-6667	398	17	,	,	PUNCT
ejpam-6667	398	18	d22	d22	PROPN
ejpam-6667	398	19	,	,	PUNCT
ejpam-6667	398	20	we	we	PRON
ejpam-6667	398	21	obtain	obtain	VERB
ejpam-6667	398	22	the	the	DET
ejpam-6667	398	23	required	require	VERB
ejpam-6667	398	24	result	result	NOUN
ejpam-6667	398	25	∥[b	∥[b	PROPN
ejpam-6667	398	26	,	,	PUNCT
ejpam-6667	398	27	h∗	h∗	PROPN
ejpam-6667	398	28	α]fχb∥lp2(·)(wp2	α]fχb∥lp2(·)(wp2	NUM
ejpam-6667	398	29	(	(	PUNCT
ejpam-6667	398	30	·	·	PUNCT
ejpam-6667	398	31	)	)	PUNCT
ejpam-6667	398	32	)	)	PUNCT
ejpam-6667	399	1	≤	≤	PROPN
ejpam-6667	399	2	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	399	3	(	(	PUNCT
ejpam-6667	399	4	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	wp1(·))|b|λ2∥χb∥lp2(·)(wp2	PROPN
ejpam-6667	399	5	(	(	PUNCT
ejpam-6667	399	6	·	·	PUNCT
ejpam-6667	399	7	)	)	PUNCT
ejpam-6667	399	8	)	)	PUNCT
ejpam-6667	400	1	∥[b	∥[b	PROPN
ejpam-6667	400	2	,	,	PUNCT
ejpam-6667	400	3	h∗	h∗	PROPN
ejpam-6667	400	4	α]f∥ḃp2(·),λ2	α]f∥ḃp2(·),λ2	PROPN
ejpam-6667	400	5	(	(	PUNCT
ejpam-6667	400	6	wp2	wp2	PROPN
ejpam-6667	400	7	(	(	PUNCT
ejpam-6667	400	8	·	·	PUNCT
ejpam-6667	400	9	)	)	PUNCT
ejpam-6667	400	10	)	)	PUNCT
ejpam-6667	400	11	≤	≤	PROPN
ejpam-6667	401	1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	c∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	PROPN
ejpam-6667	401	2	(	(	PUNCT
ejpam-6667	401	3	wp1	wp1	PROPN
ejpam-6667	401	4	(	(	PUNCT
ejpam-6667	401	5	·	·	PUNCT
ejpam-6667	401	6	)	)	PUNCT
ejpam-6667	401	7	)	)	PUNCT
ejpam-6667	401	8	.	.	PUNCT
ejpam-6667	402	1	□	□	PUNCT
ejpam-6667	402	2	5	5	X
ejpam-6667	402	3	.	.	X
ejpam-6667	402	4	conclusion	conclusion	NOUN
ejpam-6667	402	5	this	this	DET
ejpam-6667	402	6	scholarly	scholarly	ADJ
ejpam-6667	402	7	treatise	treatise	NOUN
ejpam-6667	402	8	vouchsafes	vouchsafe	VERB
ejpam-6667	402	9	momentous	momentous	ADJ
ejpam-6667	402	10	progressions	progression	NOUN
ejpam-6667	402	11	in	in	ADP
ejpam-6667	402	12	the	the	DET
ejpam-6667	402	13	analytical	analytical	ADJ
ejpam-6667	402	14	dissection	dissection	NOUN
ejpam-6667	402	15	of	of	ADP
ejpam-6667	402	16	fractional	fractional	ADJ
ejpam-6667	402	17	hardy	hardy	ADJ
ejpam-6667	402	18	operators	operator	NOUN
ejpam-6667	402	19	,	,	PUNCT
ejpam-6667	402	20	meticulously	meticulously	ADV
ejpam-6667	402	21	ensconced	ensconce	VERB
ejpam-6667	402	22	within	within	ADP
ejpam-6667	402	23	the	the	DET
ejpam-6667	402	24	structural	structural	ADJ
ejpam-6667	402	25	fabric	fabric	NOUN
ejpam-6667	402	26	of	of	ADP
ejpam-6667	402	27	m.	m.	PROPN
ejpam-6667	402	28	asim	asim	PROPN
ejpam-6667	402	29	,	,	PUNCT
ejpam-6667	402	30	k.	k.	PROPN
ejpam-6667	402	31	suwais	suwais	PROPN
ejpam-6667	402	32	,	,	PUNCT
ejpam-6667	402	33	n.	n.	PROPN
ejpam-6667	402	34	mlaiki	mlaiki	PROPN
ejpam-6667	402	35	/	/	SYM
ejpam-6667	402	36	eur	eur	PROPN
ejpam-6667	402	37	.	.	PUNCT
ejpam-6667	403	1	j.	j.	PROPN
ejpam-6667	403	2	pure	pure	PROPN
ejpam-6667	403	3	appl	appl	PROPN
ejpam-6667	403	4	.	.	PROPN
ejpam-6667	403	5	math	math	PROPN
ejpam-6667	403	6	,	,	PUNCT
ejpam-6667	403	7	18	18	NUM
ejpam-6667	403	8	(	(	PUNCT
ejpam-6667	403	9	4	4	NUM
ejpam-6667	403	10	)	)	PUNCT
ejpam-6667	403	11	(	(	PUNCT
ejpam-6667	403	12	2025	2025	NUM
ejpam-6667	403	13	)	)	PUNCT
ejpam-6667	403	14	,	,	PUNCT
ejpam-6667	403	15	6667	6667	NUM
ejpam-6667	403	16	17	17	NUM
ejpam-6667	403	17	of	of	ADP
ejpam-6667	403	18	20	20	NUM
ejpam-6667	403	19	weighted	weight	VERB
ejpam-6667	403	20	central	central	ADJ
ejpam-6667	403	21	morrey	morrey	NOUN
ejpam-6667	403	22	spaces	space	NOUN
ejpam-6667	403	23	imbued	imbue	VERB
ejpam-6667	403	24	with	with	ADP
ejpam-6667	403	25	variable	variable	ADJ
ejpam-6667	403	26	exponents	exponent	NOUN
ejpam-6667	403	27	.	.	PUNCT
ejpam-6667	404	1	the	the	DET
ejpam-6667	404	2	present	present	ADJ
ejpam-6667	404	3	intellectual	intellectual	ADJ
ejpam-6667	404	4	enterprise	enterprise	NOUN
ejpam-6667	404	5	is	be	AUX
ejpam-6667	404	6	poised	poise	VERB
ejpam-6667	404	7	to	to	PART
ejpam-6667	404	8	inaugurate	inaugurate	VERB
ejpam-6667	404	9	uncharted	uncharted	ADJ
ejpam-6667	404	10	pathways	pathway	NOUN
ejpam-6667	404	11	for	for	ADP
ejpam-6667	404	12	erudition	erudition	NOUN
ejpam-6667	404	13	in	in	ADP
ejpam-6667	404	14	the	the	DET
ejpam-6667	404	15	mathematical	mathematical	ADJ
ejpam-6667	404	16	and	and	CCONJ
ejpam-6667	404	17	physical	physical	ADJ
ejpam-6667	404	18	sciences	science	NOUN
ejpam-6667	404	19	—	—	PUNCT
ejpam-6667	404	20	most	most	ADV
ejpam-6667	404	21	conspicuously	conspicuously	ADV
ejpam-6667	404	22	within	within	ADP
ejpam-6667	404	23	the	the	DET
ejpam-6667	404	24	abstruse	abstruse	ADJ
ejpam-6667	404	25	territories	territory	NOUN
ejpam-6667	404	26	of	of	ADP
ejpam-6667	404	27	quantum	quantum	ADJ
ejpam-6667	404	28	mechanics	mechanic	NOUN
ejpam-6667	404	29	and	and	CCONJ
ejpam-6667	404	30	mathematical	mathematical	ADJ
ejpam-6667	404	31	modeling	modeling	NOUN
ejpam-6667	404	32	—	—	PUNCT
ejpam-6667	404	33	thereby	thereby	ADV
ejpam-6667	404	34	engendering	engender	VERB
ejpam-6667	404	35	novel	novel	ADJ
ejpam-6667	404	36	prospects	prospect	NOUN
ejpam-6667	404	37	for	for	ADP
ejpam-6667	404	38	exploratory	exploratory	ADJ
ejpam-6667	404	39	inquiry	inquiry	NOUN
ejpam-6667	404	40	and	and	CCONJ
ejpam-6667	404	41	theoretical	theoretical	ADJ
ejpam-6667	404	42	augmentation	augmentation	NOUN
ejpam-6667	404	43	.	.	PUNCT
ejpam-6667	405	1	acknowledgements	acknowledgement	VERB
ejpam-6667	405	2	the	the	DET
ejpam-6667	405	3	author	author	NOUN
ejpam-6667	405	4	khaled	khaled	PROPN
ejpam-6667	405	5	suwais	suwais	PROPN
ejpam-6667	405	6	would	would	AUX
ejpam-6667	405	7	like	like	VERB
ejpam-6667	405	8	to	to	PART
ejpam-6667	405	9	thank	thank	VERB
ejpam-6667	405	10	arab	arab	PROPN
ejpam-6667	405	11	open	open	PROPN
ejpam-6667	405	12	university	university	PROPN
ejpam-6667	405	13	for	for	ADP
ejpam-6667	405	14	supporting	support	VERB
ejpam-6667	405	15	this	this	DET
ejpam-6667	405	16	work	work	NOUN
ejpam-6667	405	17	.	.	PUNCT
ejpam-6667	406	1	the	the	DET
ejpam-6667	406	2	authors	author	NOUN
ejpam-6667	406	3	n.	n.	PROPN
ejpam-6667	406	4	mlaiki	mlaiki	PROPN
ejpam-6667	406	5	would	would	AUX
ejpam-6667	406	6	like	like	VERB
ejpam-6667	406	7	to	to	PART
ejpam-6667	406	8	thank	thank	VERB
ejpam-6667	406	9	prince	prince	PROPN
ejpam-6667	406	10	sultan	sultan	PROPN
ejpam-6667	406	11	university	university	PROPN
ejpam-6667	406	12	for	for	ADP
ejpam-6667	406	13	the	the	DET
ejpam-6667	406	14	support	support	NOUN
ejpam-6667	406	15	through	through	ADP
ejpam-6667	406	16	the	the	DET
ejpam-6667	406	17	tas	tas	PROPN
ejpam-6667	406	18	research	research	NOUN
ejpam-6667	406	19	lab	lab	NOUN
ejpam-6667	406	20	.	.	PUNCT
ejpam-6667	407	1	authors	author	NOUN
ejpam-6667	407	2	’	'	PUNCT
ejpam-6667	407	3	contributions	contribution	NOUN
ejpam-6667	407	4	m.a	m.a	PROPN
ejpam-6667	407	5	.	.	PROPN
ejpam-6667	407	6	,	,	PUNCT
ejpam-6667	407	7	s.h	s.h	PROPN
ejpam-6667	407	8	.	.	PROPN
ejpam-6667	407	9	and	and	CCONJ
ejpam-6667	407	10	n.m	n.m	PROPN
ejpam-6667	407	11	.	.	PROPN
ejpam-6667	407	12	wrote	write	VERB
ejpam-6667	407	13	the	the	DET
ejpam-6667	407	14	main	main	ADJ
ejpam-6667	407	15	manuscript	manuscript	NOUN
ejpam-6667	407	16	text	text	NOUN
ejpam-6667	407	17	.	.	PUNCT
ejpam-6667	408	1	all	all	DET
ejpam-6667	408	2	authors	author	NOUN
ejpam-6667	408	3	reviewed	review	VERB
ejpam-6667	408	4	the	the	DET
ejpam-6667	408	5	manuscript	manuscript	NOUN
ejpam-6667	408	6	.	.	PUNCT
ejpam-6667	409	1	references	reference	NOUN
ejpam-6667	409	2	[	[	X
ejpam-6667	409	3	1	1	NUM
ejpam-6667	409	4	]	]	PUNCT
ejpam-6667	409	5	g.	g.	PROPN
ejpam-6667	409	6	h.	h.	PROPN
ejpam-6667	409	7	hardy	hardy	PROPN
ejpam-6667	409	8	.	.	PUNCT
ejpam-6667	410	1	note	note	NOUN
ejpam-6667	410	2	on	on	ADP
ejpam-6667	410	3	a	a	DET
ejpam-6667	410	4	theorem	theorem	NOUN
ejpam-6667	410	5	of	of	ADP
ejpam-6667	410	6	hilbert	hilbert	PROPN
ejpam-6667	410	7	.	.	PUNCT
ejpam-6667	411	1	mathematische	mathematische	PROPN
ejpam-6667	411	2	zeitschrift	zeitschrift	NOUN
ejpam-6667	411	3	,	,	PUNCT
ejpam-6667	411	4	6:314–317	6:314–317	NUM
ejpam-6667	411	5	,	,	PUNCT
ejpam-6667	411	6	1920	1920	NUM
ejpam-6667	411	7	.	.	PUNCT
ejpam-6667	412	1	[	[	X
ejpam-6667	412	2	2	2	NUM
ejpam-6667	412	3	]	]	PUNCT
ejpam-6667	412	4	w.	w.	PROPN
ejpam-6667	412	5	g.	g.	PROPN
ejpam-6667	412	6	faris	faris	PROPN
ejpam-6667	412	7	.	.	PUNCT
ejpam-6667	413	1	weak	weak	ADJ
ejpam-6667	413	2	lebesgue	lebesgue	NOUN
ejpam-6667	413	3	spaces	space	NOUN
ejpam-6667	413	4	and	and	CCONJ
ejpam-6667	413	5	quantum	quantum	ADJ
ejpam-6667	413	6	mechanical	mechanical	ADJ
ejpam-6667	413	7	binding	binding	NOUN
ejpam-6667	413	8	.	.	PUNCT
ejpam-6667	414	1	duke	duke	PROPN
ejpam-6667	414	2	mathematical	mathematical	PROPN
ejpam-6667	414	3	journal	journal	PROPN
ejpam-6667	414	4	,	,	PUNCT
ejpam-6667	414	5	43:365–373	43:365–373	PROPN
ejpam-6667	414	6	,	,	PUNCT
ejpam-6667	414	7	1976	1976	NUM
ejpam-6667	414	8	.	.	PUNCT
ejpam-6667	415	1	[	[	X
ejpam-6667	415	2	3	3	X
ejpam-6667	415	3	]	]	PUNCT
ejpam-6667	415	4	z.	z.	PROPN
ejpam-6667	415	5	fu	fu	PROPN
ejpam-6667	415	6	,	,	PUNCT
ejpam-6667	415	7	z.	z.	PROPN
ejpam-6667	415	8	liu	liu	PROPN
ejpam-6667	415	9	,	,	PUNCT
ejpam-6667	415	10	s.	s.	PROPN
ejpam-6667	415	11	lu	lu	PROPN
ejpam-6667	415	12	,	,	PUNCT
ejpam-6667	415	13	and	and	CCONJ
ejpam-6667	415	14	h.	h.	PROPN
ejpam-6667	415	15	wang	wang	PROPN
ejpam-6667	415	16	.	.	PUNCT
ejpam-6667	416	1	characterization	characterization	NOUN
ejpam-6667	416	2	for	for	ADP
ejpam-6667	416	3	commutators	commutator	NOUN
ejpam-6667	416	4	of	of	ADP
ejpam-6667	416	5	ndimensional	ndimensional	ADJ
ejpam-6667	416	6	fractional	fractional	ADJ
ejpam-6667	416	7	hardy	hardy	ADJ
ejpam-6667	416	8	operators	operator	NOUN
ejpam-6667	416	9	.	.	PUNCT
ejpam-6667	417	1	science	science	NOUN
ejpam-6667	417	2	in	in	ADP
ejpam-6667	417	3	china	china	PROPN
ejpam-6667	417	4	series	series	PROPN
ejpam-6667	417	5	a	a	PRON
ejpam-6667	417	6	:	:	PUNCT
ejpam-6667	417	7	mathematics	mathematic	NOUN
ejpam-6667	417	8	,	,	PUNCT
ejpam-6667	417	9	50:1418–1426	50:1418–1426	NUM
ejpam-6667	417	10	,	,	PUNCT
ejpam-6667	417	11	2007	2007	NUM
ejpam-6667	417	12	.	.	PUNCT
ejpam-6667	418	1	[	[	X
ejpam-6667	418	2	4	4	X
ejpam-6667	418	3	]	]	X
ejpam-6667	418	4	o.	o.	NOUN
ejpam-6667	418	5	kováčik	kováčik	PROPN
ejpam-6667	418	6	and	and	CCONJ
ejpam-6667	418	7	j.	j.	PROPN
ejpam-6667	418	8	rákosńık	rákosńık	PROPN
ejpam-6667	418	9	.	.	PUNCT
ejpam-6667	419	1	on	on	ADP
ejpam-6667	419	2	spaces	space	NOUN
ejpam-6667	419	3	lp(x	lp(x	PUNCT
ejpam-6667	419	4	)	)	PUNCT
ejpam-6667	419	5	and	and	CCONJ
ejpam-6667	419	6	wk	wk	PROPN
ejpam-6667	419	7	,	,	PUNCT
ejpam-6667	419	8	p(x	p(x	PROPN
ejpam-6667	419	9	)	)	PUNCT
ejpam-6667	419	10	.	.	PUNCT
ejpam-6667	420	1	czechoslovak	czechoslovak	ADJ
ejpam-6667	420	2	mathematical	mathematical	PROPN
ejpam-6667	420	3	journal	journal	PROPN
ejpam-6667	420	4	,	,	PUNCT
ejpam-6667	420	5	41(4):592–618	41(4):592–618	NOUN
ejpam-6667	420	6	,	,	PUNCT
ejpam-6667	420	7	1991	1991	NUM
ejpam-6667	420	8	.	.	PUNCT
ejpam-6667	421	1	[	[	X
ejpam-6667	421	2	5	5	X
ejpam-6667	421	3	]	]	PUNCT
ejpam-6667	421	4	s.	s.	PROPN
ejpam-6667	421	5	samko	samko	PROPN
ejpam-6667	421	6	.	.	PUNCT
ejpam-6667	422	1	hardy	hardy	ADJ
ejpam-6667	422	2	inequality	inequality	NOUN
ejpam-6667	422	3	in	in	ADP
ejpam-6667	422	4	the	the	DET
ejpam-6667	422	5	generalized	generalized	ADJ
ejpam-6667	422	6	lebesgue	lebesgue	NOUN
ejpam-6667	422	7	spaces	space	NOUN
ejpam-6667	422	8	.	.	PUNCT
ejpam-6667	423	1	fractional	fractional	ADJ
ejpam-6667	423	2	calculus	calculus	NOUN
ejpam-6667	423	3	and	and	CCONJ
ejpam-6667	423	4	applied	apply	VERB
ejpam-6667	423	5	analysis	analysis	NOUN
ejpam-6667	423	6	,	,	PUNCT
ejpam-6667	423	7	6:355–362	6:355–362	PROPN
ejpam-6667	423	8	,	,	PUNCT
ejpam-6667	423	9	2003	2003	NUM
ejpam-6667	423	10	.	.	PUNCT
ejpam-6667	424	1	[	[	X
ejpam-6667	424	2	6	6	NUM
ejpam-6667	424	3	]	]	X
ejpam-6667	424	4	lars	lar	NOUN
ejpam-6667	424	5	diening	diening	PROPN
ejpam-6667	424	6	and	and	CCONJ
ejpam-6667	424	7	stefan	stefan	PROPN
ejpam-6667	424	8	samko	samko	PROPN
ejpam-6667	424	9	.	.	PUNCT
ejpam-6667	425	1	hardy	hardy	ADJ
ejpam-6667	425	2	inequality	inequality	NOUN
ejpam-6667	425	3	in	in	ADP
ejpam-6667	425	4	variable	variable	ADJ
ejpam-6667	425	5	exponent	exponent	NOUN
ejpam-6667	425	6	lebesgue	lebesgue	NOUN
ejpam-6667	425	7	spaces	space	VERB
ejpam-6667	425	8	.	.	PUNCT
ejpam-6667	426	1	fractional	fractional	ADJ
ejpam-6667	426	2	calculus	calculus	NOUN
ejpam-6667	426	3	and	and	CCONJ
ejpam-6667	426	4	applied	apply	VERB
ejpam-6667	426	5	analysis	analysis	NOUN
ejpam-6667	426	6	,	,	PUNCT
ejpam-6667	426	7	10:1–18	10:1–18	NUM
ejpam-6667	426	8	,	,	PUNCT
ejpam-6667	426	9	2007	2007	NUM
ejpam-6667	426	10	.	.	PUNCT
ejpam-6667	427	1	[	[	X
ejpam-6667	427	2	7	7	X
ejpam-6667	427	3	]	]	PUNCT
ejpam-6667	427	4	p.	p.	NOUN
ejpam-6667	427	5	harjulehto	harjulehto	PROPN
ejpam-6667	427	6	,	,	PUNCT
ejpam-6667	427	7	p.	p.	NOUN
ejpam-6667	427	8	hästö	hästö	PROPN
ejpam-6667	427	9	,	,	PUNCT
ejpam-6667	427	10	and	and	CCONJ
ejpam-6667	427	11	m.	m.	PROPN
ejpam-6667	427	12	koskenoja	koskenoja	PROPN
ejpam-6667	427	13	.	.	PUNCT
ejpam-6667	428	1	hardy	hardy	ADJ
ejpam-6667	428	2	inequality	inequality	NOUN
ejpam-6667	428	3	in	in	ADP
ejpam-6667	428	4	variable	variable	ADJ
ejpam-6667	428	5	exponent	exponent	NOUN
ejpam-6667	428	6	sobolev	sobolev	NOUN
ejpam-6667	428	7	space	space	NOUN
ejpam-6667	428	8	.	.	PUNCT
ejpam-6667	429	1	georgian	georgian	PROPN
ejpam-6667	429	2	mathematical	mathematical	PROPN
ejpam-6667	429	3	journal	journal	PROPN
ejpam-6667	429	4	,	,	PUNCT
ejpam-6667	429	5	12:431–442	12:431–442	PROPN
ejpam-6667	429	6	,	,	PUNCT
ejpam-6667	429	7	2005	2005	NUM
ejpam-6667	429	8	.	.	PUNCT
ejpam-6667	430	1	[	[	X
ejpam-6667	430	2	8	8	X
ejpam-6667	430	3	]	]	X
ejpam-6667	430	4	j.	j.	PROPN
ejpam-6667	430	5	l.	l.	PROPN
ejpam-6667	430	6	wu	wu	PROPN
ejpam-6667	430	7	and	and	CCONJ
ejpam-6667	430	8	q.	q.	PROPN
ejpam-6667	430	9	g.	g.	PROPN
ejpam-6667	430	10	liu	liu	PROPN
ejpam-6667	430	11	.	.	PUNCT
ejpam-6667	431	1	λ	λ	ADJ
ejpam-6667	431	2	-	-	ADJ
ejpam-6667	431	3	central	central	ADJ
ejpam-6667	431	4	bmo	bmo	NOUN
ejpam-6667	431	5	estimates	estimate	NOUN
ejpam-6667	431	6	for	for	ADP
ejpam-6667	431	7	higher	high	ADJ
ejpam-6667	431	8	order	order	NOUN
ejpam-6667	431	9	commutators	commutator	NOUN
ejpam-6667	431	10	of	of	ADP
ejpam-6667	431	11	hardy	hardy	ADJ
ejpam-6667	431	12	operators	operator	NOUN
ejpam-6667	431	13	.	.	PUNCT
ejpam-6667	432	1	communications	communication	NOUN
ejpam-6667	432	2	in	in	ADP
ejpam-6667	432	3	mathematical	mathematical	ADJ
ejpam-6667	432	4	research	research	NOUN
ejpam-6667	432	5	,	,	PUNCT
ejpam-6667	432	6	30:201–206	30:201–206	PROPN
ejpam-6667	432	7	,	,	PUNCT
ejpam-6667	432	8	2014	2014	NUM
ejpam-6667	432	9	.	.	PUNCT
ejpam-6667	433	1	[	[	X
ejpam-6667	433	2	9	9	NUM
ejpam-6667	433	3	]	]	PUNCT
ejpam-6667	433	4	a.	a.	NOUN
ejpam-6667	433	5	hussain	hussain	PROPN
ejpam-6667	433	6	and	and	CCONJ
ejpam-6667	433	7	m.	m.	PROPN
ejpam-6667	433	8	asim	asim	PROPN
ejpam-6667	433	9	.	.	PUNCT
ejpam-6667	434	1	commutators	commutator	NOUN
ejpam-6667	434	2	of	of	ADP
ejpam-6667	434	3	the	the	DET
ejpam-6667	434	4	fractional	fractional	ADJ
ejpam-6667	434	5	hardy	hardy	ADJ
ejpam-6667	434	6	operator	operator	NOUN
ejpam-6667	434	7	on	on	ADP
ejpam-6667	434	8	weighted	weight	VERB
ejpam-6667	434	9	variable	variable	ADJ
ejpam-6667	434	10	herz	herz	PROPN
ejpam-6667	434	11	-	-	PUNCT
ejpam-6667	434	12	morrey	morrey	PROPN
ejpam-6667	434	13	spaces	space	NOUN
ejpam-6667	434	14	.	.	PUNCT
ejpam-6667	435	1	journal	journal	NOUN
ejpam-6667	435	2	of	of	ADP
ejpam-6667	435	3	function	function	NOUN
ejpam-6667	435	4	spaces	space	NOUN
ejpam-6667	435	5	,	,	PUNCT
ejpam-6667	435	6	pages	page	NOUN
ejpam-6667	435	7	article	article	NOUN
ejpam-6667	435	8	i	i	PROPN
ejpam-6667	435	9	d	d	PROPN
ejpam-6667	435	10	9705250	9705250	NUM
ejpam-6667	435	11	,	,	PUNCT
ejpam-6667	435	12	8	8	NUM
ejpam-6667	435	13	pages	page	NOUN
ejpam-6667	435	14	,	,	PUNCT
ejpam-6667	435	15	2021	2021	NUM
ejpam-6667	435	16	.	.	PUNCT
ejpam-6667	436	1	[	[	X
ejpam-6667	436	2	10	10	NUM
ejpam-6667	436	3	]	]	PUNCT
ejpam-6667	436	4	m.	m.	NOUN
ejpam-6667	436	5	asim	asim	PROPN
ejpam-6667	436	6	and	and	CCONJ
ejpam-6667	436	7	a.	a.	NOUN
ejpam-6667	436	8	hussain	hussain	PROPN
ejpam-6667	436	9	.	.	PUNCT
ejpam-6667	437	1	weighted	weight	VERB
ejpam-6667	437	2	variable	variable	ADJ
ejpam-6667	437	3	morrey	morrey	PROPN
ejpam-6667	437	4	-	-	PUNCT
ejpam-6667	437	5	herz	herz	PROPN
ejpam-6667	437	6	estimates	estimate	NOUN
ejpam-6667	437	7	for	for	ADP
ejpam-6667	437	8	fractional	fractional	ADJ
ejpam-6667	437	9	hardy	hardy	ADJ
ejpam-6667	437	10	operators	operator	NOUN
ejpam-6667	437	11	.	.	PUNCT
ejpam-6667	438	1	journal	journal	PROPN
ejpam-6667	438	2	of	of	ADP
ejpam-6667	438	3	inequalities	inequality	NOUN
ejpam-6667	438	4	and	and	CCONJ
ejpam-6667	438	5	applications	application	NOUN
ejpam-6667	438	6	,	,	PUNCT
ejpam-6667	438	7	pages	page	NOUN
ejpam-6667	438	8	article	article	NOUN
ejpam-6667	438	9	i	i	PROPN
ejpam-6667	438	10	d	d	PROPN
ejpam-6667	438	11	2739	2739	NUM
ejpam-6667	438	12	,	,	PUNCT
ejpam-6667	438	13	13	13	NUM
ejpam-6667	438	14	pages	page	NOUN
ejpam-6667	438	15	,	,	PUNCT
ejpam-6667	438	16	2021	2021	NUM
ejpam-6667	438	17	.	.	PUNCT
ejpam-6667	439	1	m.	m.	PROPN
ejpam-6667	439	2	asim	asim	PROPN
ejpam-6667	439	3	,	,	PUNCT
ejpam-6667	439	4	k.	k.	PROPN
ejpam-6667	439	5	suwais	suwais	PROPN
ejpam-6667	439	6	,	,	PUNCT
ejpam-6667	439	7	n.	n.	PROPN
ejpam-6667	439	8	mlaiki	mlaiki	PROPN
ejpam-6667	439	9	/	/	SYM
ejpam-6667	439	10	eur	eur	PROPN
ejpam-6667	439	11	.	.	PUNCT
ejpam-6667	440	1	j.	j.	PROPN
ejpam-6667	440	2	pure	pure	PROPN
ejpam-6667	440	3	appl	appl	PROPN
ejpam-6667	440	4	.	.	PROPN
ejpam-6667	440	5	math	math	PROPN
ejpam-6667	440	6	,	,	PUNCT
ejpam-6667	440	7	18	18	NUM
ejpam-6667	440	8	(	(	PUNCT
ejpam-6667	440	9	4	4	NUM
ejpam-6667	440	10	)	)	PUNCT
ejpam-6667	440	11	(	(	PUNCT
ejpam-6667	440	12	2025	2025	NUM
ejpam-6667	440	13	)	)	PUNCT
ejpam-6667	440	14	,	,	PUNCT
ejpam-6667	440	15	6667	6667	NUM
ejpam-6667	440	16	18	18	NUM
ejpam-6667	440	17	of	of	ADP
ejpam-6667	440	18	20	20	NUM
ejpam-6667	440	19	[	[	SYM
ejpam-6667	440	20	11	11	NUM
ejpam-6667	440	21	]	]	PUNCT
ejpam-6667	440	22	m.	m.	NOUN
ejpam-6667	440	23	asim	asim	PROPN
ejpam-6667	440	24	,	,	PUNCT
ejpam-6667	440	25	i.	i.	PROPN
ejpam-6667	440	26	ayoob	ayoob	PROPN
ejpam-6667	440	27	,	,	PUNCT
ejpam-6667	440	28	a.	a.	NOUN
ejpam-6667	440	29	hussain	hussain	PROPN
ejpam-6667	440	30	,	,	PUNCT
ejpam-6667	440	31	and	and	CCONJ
ejpam-6667	440	32	n.	n.	PROPN
ejpam-6667	440	33	mlaiki	mlaiki	PROPN
ejpam-6667	440	34	.	.	PUNCT
ejpam-6667	441	1	weighted	weight	VERB
ejpam-6667	441	2	estimates	estimate	NOUN
ejpam-6667	441	3	for	for	ADP
ejpam-6667	441	4	fractional	fractional	ADJ
ejpam-6667	441	5	bilinear	bilinear	VERB
ejpam-6667	441	6	hardy	hardy	ADJ
ejpam-6667	441	7	operators	operator	NOUN
ejpam-6667	441	8	on	on	ADP
ejpam-6667	441	9	variable	variable	ADJ
ejpam-6667	441	10	exponent	exponent	NOUN
ejpam-6667	441	11	morrey	morrey	PROPN
ejpam-6667	441	12	-	-	PUNCT
ejpam-6667	441	13	herz	herz	PROPN
ejpam-6667	441	14	space	space	NOUN
ejpam-6667	441	15	.	.	PUNCT
ejpam-6667	442	1	journal	journal	PROPN
ejpam-6667	442	2	of	of	ADP
ejpam-6667	442	3	inequalities	inequality	NOUN
ejpam-6667	442	4	and	and	CCONJ
ejpam-6667	442	5	applications	application	NOUN
ejpam-6667	442	6	,	,	PUNCT
ejpam-6667	442	7	2024:11	2024:11	NUM
ejpam-6667	442	8	,	,	PUNCT
ejpam-6667	442	9	2024	2024	NUM
ejpam-6667	442	10	.	.	PUNCT
ejpam-6667	443	1	[	[	X
ejpam-6667	443	2	12	12	NUM
ejpam-6667	443	3	]	]	PUNCT
ejpam-6667	443	4	a.	a.	NOUN
ejpam-6667	443	5	hussain	hussain	PROPN
ejpam-6667	443	6	,	,	PUNCT
ejpam-6667	443	7	m.	m.	NOUN
ejpam-6667	443	8	asim	asim	PROPN
ejpam-6667	443	9	,	,	PUNCT
ejpam-6667	443	10	and	and	CCONJ
ejpam-6667	443	11	f.	f.	PROPN
ejpam-6667	443	12	jarad	jarad	PROPN
ejpam-6667	443	13	.	.	PUNCT
ejpam-6667	444	1	variable	variable	ADJ
ejpam-6667	444	2	λ	λ	ADJ
ejpam-6667	444	3	-	-	ADJ
ejpam-6667	444	4	central	central	ADJ
ejpam-6667	444	5	morrey	morrey	NOUN
ejpam-6667	444	6	space	space	NOUN
ejpam-6667	444	7	estimates	estimate	NOUN
ejpam-6667	444	8	for	for	ADP
ejpam-6667	444	9	the	the	DET
ejpam-6667	444	10	fractional	fractional	ADJ
ejpam-6667	444	11	hardy	hardy	ADJ
ejpam-6667	444	12	operators	operator	NOUN
ejpam-6667	444	13	and	and	CCONJ
ejpam-6667	444	14	commutators	commutator	NOUN
ejpam-6667	444	15	.	.	PUNCT
ejpam-6667	445	1	journal	journal	NOUN
ejpam-6667	445	2	of	of	ADP
ejpam-6667	445	3	mathematics	mathematic	NOUN
ejpam-6667	445	4	,	,	PUNCT
ejpam-6667	445	5	pages	page	NOUN
ejpam-6667	445	6	article	article	NOUN
ejpam-6667	445	7	i	i	PROPN
ejpam-6667	445	8	d	d	PROPN
ejpam-6667	445	9	5855068	5855068	NUM
ejpam-6667	445	10	,	,	PUNCT
ejpam-6667	445	11	13	13	NUM
ejpam-6667	445	12	pages	page	NOUN
ejpam-6667	445	13	,	,	PUNCT
ejpam-6667	445	14	2022	2022	NUM
ejpam-6667	445	15	.	.	PUNCT
ejpam-6667	446	1	[	[	X
ejpam-6667	446	2	13	13	NUM
ejpam-6667	446	3	]	]	PUNCT
ejpam-6667	446	4	m.	m.	NOUN
ejpam-6667	446	5	izuki	izuki	PROPN
ejpam-6667	446	6	.	.	PUNCT
ejpam-6667	446	7	boundedness	boundedness	PROPN
ejpam-6667	446	8	of	of	ADP
ejpam-6667	446	9	commutators	commutator	NOUN
ejpam-6667	446	10	on	on	ADP
ejpam-6667	446	11	herz	herz	PROPN
ejpam-6667	446	12	spaces	space	NOUN
ejpam-6667	446	13	with	with	ADP
ejpam-6667	446	14	variable	variable	ADJ
ejpam-6667	446	15	exponent	exponent	NOUN
ejpam-6667	446	16	.	.	PUNCT
ejpam-6667	447	1	rendiconti	rendiconti	PROPN
ejpam-6667	447	2	del	del	PROPN
ejpam-6667	447	3	circolo	circolo	PROPN
ejpam-6667	447	4	matematico	matematico	NOUN
ejpam-6667	447	5	di	di	NOUN
ejpam-6667	447	6	palermo	palermo	NOUN
ejpam-6667	447	7	,	,	PUNCT
ejpam-6667	447	8	59:199–213	59:199–213	PROPN
ejpam-6667	447	9	,	,	PUNCT
ejpam-6667	447	10	2010	2010	NUM
ejpam-6667	447	11	.	.	PUNCT
ejpam-6667	448	1	[	[	X
ejpam-6667	448	2	14	14	NUM
ejpam-6667	448	3	]	]	X
ejpam-6667	448	4	m.	m.	NOUN
ejpam-6667	448	5	izuki	izuki	PROPN
ejpam-6667	448	6	and	and	CCONJ
ejpam-6667	448	7	k.	k.	PROPN
ejpam-6667	448	8	tachizawa	tachizawa	PROPN
ejpam-6667	448	9	.	.	PUNCT
ejpam-6667	449	1	wavelet	wavelet	NOUN
ejpam-6667	449	2	characterizations	characterization	NOUN
ejpam-6667	449	3	of	of	ADP
ejpam-6667	449	4	weighted	weight	VERB
ejpam-6667	449	5	herz	herz	PROPN
ejpam-6667	449	6	spaces	space	NOUN
ejpam-6667	449	7	.	.	PUNCT
ejpam-6667	450	1	scientiae	scientiae	PROPN
ejpam-6667	450	2	mathematicae	mathematicae	PROPN
ejpam-6667	450	3	japonicae	japonicae	PROPN
ejpam-6667	450	4	,	,	PUNCT
ejpam-6667	450	5	67:353–363	67:353–363	PROPN
ejpam-6667	450	6	,	,	PUNCT
ejpam-6667	450	7	2008	2008	NUM
ejpam-6667	450	8	.	.	PUNCT
ejpam-6667	451	1	[	[	X
ejpam-6667	451	2	15	15	NUM
ejpam-6667	451	3	]	]	X
ejpam-6667	451	4	s.	s.	PROPN
ejpam-6667	451	5	lu	lu	PROPN
ejpam-6667	451	6	,	,	PUNCT
ejpam-6667	451	7	k.	k.	PROPN
ejpam-6667	451	8	yabuta	yabuta	PROPN
ejpam-6667	451	9	,	,	PUNCT
ejpam-6667	451	10	and	and	CCONJ
ejpam-6667	451	11	k.	k.	PROPN
ejpam-6667	451	12	yang	yang	PROPN
ejpam-6667	451	13	.	.	PUNCT
ejpam-6667	452	1	boundedness	boundedness	PROPN
ejpam-6667	452	2	of	of	ADP
ejpam-6667	452	3	some	some	DET
ejpam-6667	452	4	sublinear	sublinear	NOUN
ejpam-6667	452	5	operators	operator	NOUN
ejpam-6667	452	6	in	in	ADP
ejpam-6667	452	7	weighted	weight	VERB
ejpam-6667	452	8	herz	herz	ADJ
ejpam-6667	452	9	-	-	PUNCT
ejpam-6667	452	10	type	type	NOUN
ejpam-6667	452	11	spaces	space	NOUN
ejpam-6667	452	12	.	.	PUNCT
ejpam-6667	453	1	kodai	kodai	PROPN
ejpam-6667	453	2	mathematical	mathematical	PROPN
ejpam-6667	453	3	journal	journal	PROPN
ejpam-6667	453	4	,	,	PUNCT
ejpam-6667	453	5	23:391–410	23:391–410	PROPN
ejpam-6667	453	6	,	,	PUNCT
ejpam-6667	453	7	2000	2000	NUM
ejpam-6667	453	8	.	.	PUNCT
ejpam-6667	454	1	[	[	X
ejpam-6667	454	2	16	16	NUM
ejpam-6667	454	3	]	]	X
ejpam-6667	454	4	m.	m.	NOUN
ejpam-6667	454	5	izuki	izuki	PROPN
ejpam-6667	454	6	and	and	CCONJ
ejpam-6667	454	7	t.	t.	PROPN
ejpam-6667	454	8	noi	noi	PROPN
ejpam-6667	454	9	.	.	PUNCT
ejpam-6667	455	1	boundedness	boundedness	PROPN
ejpam-6667	455	2	of	of	ADP
ejpam-6667	455	3	fractional	fractional	ADJ
ejpam-6667	455	4	integrals	integral	NOUN
ejpam-6667	455	5	on	on	ADP
ejpam-6667	455	6	weighted	weight	VERB
ejpam-6667	455	7	herz	herz	PROPN
ejpam-6667	455	8	spaces	space	NOUN
ejpam-6667	455	9	with	with	ADP
ejpam-6667	455	10	variable	variable	ADJ
ejpam-6667	455	11	exponent	exponent	NOUN
ejpam-6667	455	12	.	.	PUNCT
ejpam-6667	456	1	journal	journal	PROPN
ejpam-6667	456	2	of	of	ADP
ejpam-6667	456	3	inequalities	inequality	NOUN
ejpam-6667	456	4	and	and	CCONJ
ejpam-6667	456	5	applications	application	NOUN
ejpam-6667	456	6	,	,	PUNCT
ejpam-6667	456	7	2016:199	2016:199	NOUN
ejpam-6667	456	8	,	,	PUNCT
ejpam-6667	456	9	2016	2016	NUM
ejpam-6667	456	10	.	.	PUNCT
ejpam-6667	457	1	[	[	X
ejpam-6667	457	2	17	17	NUM
ejpam-6667	457	3	]	]	PUNCT
ejpam-6667	457	4	a.	a.	PROPN
ejpam-6667	457	5	almeida	almeida	PROPN
ejpam-6667	457	6	and	and	CCONJ
ejpam-6667	457	7	d.	d.	PROPN
ejpam-6667	457	8	drihem	drihem	PROPN
ejpam-6667	457	9	.	.	PUNCT
ejpam-6667	458	1	maximal	maximal	ADJ
ejpam-6667	458	2	,	,	PUNCT
ejpam-6667	458	3	potential	potential	ADJ
ejpam-6667	458	4	and	and	CCONJ
ejpam-6667	458	5	singular	singular	ADJ
ejpam-6667	458	6	type	type	NOUN
ejpam-6667	458	7	operators	operator	NOUN
ejpam-6667	458	8	on	on	ADP
ejpam-6667	458	9	herz	herz	PROPN
ejpam-6667	458	10	spaces	space	NOUN
ejpam-6667	458	11	with	with	ADP
ejpam-6667	458	12	variable	variable	ADJ
ejpam-6667	458	13	exponents	exponent	NOUN
ejpam-6667	458	14	.	.	PUNCT
ejpam-6667	459	1	journal	journal	NOUN
ejpam-6667	459	2	of	of	ADP
ejpam-6667	459	3	mathematical	mathematical	ADJ
ejpam-6667	459	4	analysis	analysis	NOUN
ejpam-6667	459	5	and	and	CCONJ
ejpam-6667	459	6	applications	application	NOUN
ejpam-6667	459	7	,	,	PUNCT
ejpam-6667	459	8	394:781–795	394:781–795	NUM
ejpam-6667	459	9	,	,	PUNCT
ejpam-6667	459	10	2012	2012	NUM
ejpam-6667	459	11	.	.	PUNCT
ejpam-6667	460	1	[	[	X
ejpam-6667	460	2	18	18	NUM
ejpam-6667	460	3	]	]	X
ejpam-6667	460	4	b.	b.	PROPN
ejpam-6667	460	5	dong	dong	PROPN
ejpam-6667	460	6	and	and	CCONJ
ejpam-6667	460	7	j.	j.	PROPN
ejpam-6667	460	8	xu	xu	PROPN
ejpam-6667	460	9	.	.	PUNCT
ejpam-6667	461	1	new	new	ADJ
ejpam-6667	461	2	herz	herz	PROPN
ejpam-6667	461	3	type	type	NOUN
ejpam-6667	461	4	besov	besov	NOUN
ejpam-6667	461	5	and	and	CCONJ
ejpam-6667	461	6	triebel	triebel	NOUN
ejpam-6667	461	7	-	-	PUNCT
ejpam-6667	461	8	lizorkin	lizorkin	NOUN
ejpam-6667	461	9	spaces	space	NOUN
ejpam-6667	461	10	with	with	ADP
ejpam-6667	461	11	variable	variable	ADJ
ejpam-6667	461	12	exponents	exponent	NOUN
ejpam-6667	461	13	.	.	PUNCT
ejpam-6667	462	1	journal	journal	NOUN
ejpam-6667	462	2	of	of	ADP
ejpam-6667	462	3	function	function	NOUN
ejpam-6667	462	4	spaces	space	NOUN
ejpam-6667	462	5	and	and	CCONJ
ejpam-6667	462	6	applications	application	NOUN
ejpam-6667	462	7	,	,	PUNCT
ejpam-6667	462	8	2012	2012	NUM
ejpam-6667	462	9	:	:	PUNCT
ejpam-6667	462	10	article	article	NOUN
ejpam-6667	462	11	i	i	PROPN
ejpam-6667	462	12	d	d	PROPN
ejpam-6667	462	13	384593	384593	NUM
ejpam-6667	462	14	,	,	PUNCT
ejpam-6667	462	15	27	27	NUM
ejpam-6667	462	16	pages	page	NOUN
ejpam-6667	462	17	,	,	PUNCT
ejpam-6667	462	18	2012	2012	NUM
ejpam-6667	462	19	.	.	PUNCT
ejpam-6667	463	1	[	[	X
ejpam-6667	463	2	19	19	NUM
ejpam-6667	463	3	]	]	X
ejpam-6667	463	4	d.	d.	PROPN
ejpam-6667	463	5	drihem	drihem	PROPN
ejpam-6667	463	6	and	and	CCONJ
ejpam-6667	463	7	f.	f.	PROPN
ejpam-6667	463	8	seghiri	seghiri	PROPN
ejpam-6667	463	9	.	.	PUNCT
ejpam-6667	464	1	notes	note	NOUN
ejpam-6667	464	2	on	on	ADP
ejpam-6667	464	3	the	the	DET
ejpam-6667	464	4	herz	herz	ADJ
ejpam-6667	464	5	-	-	PUNCT
ejpam-6667	464	6	type	type	NOUN
ejpam-6667	464	7	hardy	hardy	ADJ
ejpam-6667	464	8	spaces	space	NOUN
ejpam-6667	464	9	of	of	ADP
ejpam-6667	464	10	variable	variable	ADJ
ejpam-6667	464	11	smoothness	smoothness	NOUN
ejpam-6667	464	12	and	and	CCONJ
ejpam-6667	464	13	integrability	integrability	NOUN
ejpam-6667	464	14	.	.	PUNCT
ejpam-6667	465	1	mathematical	mathematical	ADJ
ejpam-6667	465	2	inequalities	inequality	NOUN
ejpam-6667	465	3	and	and	CCONJ
ejpam-6667	465	4	applications	application	NOUN
ejpam-6667	465	5	,	,	PUNCT
ejpam-6667	465	6	19:145–165	19:145–165	NUM
ejpam-6667	465	7	,	,	PUNCT
ejpam-6667	465	8	2016	2016	NUM
ejpam-6667	465	9	.	.	PUNCT
ejpam-6667	466	1	[	[	X
ejpam-6667	466	2	20	20	NUM
ejpam-6667	466	3	]	]	PUNCT
ejpam-6667	466	4	m.	m.	NOUN
ejpam-6667	466	5	izuki	izuki	PROPN
ejpam-6667	466	6	.	.	PUNCT
ejpam-6667	467	1	herz	herz	PROPN
ejpam-6667	467	2	and	and	CCONJ
ejpam-6667	467	3	amalgam	amalgam	NOUN
ejpam-6667	467	4	spaces	space	NOUN
ejpam-6667	467	5	with	with	ADP
ejpam-6667	467	6	variable	variable	ADJ
ejpam-6667	467	7	exponent	exponent	NOUN
ejpam-6667	467	8	,	,	PUNCT
ejpam-6667	467	9	the	the	DET
ejpam-6667	467	10	haar	haar	NOUN
ejpam-6667	467	11	wavelets	wavelet	NOUN
ejpam-6667	467	12	and	and	CCONJ
ejpam-6667	467	13	greediness	greediness	NOUN
ejpam-6667	467	14	of	of	ADP
ejpam-6667	467	15	the	the	DET
ejpam-6667	467	16	wavelet	wavelet	NOUN
ejpam-6667	467	17	system	system	NOUN
ejpam-6667	467	18	.	.	PUNCT
ejpam-6667	468	1	east	east	PROPN
ejpam-6667	468	2	journal	journal	PROPN
ejpam-6667	468	3	on	on	ADP
ejpam-6667	468	4	approximations	approximation	NOUN
ejpam-6667	468	5	,	,	PUNCT
ejpam-6667	468	6	15:87–109	15:87–109	NUM
ejpam-6667	468	7	,	,	PUNCT
ejpam-6667	468	8	2009	2009	NUM
ejpam-6667	468	9	.	.	PUNCT
ejpam-6667	469	1	[	[	X
ejpam-6667	469	2	21	21	NUM
ejpam-6667	469	3	]	]	X
ejpam-6667	469	4	m.	m.	NOUN
ejpam-6667	469	5	izuki	izuki	PROPN
ejpam-6667	469	6	.	.	PUNCT
ejpam-6667	469	7	boundedness	boundedness	PROPN
ejpam-6667	469	8	of	of	ADP
ejpam-6667	469	9	commutators	commutator	NOUN
ejpam-6667	469	10	on	on	ADP
ejpam-6667	469	11	herz	herz	PROPN
ejpam-6667	469	12	spaces	space	NOUN
ejpam-6667	469	13	with	with	ADP
ejpam-6667	469	14	variable	variable	ADJ
ejpam-6667	469	15	exponent	exponent	NOUN
ejpam-6667	469	16	.	.	PUNCT
ejpam-6667	470	1	rendiconti	rendiconti	PROPN
ejpam-6667	470	2	del	del	PROPN
ejpam-6667	470	3	circolo	circolo	PROPN
ejpam-6667	470	4	matematico	matematico	NOUN
ejpam-6667	470	5	di	di	NOUN
ejpam-6667	470	6	palermo	palermo	PROPN
ejpam-6667	470	7	,	,	PUNCT
ejpam-6667	470	8	series	series	NOUN
ejpam-6667	470	9	2	2	NUM
ejpam-6667	470	10	,	,	PUNCT
ejpam-6667	470	11	59:199–213	59:199–213	NUM
ejpam-6667	470	12	,	,	PUNCT
ejpam-6667	470	13	2010	2010	NUM
ejpam-6667	470	14	.	.	PUNCT
ejpam-6667	471	1	[	[	X
ejpam-6667	471	2	22	22	NUM
ejpam-6667	471	3	]	]	PUNCT
ejpam-6667	471	4	m.	m.	NOUN
ejpam-6667	471	5	izuki	izuki	PROPN
ejpam-6667	471	6	.	.	PUNCT
ejpam-6667	472	1	commutators	commutator	NOUN
ejpam-6667	472	2	of	of	ADP
ejpam-6667	472	3	fractional	fractional	ADJ
ejpam-6667	472	4	integrals	integral	NOUN
ejpam-6667	472	5	on	on	ADP
ejpam-6667	472	6	lebesgue	lebesgue	NOUN
ejpam-6667	472	7	and	and	CCONJ
ejpam-6667	472	8	herz	herz	PROPN
ejpam-6667	472	9	spaces	space	NOUN
ejpam-6667	472	10	with	with	ADP
ejpam-6667	472	11	variable	variable	ADJ
ejpam-6667	472	12	exponent	exponent	NOUN
ejpam-6667	472	13	.	.	PUNCT
ejpam-6667	473	1	rendiconti	rendiconti	PROPN
ejpam-6667	473	2	del	del	PROPN
ejpam-6667	473	3	circolo	circolo	PROPN
ejpam-6667	473	4	matematico	matematico	NOUN
ejpam-6667	473	5	di	di	NOUN
ejpam-6667	473	6	palermo	palermo	PROPN
ejpam-6667	473	7	,	,	PUNCT
ejpam-6667	473	8	series	series	NOUN
ejpam-6667	473	9	2	2	NUM
ejpam-6667	473	10	,	,	PUNCT
ejpam-6667	473	11	59:461–472	59:461–472	NUM
ejpam-6667	473	12	,	,	PUNCT
ejpam-6667	473	13	2010	2010	NUM
ejpam-6667	473	14	.	.	PUNCT
ejpam-6667	474	1	[	[	X
ejpam-6667	474	2	23	23	NUM
ejpam-6667	474	3	]	]	X
ejpam-6667	474	4	m.	m.	NOUN
ejpam-6667	474	5	izuki	izuki	PROPN
ejpam-6667	474	6	.	.	PUNCT
ejpam-6667	474	7	fractional	fractional	ADJ
ejpam-6667	474	8	integrals	integral	NOUN
ejpam-6667	474	9	on	on	ADP
ejpam-6667	474	10	herz	herz	ADJ
ejpam-6667	474	11	-	-	PUNCT
ejpam-6667	474	12	morrey	morrey	PROPN
ejpam-6667	474	13	spaces	space	NOUN
ejpam-6667	474	14	with	with	ADP
ejpam-6667	474	15	variable	variable	ADJ
ejpam-6667	474	16	exponent	exponent	NOUN
ejpam-6667	474	17	.	.	PUNCT
ejpam-6667	475	1	hiroshima	hiroshima	PROPN
ejpam-6667	475	2	mathematical	mathematical	PROPN
ejpam-6667	475	3	journal	journal	PROPN
ejpam-6667	475	4	,	,	PUNCT
ejpam-6667	475	5	40:343–355	40:343–355	PROPN
ejpam-6667	475	6	,	,	PUNCT
ejpam-6667	475	7	2010	2010	NUM
ejpam-6667	475	8	.	.	PUNCT
ejpam-6667	476	1	[	[	X
ejpam-6667	476	2	24	24	NUM
ejpam-6667	476	3	]	]	PUNCT
ejpam-6667	476	4	m.	m.	NOUN
ejpam-6667	476	5	izuki	izuki	PROPN
ejpam-6667	476	6	.	.	PUNCT
ejpam-6667	476	7	vector	vector	NOUN
ejpam-6667	476	8	-	-	PUNCT
ejpam-6667	476	9	valued	value	VERB
ejpam-6667	476	10	inequalities	inequality	NOUN
ejpam-6667	476	11	on	on	ADP
ejpam-6667	476	12	herz	herz	PROPN
ejpam-6667	476	13	spaces	space	NOUN
ejpam-6667	476	14	and	and	CCONJ
ejpam-6667	476	15	characterizations	characterization	NOUN
ejpam-6667	476	16	of	of	ADP
ejpam-6667	476	17	herzsobolev	herzsobolev	ADJ
ejpam-6667	476	18	spaces	space	NOUN
ejpam-6667	476	19	with	with	ADP
ejpam-6667	476	20	variable	variable	ADJ
ejpam-6667	476	21	exponent	exponent	NOUN
ejpam-6667	476	22	.	.	PUNCT
ejpam-6667	477	1	glasnik	glasnik	PROPN
ejpam-6667	477	2	matematicki	matematicki	PROPN
ejpam-6667	477	3	,	,	PUNCT
ejpam-6667	477	4	45:475–503	45:475–503	PROPN
ejpam-6667	477	5	,	,	PUNCT
ejpam-6667	477	6	2010	2010	NUM
ejpam-6667	477	7	.	.	PUNCT
ejpam-6667	478	1	[	[	X
ejpam-6667	478	2	25	25	NUM
ejpam-6667	478	3	]	]	PUNCT
ejpam-6667	478	4	m.	m.	NOUN
ejpam-6667	478	5	izuki	izuki	PROPN
ejpam-6667	478	6	and	and	CCONJ
ejpam-6667	478	7	t.	t.	PROPN
ejpam-6667	478	8	noi	noi	PROPN
ejpam-6667	478	9	.	.	PUNCT
ejpam-6667	479	1	duality	duality	NOUN
ejpam-6667	479	2	of	of	ADP
ejpam-6667	479	3	besov	besov	NOUN
ejpam-6667	479	4	,	,	PUNCT
ejpam-6667	479	5	triebel	triebel	NOUN
ejpam-6667	479	6	-	-	PUNCT
ejpam-6667	479	7	lizorkin	lizorkin	NOUN
ejpam-6667	479	8	and	and	CCONJ
ejpam-6667	479	9	herz	herz	PROPN
ejpam-6667	479	10	spaces	space	NOUN
ejpam-6667	479	11	with	with	ADP
ejpam-6667	479	12	variable	variable	ADJ
ejpam-6667	479	13	exponents	exponent	NOUN
ejpam-6667	479	14	.	.	PUNCT
ejpam-6667	480	1	rendiconti	rendiconti	ADJ
ejpam-6667	480	2	del	del	PROPN
ejpam-6667	480	3	circolo	circolo	PROPN
ejpam-6667	480	4	matematico	matematico	NOUN
ejpam-6667	480	5	di	di	NOUN
ejpam-6667	480	6	palermo	palermo	PROPN
ejpam-6667	480	7	,	,	PUNCT
ejpam-6667	480	8	series	series	NOUN
ejpam-6667	480	9	2	2	NUM
ejpam-6667	480	10	,	,	PUNCT
ejpam-6667	480	11	63:221–245	63:221–245	PROPN
ejpam-6667	480	12	,	,	PUNCT
ejpam-6667	480	13	2014	2014	NUM
ejpam-6667	480	14	.	.	PUNCT
ejpam-6667	481	1	[	[	X
ejpam-6667	481	2	26	26	NUM
ejpam-6667	481	3	]	]	PUNCT
ejpam-6667	481	4	m.	m.	NOUN
ejpam-6667	481	5	izuki	izuki	PROPN
ejpam-6667	481	6	and	and	CCONJ
ejpam-6667	481	7	t.	t.	PROPN
ejpam-6667	481	8	noi	noi	PROPN
ejpam-6667	481	9	.	.	PUNCT
ejpam-6667	482	1	hardy	hardy	ADJ
ejpam-6667	482	2	spaces	space	NOUN
ejpam-6667	482	3	associated	associate	VERB
ejpam-6667	482	4	to	to	ADP
ejpam-6667	482	5	critical	critical	ADJ
ejpam-6667	482	6	herz	herz	PROPN
ejpam-6667	482	7	spaces	space	NOUN
ejpam-6667	482	8	with	with	ADP
ejpam-6667	482	9	variable	variable	ADJ
ejpam-6667	482	10	exponent	exponent	NOUN
ejpam-6667	482	11	.	.	PUNCT
ejpam-6667	483	1	mediterranean	mediterranean	PROPN
ejpam-6667	483	2	journal	journal	PROPN
ejpam-6667	483	3	of	of	ADP
ejpam-6667	483	4	mathematics	mathematic	NOUN
ejpam-6667	483	5	,	,	PUNCT
ejpam-6667	483	6	13:2981–3013	13:2981–3013	NUM
ejpam-6667	483	7	,	,	PUNCT
ejpam-6667	483	8	2016	2016	NUM
ejpam-6667	483	9	.	.	PUNCT
ejpam-6667	484	1	[	[	X
ejpam-6667	484	2	27	27	NUM
ejpam-6667	484	3	]	]	X
ejpam-6667	484	4	y.	y.	PROPN
ejpam-6667	484	5	lu	lu	PROPN
ejpam-6667	484	6	and	and	CCONJ
ejpam-6667	484	7	y.	y.	PROPN
ejpam-6667	484	8	zhu	zhu	PROPN
ejpam-6667	484	9	.	.	PUNCT
ejpam-6667	485	1	boundedness	boundedness	PROPN
ejpam-6667	485	2	of	of	ADP
ejpam-6667	485	3	multilinear	multilinear	PROPN
ejpam-6667	485	4	calderón	calderón	PROPN
ejpam-6667	485	5	–	–	PUNCT
ejpam-6667	485	6	zygmund	zygmund	ADJ
ejpam-6667	485	7	singular	singular	ADJ
ejpam-6667	485	8	operators	operator	NOUN
ejpam-6667	485	9	on	on	ADP
ejpam-6667	485	10	morrey	morrey	PROPN
ejpam-6667	485	11	-	-	PUNCT
ejpam-6667	485	12	herz	herz	PROPN
ejpam-6667	485	13	spaces	space	NOUN
ejpam-6667	485	14	with	with	ADP
ejpam-6667	485	15	variable	variable	ADJ
ejpam-6667	485	16	exponent	exponent	NOUN
ejpam-6667	485	17	.	.	PUNCT
ejpam-6667	486	1	acta	acta	PROPN
ejpam-6667	486	2	mathematica	mathematica	PROPN
ejpam-6667	486	3	sinica	sinica	PROPN
ejpam-6667	486	4	,	,	PUNCT
ejpam-6667	486	5	english	english	ADJ
ejpam-6667	486	6	series	series	NOUN
ejpam-6667	486	7	,	,	PUNCT
ejpam-6667	486	8	30:1180–1194	30:1180–1194	PROPN
ejpam-6667	486	9	,	,	PUNCT
ejpam-6667	486	10	2014	2014	NUM
ejpam-6667	486	11	.	.	PUNCT
ejpam-6667	487	1	[	[	X
ejpam-6667	487	2	28	28	NUM
ejpam-6667	487	3	]	]	X
ejpam-6667	487	4	h.	h.	PROPN
ejpam-6667	487	5	wang	wang	PROPN
ejpam-6667	487	6	.	.	PUNCT
ejpam-6667	488	1	commutators	commutator	NOUN
ejpam-6667	488	2	of	of	ADP
ejpam-6667	488	3	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6667	488	4	integrals	integral	NOUN
ejpam-6667	488	5	on	on	ADP
ejpam-6667	488	6	herz	herz	PROPN
ejpam-6667	488	7	spaces	space	NOUN
ejpam-6667	488	8	with	with	ADP
ejpam-6667	488	9	variable	variable	ADJ
ejpam-6667	488	10	exponent	exponent	NOUN
ejpam-6667	488	11	.	.	PUNCT
ejpam-6667	489	1	czechoslovak	czechoslovak	ADJ
ejpam-6667	489	2	mathematical	mathematical	PROPN
ejpam-6667	489	3	journal	journal	PROPN
ejpam-6667	489	4	,	,	PUNCT
ejpam-6667	489	5	66(141):251–269	66(141):251–269	PROPN
ejpam-6667	489	6	,	,	PUNCT
ejpam-6667	489	7	2016	2016	NUM
ejpam-6667	489	8	.	.	PUNCT
ejpam-6667	490	1	m.	m.	PROPN
ejpam-6667	490	2	asim	asim	PROPN
ejpam-6667	490	3	,	,	PUNCT
ejpam-6667	490	4	k.	k.	PROPN
ejpam-6667	490	5	suwais	suwais	PROPN
ejpam-6667	490	6	,	,	PUNCT
ejpam-6667	490	7	n.	n.	PROPN
ejpam-6667	490	8	mlaiki	mlaiki	PROPN
ejpam-6667	490	9	/	/	SYM
ejpam-6667	490	10	eur	eur	PROPN
ejpam-6667	490	11	.	.	PUNCT
ejpam-6667	491	1	j.	j.	PROPN
ejpam-6667	491	2	pure	pure	PROPN
ejpam-6667	491	3	appl	appl	PROPN
ejpam-6667	491	4	.	.	PROPN
ejpam-6667	491	5	math	math	PROPN
ejpam-6667	491	6	,	,	PUNCT
ejpam-6667	491	7	18	18	NUM
ejpam-6667	491	8	(	(	PUNCT
ejpam-6667	491	9	4	4	NUM
ejpam-6667	491	10	)	)	PUNCT
ejpam-6667	491	11	(	(	PUNCT
ejpam-6667	491	12	2025	2025	NUM
ejpam-6667	491	13	)	)	PUNCT
ejpam-6667	491	14	,	,	PUNCT
ejpam-6667	491	15	6667	6667	NUM
ejpam-6667	491	16	19	19	NUM
ejpam-6667	491	17	of	of	ADP
ejpam-6667	491	18	20	20	NUM
ejpam-6667	491	19	[	[	SYM
ejpam-6667	491	20	29	29	NUM
ejpam-6667	491	21	]	]	PUNCT
ejpam-6667	491	22	h.	h.	PROPN
ejpam-6667	491	23	wang	wang	PROPN
ejpam-6667	491	24	,	,	PUNCT
ejpam-6667	491	25	j.	j.	PROPN
ejpam-6667	491	26	wang	wang	PROPN
ejpam-6667	491	27	,	,	PUNCT
ejpam-6667	491	28	and	and	CCONJ
ejpam-6667	491	29	z.	z.	PROPN
ejpam-6667	491	30	fu	fu	PROPN
ejpam-6667	491	31	.	.	PUNCT
ejpam-6667	492	1	morrey	morrey	PROPN
ejpam-6667	492	2	meets	meet	VERB
ejpam-6667	492	3	herz	herz	ADJ
ejpam-6667	492	4	with	with	ADP
ejpam-6667	492	5	variable	variable	ADJ
ejpam-6667	492	6	exponent	exponent	NOUN
ejpam-6667	492	7	and	and	CCONJ
ejpam-6667	492	8	applications	application	NOUN
ejpam-6667	492	9	to	to	ADP
ejpam-6667	492	10	commutators	commutator	NOUN
ejpam-6667	492	11	of	of	ADP
ejpam-6667	492	12	homogeneous	homogeneous	ADJ
ejpam-6667	492	13	fractional	fractional	ADJ
ejpam-6667	492	14	integrals	integral	NOUN
ejpam-6667	492	15	with	with	ADP
ejpam-6667	492	16	rough	rough	ADJ
ejpam-6667	492	17	kernels	kernel	NOUN
ejpam-6667	492	18	.	.	PUNCT
ejpam-6667	493	1	journal	journal	PROPN
ejpam-6667	493	2	of	of	ADP
ejpam-6667	493	3	function	function	NOUN
ejpam-6667	493	4	spaces	space	NOUN
ejpam-6667	493	5	,	,	PUNCT
ejpam-6667	493	6	pages	page	NOUN
ejpam-6667	493	7	article	article	NOUN
ejpam-6667	493	8	i	i	PROPN
ejpam-6667	493	9	d	d	PROPN
ejpam-6667	493	10	1908794	1908794	NUM
ejpam-6667	493	11	,	,	PUNCT
ejpam-6667	493	12	11	11	NUM
ejpam-6667	493	13	pages	page	NOUN
ejpam-6667	493	14	,	,	PUNCT
ejpam-6667	493	15	2017	2017	NUM
ejpam-6667	493	16	.	.	PUNCT
ejpam-6667	494	1	[	[	X
ejpam-6667	494	2	30	30	NUM
ejpam-6667	494	3	]	]	PUNCT
ejpam-6667	494	4	z.	z.	PROPN
ejpam-6667	494	5	fu	fu	PROPN
ejpam-6667	494	6	,	,	PUNCT
ejpam-6667	494	7	s.	s.	PROPN
ejpam-6667	494	8	lu	lu	PROPN
ejpam-6667	494	9	,	,	PUNCT
ejpam-6667	494	10	h.	h.	PROPN
ejpam-6667	494	11	wang	wang	PROPN
ejpam-6667	494	12	,	,	PUNCT
ejpam-6667	494	13	and	and	CCONJ
ejpam-6667	494	14	l.	l.	PROPN
ejpam-6667	494	15	wang	wang	PROPN
ejpam-6667	494	16	.	.	PUNCT
ejpam-6667	495	1	singular	singular	PROPN
ejpam-6667	495	2	integral	integral	ADJ
ejpam-6667	495	3	operator	operator	NOUN
ejpam-6667	495	4	with	with	ADP
ejpam-6667	495	5	rough	rough	ADJ
ejpam-6667	495	6	kernel	kernel	NOUN
ejpam-6667	495	7	on	on	ADP
ejpam-6667	495	8	central	central	ADJ
ejpam-6667	495	9	morrey	morrey	NOUN
ejpam-6667	495	10	spaces	space	NOUN
ejpam-6667	495	11	with	with	ADP
ejpam-6667	495	12	variable	variable	ADJ
ejpam-6667	495	13	exponent	exponent	NOUN
ejpam-6667	495	14	.	.	PUNCT
ejpam-6667	496	1	annales	annales	PROPN
ejpam-6667	496	2	academiae	academiae	PROPN
ejpam-6667	496	3	scientiarum	scientiarum	PROPN
ejpam-6667	496	4	fennicae	fennicae	PROPN
ejpam-6667	496	5	mathematica	mathematica	PROPN
ejpam-6667	496	6	,	,	PUNCT
ejpam-6667	496	7	44:505–522	44:505–522	PROPN
ejpam-6667	496	8	,	,	PUNCT
ejpam-6667	496	9	2019	2019	NUM
ejpam-6667	496	10	.	.	PUNCT
ejpam-6667	497	1	[	[	X
ejpam-6667	497	2	31	31	NUM
ejpam-6667	497	3	]	]	PUNCT
ejpam-6667	497	4	z.	z.	PROPN
ejpam-6667	497	5	si	si	PROPN
ejpam-6667	497	6	.	.	PROPN
ejpam-6667	497	7	λ	λ	ADJ
ejpam-6667	497	8	-	-	ADJ
ejpam-6667	497	9	central	central	ADJ
ejpam-6667	497	10	bmo	bmo	NOUN
ejpam-6667	497	11	estimates	estimate	NOUN
ejpam-6667	497	12	for	for	ADP
ejpam-6667	497	13	multilinear	multilinear	NOUN
ejpam-6667	497	14	commutators	commutator	NOUN
ejpam-6667	497	15	of	of	ADP
ejpam-6667	497	16	fractional	fractional	ADJ
ejpam-6667	497	17	integrals	integral	NOUN
ejpam-6667	497	18	.	.	PUNCT
ejpam-6667	498	1	acta	acta	PROPN
ejpam-6667	498	2	mathematica	mathematica	PROPN
ejpam-6667	498	3	sinica	sinica	PROPN
ejpam-6667	498	4	,	,	PUNCT
ejpam-6667	498	5	english	english	ADJ
ejpam-6667	498	6	series	series	NOUN
ejpam-6667	498	7	,	,	PUNCT
ejpam-6667	498	8	26:2093–2108	26:2093–2108	NUM
ejpam-6667	498	9	,	,	PUNCT
ejpam-6667	498	10	2010	2010	NUM
ejpam-6667	498	11	.	.	PUNCT
ejpam-6667	499	1	[	[	X
ejpam-6667	499	2	32	32	NUM
ejpam-6667	499	3	]	]	X
ejpam-6667	499	4	y.	y.	PROPN
ejpam-6667	499	5	mizuta	mizuta	PROPN
ejpam-6667	499	6	,	,	PUNCT
ejpam-6667	499	7	t.	t.	PROPN
ejpam-6667	499	8	ohno	ohno	PROPN
ejpam-6667	499	9	,	,	PUNCT
ejpam-6667	499	10	and	and	CCONJ
ejpam-6667	499	11	t.	t.	PROPN
ejpam-6667	499	12	shimomura	shimomura	NOUN
ejpam-6667	499	13	.	.	PUNCT
ejpam-6667	500	1	boundedness	boundedness	PROPN
ejpam-6667	500	2	of	of	ADP
ejpam-6667	500	3	maximal	maximal	ADJ
ejpam-6667	500	4	operators	operator	NOUN
ejpam-6667	500	5	and	and	CCONJ
ejpam-6667	500	6	sobolev	sobolev	NOUN
ejpam-6667	500	7	’s	’s	PART
ejpam-6667	500	8	theorem	theorem	NOUN
ejpam-6667	500	9	for	for	ADP
ejpam-6667	500	10	non	non	ADJ
ejpam-6667	500	11	-	-	ADJ
ejpam-6667	500	12	homogeneous	homogeneous	ADJ
ejpam-6667	500	13	central	central	ADJ
ejpam-6667	500	14	morrey	morrey	NOUN
ejpam-6667	500	15	spaces	space	NOUN
ejpam-6667	500	16	of	of	ADP
ejpam-6667	500	17	variable	variable	ADJ
ejpam-6667	500	18	exponent	exponent	NOUN
ejpam-6667	500	19	.	.	PUNCT
ejpam-6667	501	1	hokkaido	hokkaido	PROPN
ejpam-6667	501	2	mathematical	mathematical	PROPN
ejpam-6667	501	3	journal	journal	PROPN
ejpam-6667	501	4	,	,	PUNCT
ejpam-6667	501	5	44:185–201	44:185–201	PROPN
ejpam-6667	501	6	,	,	PUNCT
ejpam-6667	501	7	2015	2015	NUM
ejpam-6667	501	8	.	.	PUNCT
ejpam-6667	502	1	[	[	X
ejpam-6667	502	2	33	33	NUM
ejpam-6667	502	3	]	]	X
ejpam-6667	502	4	d.	d.	PROPN
ejpam-6667	502	5	cruz	cruz	PROPN
ejpam-6667	502	6	-	-	PUNCT
ejpam-6667	502	7	uribe	uribe	PROPN
ejpam-6667	502	8	,	,	PUNCT
ejpam-6667	502	9	a.	a.	NOUN
ejpam-6667	502	10	fiorenza	fiorenza	PROPN
ejpam-6667	502	11	,	,	PUNCT
ejpam-6667	502	12	j.	j.	PROPN
ejpam-6667	502	13	m.	m.	PROPN
ejpam-6667	502	14	martell	martell	PROPN
ejpam-6667	502	15	,	,	PUNCT
ejpam-6667	502	16	and	and	CCONJ
ejpam-6667	502	17	c.	c.	PROPN
ejpam-6667	502	18	pérez	pérez	PROPN
ejpam-6667	502	19	.	.	PUNCT
ejpam-6667	503	1	the	the	DET
ejpam-6667	503	2	boundedness	boundedness	NOUN
ejpam-6667	503	3	of	of	ADP
ejpam-6667	503	4	classical	classical	ADJ
ejpam-6667	503	5	operators	operator	NOUN
ejpam-6667	503	6	on	on	ADP
ejpam-6667	503	7	variable	variable	ADJ
ejpam-6667	503	8	lp	lp	NOUN
ejpam-6667	503	9	spaces	space	NOUN
ejpam-6667	503	10	.	.	PUNCT
ejpam-6667	504	1	annales	annale	NOUN
ejpam-6667	504	2	academiae	academiae	PROPN
ejpam-6667	504	3	scientiarum	scientiarum	PROPN
ejpam-6667	504	4	fennicae	fennicae	PROPN
ejpam-6667	504	5	mathematica	mathematica	PROPN
ejpam-6667	504	6	,	,	PUNCT
ejpam-6667	504	7	31:239–264	31:239–264	NUM
ejpam-6667	504	8	,	,	PUNCT
ejpam-6667	504	9	2006	2006	NUM
ejpam-6667	504	10	.	.	PUNCT
ejpam-6667	505	1	[	[	X
ejpam-6667	505	2	34	34	NUM
ejpam-6667	505	3	]	]	PUNCT
ejpam-6667	505	4	m.	m.	NOUN
ejpam-6667	505	5	sultan	sultan	PROPN
ejpam-6667	505	6	,	,	PUNCT
ejpam-6667	505	7	b.	b.	PROPN
ejpam-6667	505	8	sultan	sultan	PROPN
ejpam-6667	505	9	,	,	PUNCT
ejpam-6667	505	10	a.	a.	NOUN
ejpam-6667	505	11	aloqaily	aloqaily	ADV
ejpam-6667	505	12	,	,	PUNCT
ejpam-6667	505	13	and	and	CCONJ
ejpam-6667	505	14	n.	n.	PROPN
ejpam-6667	505	15	mlaiki	mlaiki	PROPN
ejpam-6667	505	16	.	.	PUNCT
ejpam-6667	506	1	boundedness	boundedness	NOUN
ejpam-6667	506	2	of	of	ADP
ejpam-6667	506	3	some	some	DET
ejpam-6667	506	4	operators	operator	NOUN
ejpam-6667	506	5	on	on	ADP
ejpam-6667	506	6	grand	grand	ADJ
ejpam-6667	506	7	herz	herz	PROPN
ejpam-6667	506	8	spaces	space	NOUN
ejpam-6667	506	9	with	with	ADP
ejpam-6667	506	10	variable	variable	ADJ
ejpam-6667	506	11	exponent	exponent	NOUN
ejpam-6667	506	12	.	.	PUNCT
ejpam-6667	507	1	aims	aim	VERB
ejpam-6667	507	2	mathematics	mathematic	NOUN
ejpam-6667	507	3	,	,	PUNCT
ejpam-6667	507	4	8:12964–12985	8:12964–12985	NUM
ejpam-6667	507	5	,	,	PUNCT
ejpam-6667	507	6	2023	2023	NUM
ejpam-6667	507	7	.	.	PUNCT
ejpam-6667	508	1	[	[	X
ejpam-6667	508	2	35	35	NUM
ejpam-6667	508	3	]	]	PUNCT
ejpam-6667	508	4	b.	b.	PROPN
ejpam-6667	508	5	sultan	sultan	PROPN
ejpam-6667	508	6	,	,	PUNCT
ejpam-6667	508	7	f.	f.	PROPN
ejpam-6667	508	8	azmi	azmi	PROPN
ejpam-6667	508	9	,	,	PUNCT
ejpam-6667	508	10	m.	m.	NOUN
ejpam-6667	508	11	sultan	sultan	PROPN
ejpam-6667	508	12	,	,	PUNCT
ejpam-6667	508	13	m.	m.	NOUN
ejpam-6667	508	14	mehmood	mehmood	PROPN
ejpam-6667	508	15	,	,	PUNCT
ejpam-6667	508	16	and	and	CCONJ
ejpam-6667	508	17	n.	n.	PROPN
ejpam-6667	508	18	mlaiki	mlaiki	PROPN
ejpam-6667	508	19	.	.	PUNCT
ejpam-6667	509	1	boundedness	boundedness	PROPN
ejpam-6667	509	2	of	of	ADP
ejpam-6667	509	3	riesz	riesz	PROPN
ejpam-6667	509	4	potential	potential	ADJ
ejpam-6667	509	5	operator	operator	NOUN
ejpam-6667	509	6	on	on	ADP
ejpam-6667	509	7	grand	grand	ADJ
ejpam-6667	509	8	herz	herz	PROPN
ejpam-6667	509	9	-	-	PUNCT
ejpam-6667	509	10	morrey	morrey	PROPN
ejpam-6667	509	11	spaces	space	NOUN
ejpam-6667	509	12	.	.	PUNCT
ejpam-6667	510	1	axioms	axiom	NOUN
ejpam-6667	510	2	,	,	PUNCT
ejpam-6667	510	3	11(11):583	11(11):583	NUM
ejpam-6667	510	4	,	,	PUNCT
ejpam-6667	510	5	2022	2022	NUM
ejpam-6667	510	6	.	.	PUNCT
ejpam-6667	511	1	[	[	X
ejpam-6667	511	2	36	36	NUM
ejpam-6667	511	3	]	]	X
ejpam-6667	511	4	muhammad	muhammad	PROPN
ejpam-6667	511	5	asim	asim	PROPN
ejpam-6667	511	6	and	and	CCONJ
ejpam-6667	511	7	ghada	ghada	PROPN
ejpam-6667	511	8	alnemer	alnemer	PROPN
ejpam-6667	511	9	.	.	PUNCT
ejpam-6667	512	1	analytical	analytical	ADJ
ejpam-6667	512	2	findings	finding	NOUN
ejpam-6667	512	3	on	on	ADP
ejpam-6667	512	4	bilinear	bilinear	PROPN
ejpam-6667	512	5	fractional	fractional	ADJ
ejpam-6667	512	6	hardy	hardy	ADJ
ejpam-6667	512	7	operators	operator	NOUN
ejpam-6667	512	8	in	in	ADP
ejpam-6667	512	9	weighted	weight	VERB
ejpam-6667	512	10	central	central	ADJ
ejpam-6667	512	11	morrey	morrey	NOUN
ejpam-6667	512	12	spaces	space	NOUN
ejpam-6667	512	13	with	with	ADP
ejpam-6667	512	14	variable	variable	ADJ
ejpam-6667	512	15	exponents	exponent	NOUN
ejpam-6667	512	16	.	.	PUNCT
ejpam-6667	513	1	aims	aim	VERB
ejpam-6667	513	2	mathematics	mathematic	NOUN
ejpam-6667	513	3	,	,	PUNCT
ejpam-6667	513	4	10(5):10431–10451	10(5):10431–10451	NUM
ejpam-6667	513	5	,	,	PUNCT
ejpam-6667	513	6	2025	2025	NUM
ejpam-6667	513	7	.	.	PUNCT
ejpam-6667	514	1	[	[	X
ejpam-6667	514	2	37	37	NUM
ejpam-6667	514	3	]	]	PUNCT
ejpam-6667	514	4	b.	b.	PROPN
ejpam-6667	514	5	sultan	sultan	PROPN
ejpam-6667	514	6	,	,	PUNCT
ejpam-6667	514	7	m.	m.	NOUN
ejpam-6667	514	8	sultan	sultan	PROPN
ejpam-6667	514	9	,	,	PUNCT
ejpam-6667	514	10	m.	m.	PROPN
ejpam-6667	514	11	mehmood	mehmood	PROPN
ejpam-6667	514	12	,	,	PUNCT
ejpam-6667	514	13	f.	f.	PROPN
ejpam-6667	514	14	azmi	azmi	PROPN
ejpam-6667	514	15	,	,	PUNCT
ejpam-6667	514	16	m.	m.	NOUN
ejpam-6667	514	17	a.	a.	NOUN
ejpam-6667	514	18	alghafli	alghafli	PROPN
ejpam-6667	514	19	,	,	PUNCT
ejpam-6667	514	20	and	and	CCONJ
ejpam-6667	514	21	n.	n.	PROPN
ejpam-6667	514	22	mlaiki	mlaiki	PROPN
ejpam-6667	514	23	.	.	PUNCT
ejpam-6667	515	1	boundedness	boundedness	PROPN
ejpam-6667	515	2	of	of	ADP
ejpam-6667	515	3	fractional	fractional	ADJ
ejpam-6667	515	4	integrals	integral	NOUN
ejpam-6667	515	5	on	on	ADP
ejpam-6667	515	6	grand	grand	ADJ
ejpam-6667	515	7	weighted	weight	VERB
ejpam-6667	515	8	herz	herz	PROPN
ejpam-6667	515	9	spaces	space	NOUN
ejpam-6667	515	10	with	with	ADP
ejpam-6667	515	11	variable	variable	ADJ
ejpam-6667	515	12	exponent	exponent	NOUN
ejpam-6667	515	13	.	.	PUNCT
ejpam-6667	516	1	aims	aim	VERB
ejpam-6667	516	2	mathematics	mathematic	NOUN
ejpam-6667	516	3	,	,	PUNCT
ejpam-6667	516	4	8:752–764	8:752–764	NOUN
ejpam-6667	516	5	,	,	PUNCT
ejpam-6667	516	6	2023	2023	NUM
ejpam-6667	516	7	.	.	PUNCT
ejpam-6667	517	1	[	[	X
ejpam-6667	517	2	38	38	NUM
ejpam-6667	517	3	]	]	PUNCT
ejpam-6667	517	4	b.	b.	PROPN
ejpam-6667	517	5	sultan	sultan	PROPN
ejpam-6667	517	6	,	,	PUNCT
ejpam-6667	517	7	f.	f.	PROPN
ejpam-6667	517	8	m.	m.	PROPN
ejpam-6667	517	9	azmi	azmi	PROPN
ejpam-6667	517	10	,	,	PUNCT
ejpam-6667	517	11	m.	m.	NOUN
ejpam-6667	517	12	sultan	sultan	PROPN
ejpam-6667	517	13	,	,	PUNCT
ejpam-6667	517	14	t.	t.	PROPN
ejpam-6667	517	15	mahmood	mahmood	PROPN
ejpam-6667	517	16	,	,	PUNCT
ejpam-6667	517	17	n.	n.	PROPN
ejpam-6667	517	18	mlaiki	mlaiki	PROPN
ejpam-6667	517	19	,	,	PUNCT
ejpam-6667	517	20	and	and	CCONJ
ejpam-6667	517	21	n.	n.	NOUN
ejpam-6667	517	22	souayah	souayah	NOUN
ejpam-6667	517	23	.	.	PUNCT
ejpam-6667	518	1	boundedness	boundedness	NOUN
ejpam-6667	518	2	of	of	ADP
ejpam-6667	518	3	fractional	fractional	ADJ
ejpam-6667	518	4	integrals	integral	NOUN
ejpam-6667	518	5	on	on	ADP
ejpam-6667	518	6	grand	grand	ADJ
ejpam-6667	518	7	weighted	weight	VERB
ejpam-6667	518	8	herz	herz	PROPN
ejpam-6667	518	9	-	-	PUNCT
ejpam-6667	518	10	morrey	morrey	PROPN
ejpam-6667	518	11	spaces	space	NOUN
ejpam-6667	518	12	with	with	ADP
ejpam-6667	518	13	variable	variable	ADJ
ejpam-6667	518	14	exponent	exponent	NOUN
ejpam-6667	518	15	.	.	PUNCT
ejpam-6667	519	1	fractal	fractal	PROPN
ejpam-6667	519	2	and	and	CCONJ
ejpam-6667	519	3	fractional	fractional	ADJ
ejpam-6667	519	4	,	,	PUNCT
ejpam-6667	519	5	6:660	6:660	NOUN
ejpam-6667	519	6	,	,	PUNCT
ejpam-6667	519	7	2022	2022	NUM
ejpam-6667	519	8	.	.	PUNCT
ejpam-6667	520	1	[	[	X
ejpam-6667	520	2	39	39	NUM
ejpam-6667	520	3	]	]	PUNCT
ejpam-6667	520	4	d.	d.	PROPN
ejpam-6667	520	5	cruz	cruz	PROPN
ejpam-6667	520	6	-	-	PUNCT
ejpam-6667	520	7	uribe	uribe	PROPN
ejpam-6667	520	8	and	and	CCONJ
ejpam-6667	520	9	a.	a.	NOUN
ejpam-6667	520	10	fiorenza	fiorenza	PROPN
ejpam-6667	520	11	.	.	PUNCT
ejpam-6667	521	1	variable	variable	ADJ
ejpam-6667	521	2	lebesgue	lebesgue	PROPN
ejpam-6667	521	3	spaces	space	VERB
ejpam-6667	521	4	:	:	PUNCT
ejpam-6667	521	5	foundations	foundation	NOUN
ejpam-6667	521	6	and	and	CCONJ
ejpam-6667	521	7	harmonic	harmonic	ADJ
ejpam-6667	521	8	analysis	analysis	NOUN
ejpam-6667	521	9	.	.	PUNCT
ejpam-6667	522	1	applied	apply	VERB
ejpam-6667	522	2	and	and	CCONJ
ejpam-6667	522	3	numerical	numerical	ADJ
ejpam-6667	522	4	harmonic	harmonic	ADJ
ejpam-6667	522	5	analysis	analysis	NOUN
ejpam-6667	522	6	.	.	PUNCT
ejpam-6667	523	1	springer	springer	NOUN
ejpam-6667	523	2	,	,	PUNCT
ejpam-6667	523	3	heidelberg	heidelberg	PROPN
ejpam-6667	523	4	,	,	PUNCT
ejpam-6667	523	5	2013	2013	NUM
ejpam-6667	523	6	.	.	PUNCT
ejpam-6667	524	1	[	[	X
ejpam-6667	524	2	40	40	NUM
ejpam-6667	524	3	]	]	X
ejpam-6667	524	4	l.	l.	PROPN
ejpam-6667	524	5	diening	diening	PROPN
ejpam-6667	524	6	,	,	PUNCT
ejpam-6667	524	7	p.	p.	PROPN
ejpam-6667	524	8	harjulehto	harjulehto	PROPN
ejpam-6667	524	9	,	,	PUNCT
ejpam-6667	524	10	p.	p.	NOUN
ejpam-6667	524	11	hästö	hästö	PROPN
ejpam-6667	524	12	,	,	PUNCT
ejpam-6667	524	13	and	and	CCONJ
ejpam-6667	524	14	m.	m.	PROPN
ejpam-6667	524	15	r̊užička	r̊užička	PROPN
ejpam-6667	524	16	.	.	PUNCT
ejpam-6667	525	1	lebesgue	lebesgue	PROPN
ejpam-6667	525	2	and	and	CCONJ
ejpam-6667	525	3	sobolev	sobolev	NOUN
ejpam-6667	525	4	spaces	space	NOUN
ejpam-6667	525	5	with	with	ADP
ejpam-6667	525	6	variable	variable	ADJ
ejpam-6667	525	7	exponents	exponent	NOUN
ejpam-6667	525	8	,	,	PUNCT
ejpam-6667	525	9	volume	volume	NOUN
ejpam-6667	525	10	2017	2017	NUM
ejpam-6667	525	11	of	of	ADP
ejpam-6667	525	12	lecture	lecture	NOUN
ejpam-6667	525	13	notes	note	NOUN
ejpam-6667	525	14	in	in	ADP
ejpam-6667	525	15	mathematics	mathematic	NOUN
ejpam-6667	525	16	.	.	PUNCT
ejpam-6667	526	1	springer	springer	PROPN
ejpam-6667	526	2	,	,	PUNCT
ejpam-6667	526	3	heidelberg	heidelberg	PROPN
ejpam-6667	526	4	,	,	PUNCT
ejpam-6667	526	5	2011	2011	NUM
ejpam-6667	526	6	.	.	PUNCT
ejpam-6667	527	1	[	[	X
ejpam-6667	527	2	41	41	NUM
ejpam-6667	527	3	]	]	X
ejpam-6667	527	4	m.	m.	NOUN
ejpam-6667	527	5	izuki	izuki	PROPN
ejpam-6667	527	6	,	,	PUNCT
ejpam-6667	527	7	e.	e.	PROPN
ejpam-6667	527	8	nakai	nakai	PROPN
ejpam-6667	527	9	,	,	PUNCT
ejpam-6667	527	10	and	and	CCONJ
ejpam-6667	527	11	y.	y.	PROPN
ejpam-6667	527	12	sawano	sawano	PROPN
ejpam-6667	527	13	.	.	PUNCT
ejpam-6667	528	1	function	function	NOUN
ejpam-6667	528	2	spaces	space	VERB
ejpam-6667	528	3	with	with	ADP
ejpam-6667	528	4	variable	variable	ADJ
ejpam-6667	528	5	exponents	exponent	NOUN
ejpam-6667	528	6	:	:	PUNCT
ejpam-6667	528	7	an	an	DET
ejpam-6667	528	8	introduction	introduction	NOUN
ejpam-6667	528	9	.	.	PUNCT
ejpam-6667	529	1	sci	sci	PROPN
ejpam-6667	529	2	.	.	PROPN
ejpam-6667	529	3	math	math	PROPN
ejpam-6667	529	4	.	.	PUNCT
ejpam-6667	530	1	jpn	jpn	PROPN
ejpam-6667	530	2	.	.	PROPN
ejpam-6667	530	3	,	,	PUNCT
ejpam-6667	531	1	77(2):187–315	77(2):187–315	PROPN
ejpam-6667	531	2	,	,	PUNCT
ejpam-6667	531	3	2014	2014	NUM
ejpam-6667	531	4	.	.	PUNCT
ejpam-6667	532	1	[	[	X
ejpam-6667	532	2	42	42	NUM
ejpam-6667	532	3	]	]	X
ejpam-6667	532	4	d.	d.	PROPN
ejpam-6667	532	5	c.	c.	PROPN
ejpam-6667	532	6	uribe	uribe	PROPN
ejpam-6667	532	7	,	,	PUNCT
ejpam-6667	532	8	a.	a.	NOUN
ejpam-6667	532	9	fiorenza	fiorenza	PROPN
ejpam-6667	532	10	,	,	PUNCT
ejpam-6667	532	11	and	and	CCONJ
ejpam-6667	532	12	c.	c.	PROPN
ejpam-6667	532	13	neugebauer	neugebauer	PROPN
ejpam-6667	532	14	.	.	PUNCT
ejpam-6667	533	1	the	the	DET
ejpam-6667	533	2	maximal	maximal	ADJ
ejpam-6667	533	3	function	function	NOUN
ejpam-6667	533	4	on	on	ADP
ejpam-6667	533	5	variable	variable	ADJ
ejpam-6667	533	6	lp	lp	NOUN
ejpam-6667	533	7	spaces	space	NOUN
ejpam-6667	533	8	.	.	PUNCT
ejpam-6667	534	1	ann	ann	PROPN
ejpam-6667	534	2	.	.	PUNCT
ejpam-6667	534	3	acad	acad	PROPN
ejpam-6667	534	4	.	.	PUNCT
ejpam-6667	535	1	sci	sci	PROPN
ejpam-6667	535	2	.	.	PUNCT
ejpam-6667	535	3	fenn	fenn	PROPN
ejpam-6667	535	4	.	.	PROPN
ejpam-6667	535	5	,	,	PUNCT
ejpam-6667	535	6	math	math	NOUN
ejpam-6667	535	7	.	.	PUNCT
ejpam-6667	535	8	,	,	PUNCT
ejpam-6667	535	9	28:223–238	28:223–238	PROPN
ejpam-6667	535	10	,	,	PUNCT
ejpam-6667	535	11	2003	2003	NUM
ejpam-6667	535	12	.	.	PUNCT
ejpam-6667	536	1	[	[	X
ejpam-6667	536	2	43	43	NUM
ejpam-6667	536	3	]	]	X
ejpam-6667	536	4	lars	lars	PROPN
ejpam-6667	536	5	diening	diene	VERB
ejpam-6667	536	6	.	.	PUNCT
ejpam-6667	537	1	maximal	maximal	ADJ
ejpam-6667	537	2	function	function	NOUN
ejpam-6667	537	3	on	on	ADP
ejpam-6667	537	4	generalized	generalized	ADJ
ejpam-6667	537	5	lebesgue	lebesgue	NOUN
ejpam-6667	537	6	spaces	space	NOUN
ejpam-6667	537	7	lp	lp	PROPN
ejpam-6667	537	8	(	(	PUNCT
ejpam-6667	537	9	·	·	PUNCT
ejpam-6667	537	10	)	)	PUNCT
ejpam-6667	537	11	.	.	PUNCT
ejpam-6667	538	1	mathematical	mathematical	ADJ
ejpam-6667	538	2	inequalities	inequality	NOUN
ejpam-6667	538	3	and	and	CCONJ
ejpam-6667	538	4	applications	application	NOUN
ejpam-6667	538	5	,	,	PUNCT
ejpam-6667	538	6	7:245–253	7:245–253	NUM
ejpam-6667	538	7	,	,	PUNCT
ejpam-6667	538	8	2004	2004	NUM
ejpam-6667	538	9	.	.	PUNCT
ejpam-6667	539	1	[	[	X
ejpam-6667	539	2	44	44	NUM
ejpam-6667	539	3	]	]	PUNCT
ejpam-6667	539	4	lars	lars	PROPN
ejpam-6667	539	5	diening	diene	VERB
ejpam-6667	539	6	.	.	PUNCT
ejpam-6667	540	1	maximal	maximal	ADJ
ejpam-6667	540	2	functions	function	NOUN
ejpam-6667	540	3	on	on	ADP
ejpam-6667	540	4	musielak	musielak	NOUN
ejpam-6667	540	5	-	-	PUNCT
ejpam-6667	540	6	orlicz	orlicz	ADJ
ejpam-6667	540	7	spaces	space	NOUN
ejpam-6667	540	8	and	and	CCONJ
ejpam-6667	540	9	generalized	generalized	ADJ
ejpam-6667	540	10	lebesgue	lebesgue	NOUN
ejpam-6667	540	11	spaces	space	NOUN
ejpam-6667	540	12	.	.	PUNCT
ejpam-6667	541	1	bulletin	bulletin	PROPN
ejpam-6667	541	2	des	des	PROPN
ejpam-6667	541	3	sciences	sciences	PROPN
ejpam-6667	541	4	mathématiques	mathématiques	PROPN
ejpam-6667	541	5	,	,	PUNCT
ejpam-6667	541	6	129:657–700	129:657–700	NUM
ejpam-6667	541	7	,	,	PUNCT
ejpam-6667	541	8	2005	2005	NUM
ejpam-6667	541	9	.	.	PUNCT
ejpam-6667	542	1	[	[	X
ejpam-6667	542	2	45	45	NUM
ejpam-6667	542	3	]	]	PUNCT
ejpam-6667	542	4	c.	c.	PROPN
ejpam-6667	542	5	bennett	bennett	PROPN
ejpam-6667	542	6	and	and	CCONJ
ejpam-6667	542	7	r.	r.	PROPN
ejpam-6667	542	8	sharpley	sharpley	PROPN
ejpam-6667	542	9	.	.	PUNCT
ejpam-6667	543	1	interpolation	interpolation	NOUN
ejpam-6667	543	2	of	of	ADP
ejpam-6667	543	3	operators	operator	NOUN
ejpam-6667	543	4	.	.	PUNCT
ejpam-6667	544	1	academic	academic	ADJ
ejpam-6667	544	2	press	press	PROPN
ejpam-6667	544	3	,	,	PUNCT
ejpam-6667	544	4	boston	boston	PROPN
ejpam-6667	544	5	,	,	PUNCT
ejpam-6667	544	6	1988	1988	NUM
ejpam-6667	544	7	.	.	PUNCT
ejpam-6667	545	1	m.	m.	PROPN
ejpam-6667	545	2	asim	asim	PROPN
ejpam-6667	545	3	,	,	PUNCT
ejpam-6667	545	4	k.	k.	PROPN
ejpam-6667	545	5	suwais	suwais	PROPN
ejpam-6667	545	6	,	,	PUNCT
ejpam-6667	545	7	n.	n.	PROPN
ejpam-6667	545	8	mlaiki	mlaiki	PROPN
ejpam-6667	545	9	/	/	SYM
ejpam-6667	545	10	eur	eur	PROPN
ejpam-6667	545	11	.	.	PUNCT
ejpam-6667	546	1	j.	j.	PROPN
ejpam-6667	546	2	pure	pure	PROPN
ejpam-6667	546	3	appl	appl	PROPN
ejpam-6667	546	4	.	.	PROPN
ejpam-6667	546	5	math	math	PROPN
ejpam-6667	546	6	,	,	PUNCT
ejpam-6667	546	7	18	18	NUM
ejpam-6667	546	8	(	(	PUNCT
ejpam-6667	546	9	4	4	NUM
ejpam-6667	546	10	)	)	PUNCT
ejpam-6667	546	11	(	(	PUNCT
ejpam-6667	546	12	2025	2025	NUM
ejpam-6667	546	13	)	)	PUNCT
ejpam-6667	546	14	,	,	PUNCT
ejpam-6667	546	15	6667	6667	NUM
ejpam-6667	546	16	20	20	NUM
ejpam-6667	546	17	of	of	ADP
ejpam-6667	546	18	20	20	NUM
ejpam-6667	546	19	[	[	SYM
ejpam-6667	546	20	46	46	NUM
ejpam-6667	546	21	]	]	X
ejpam-6667	546	22	m.	m.	NOUN
ejpam-6667	546	23	izuki	izuki	PROPN
ejpam-6667	546	24	.	.	PUNCT
ejpam-6667	547	1	remarks	remark	NOUN
ejpam-6667	547	2	on	on	ADP
ejpam-6667	547	3	muckenhoupt	muckenhoupt	ADJ
ejpam-6667	547	4	weights	weight	NOUN
ejpam-6667	547	5	with	with	ADP
ejpam-6667	547	6	variable	variable	ADJ
ejpam-6667	547	7	exponent	exponent	NOUN
ejpam-6667	547	8	.	.	PUNCT
ejpam-6667	548	1	sci	sci	PROPN
ejpam-6667	548	2	.	.	PROPN
ejpam-6667	548	3	math	math	PROPN
ejpam-6667	548	4	.	.	PUNCT
ejpam-6667	549	1	jpn	jpn	PROPN
ejpam-6667	549	2	.	.	PROPN
ejpam-6667	549	3	,	,	PUNCT
ejpam-6667	549	4	2(1):27–41	2(1):27–41	NUM
ejpam-6667	549	5	,	,	PUNCT
ejpam-6667	549	6	2013	2013	NUM
ejpam-6667	549	7	.	.	PUNCT
ejpam-6667	550	1	[	[	X
ejpam-6667	550	2	47	47	NUM
ejpam-6667	550	3	]	]	PUNCT
ejpam-6667	550	4	a.	a.	NOUN
ejpam-6667	550	5	y.	y.	PROPN
ejpam-6667	550	6	karlovich	karlovich	PROPN
ejpam-6667	550	7	and	and	CCONJ
ejpam-6667	550	8	i.	i.	PROPN
ejpam-6667	550	9	spitkovsky	spitkovsky	PROPN
ejpam-6667	550	10	.	.	PUNCT
ejpam-6667	551	1	the	the	DET
ejpam-6667	551	2	cauchy	cauchy	ADJ
ejpam-6667	551	3	singular	singular	ADJ
ejpam-6667	551	4	integral	integral	ADJ
ejpam-6667	551	5	operator	operator	NOUN
ejpam-6667	551	6	on	on	ADP
ejpam-6667	551	7	weighted	weight	VERB
ejpam-6667	551	8	variable	variable	ADJ
ejpam-6667	551	9	lebesgue	lebesgue	NOUN
ejpam-6667	551	10	spaces	space	NOUN
ejpam-6667	551	11	.	.	PUNCT
ejpam-6667	552	1	in	in	ADP
ejpam-6667	552	2	operator	operator	NOUN
ejpam-6667	552	3	theory	theory	NOUN
ejpam-6667	552	4	:	:	PUNCT
ejpam-6667	552	5	advances	advance	NOUN
ejpam-6667	552	6	and	and	CCONJ
ejpam-6667	552	7	applications	application	NOUN
ejpam-6667	552	8	,	,	PUNCT
ejpam-6667	552	9	volume	volume	NOUN
ejpam-6667	552	10	236	236	NUM
ejpam-6667	552	11	,	,	PUNCT
ejpam-6667	552	12	pages	page	NOUN
ejpam-6667	552	13	275–291	275–291	NUM
ejpam-6667	552	14	.	.	PUNCT
ejpam-6667	552	15	birkhäuser	birkhäuser	NOUN
ejpam-6667	552	16	,	,	PUNCT
ejpam-6667	552	17	basel	basel	PROPN
ejpam-6667	552	18	,	,	PUNCT
ejpam-6667	552	19	2014	2014	NUM
ejpam-6667	552	20	.	.	PUNCT
ejpam-6667	553	1	[	[	X
ejpam-6667	553	2	48	48	NUM
ejpam-6667	553	3	]	]	PUNCT
ejpam-6667	553	4	m.	m.	NOUN
ejpam-6667	553	5	izuki	izuki	PROPN
ejpam-6667	553	6	and	and	CCONJ
ejpam-6667	553	7	t.	t.	PROPN
ejpam-6667	553	8	noi	noi	PROPN
ejpam-6667	553	9	.	.	PUNCT
ejpam-6667	554	1	two	two	NUM
ejpam-6667	554	2	weighted	weight	VERB
ejpam-6667	554	3	herz	herz	PROPN
ejpam-6667	554	4	space	space	PROPN
ejpam-6667	554	5	variable	variable	PROPN
ejpam-6667	554	6	exponent	exponent	NOUN
ejpam-6667	554	7	.	.	PUNCT
ejpam-6667	554	8	bulletin	bulletin	NOUN
ejpam-6667	554	9	of	of	ADP
ejpam-6667	554	10	the	the	DET
ejpam-6667	554	11	malaysian	malaysian	PROPN
ejpam-6667	554	12	mathematical	mathematical	PROPN
ejpam-6667	554	13	sciences	sciences	PROPN
ejpam-6667	554	14	society	society	NOUN
ejpam-6667	554	15	,	,	PUNCT
ejpam-6667	554	16	43:169–200	43:169–200	NUM
ejpam-6667	554	17	,	,	PUNCT
ejpam-6667	554	18	2020	2020	NUM
ejpam-6667	554	19	.	.	PUNCT
ejpam-6667	555	1	[	[	X
ejpam-6667	555	2	49	49	NUM
ejpam-6667	555	3	]	]	PUNCT
ejpam-6667	555	4	m.	m.	NOUN
ejpam-6667	555	5	izuki	izuki	PROPN
ejpam-6667	555	6	and	and	CCONJ
ejpam-6667	555	7	t.	t.	PROPN
ejpam-6667	555	8	noi	noi	PROPN
ejpam-6667	555	9	.	.	PUNCT
ejpam-6667	556	1	an	an	DET
ejpam-6667	556	2	intrinsic	intrinsic	ADJ
ejpam-6667	556	3	square	square	ADJ
ejpam-6667	556	4	function	function	NOUN
ejpam-6667	556	5	on	on	ADP
ejpam-6667	556	6	weighted	weight	VERB
ejpam-6667	556	7	herz	herz	PROPN
ejpam-6667	556	8	spaces	space	NOUN
ejpam-6667	556	9	with	with	ADP
ejpam-6667	556	10	variable	variable	ADJ
ejpam-6667	556	11	exponent	exponent	NOUN
ejpam-6667	556	12	.	.	PUNCT
ejpam-6667	557	1	journal	journal	PROPN
ejpam-6667	557	2	of	of	ADP
ejpam-6667	557	3	mathematical	mathematical	ADJ
ejpam-6667	557	4	inequalities	inequality	NOUN
ejpam-6667	557	5	,	,	PUNCT
ejpam-6667	557	6	11(3):799–816	11(3):799–816	PROPN
ejpam-6667	557	7	,	,	PUNCT
ejpam-6667	557	8	2017	2017	NUM
ejpam-6667	557	9	.	.	PUNCT