id	sid	tid	token	lemma	pos
ejpam-6519	1	1	european	european	PROPN
ejpam-6519	1	2	journal	journal	PROPN
ejpam-6519	1	3	of	of	ADP
ejpam-6519	1	4	pure	pure	ADJ
ejpam-6519	1	5	and	and	CCONJ
ejpam-6519	1	6	applied	applied	ADJ
ejpam-6519	1	7	mathematics	mathematic	NOUN
ejpam-6519	1	8	2025	2025	NUM
ejpam-6519	1	9	,	,	PUNCT
ejpam-6519	1	10	vol	vol	NOUN
ejpam-6519	1	11	.	.	PROPN
ejpam-6519	1	12	18	18	NUM
ejpam-6519	1	13	,	,	PUNCT
ejpam-6519	1	14	issue	issue	NOUN
ejpam-6519	1	15	4	4	NUM
ejpam-6519	1	16	,	,	PUNCT
ejpam-6519	1	17	article	article	NOUN
ejpam-6519	1	18	number	number	NOUN
ejpam-6519	1	19	6519	6519	NUM
ejpam-6519	1	20	issn	issn	PROPN
ejpam-6519	1	21	1307	1307	NUM
ejpam-6519	1	22	-	-	SYM
ejpam-6519	1	23	5543	5543	NUM
ejpam-6519	1	24	–	–	PUNCT
ejpam-6519	1	25	ejpam.com	ejpam.com	X
ejpam-6519	1	26	published	publish	VERB
ejpam-6519	1	27	by	by	ADP
ejpam-6519	1	28	new	new	PROPN
ejpam-6519	1	29	york	york	PROPN
ejpam-6519	1	30	business	business	PROPN
ejpam-6519	1	31	global	global	PROPN
ejpam-6519	1	32	boundedness	boundedness	NOUN
ejpam-6519	1	33	of	of	ADP
ejpam-6519	1	34	the	the	DET
ejpam-6519	1	35	sublinear	sublinear	NOUN
ejpam-6519	1	36	operators	operator	NOUN
ejpam-6519	1	37	on	on	ADP
ejpam-6519	1	38	anisotropic	anisotropic	NOUN
ejpam-6519	1	39	herz	herz	ADJ
ejpam-6519	1	40	-	-	PUNCT
ejpam-6519	1	41	slice	slice	NOUN
ejpam-6519	1	42	spaces	space	NOUN
ejpam-6519	1	43	babar	babar	PROPN
ejpam-6519	1	44	sultan1	sultan1	PROPN
ejpam-6519	1	45	,	,	PUNCT
ejpam-6519	1	46	amjad	amjad	PROPN
ejpam-6519	1	47	hussain1,∗	hussain1,∗	PROPN
ejpam-6519	1	48	,	,	PUNCT
ejpam-6519	1	49	mehvish	mehvish	PROPN
ejpam-6519	1	50	sultan2	sultan2	NOUN
ejpam-6519	1	51	,	,	PUNCT
ejpam-6519	1	52	ioan	ioan	PROPN
ejpam-6519	1	53	-	-	PUNCT
ejpam-6519	1	54	lucian	lucian	PROPN
ejpam-6519	1	55	popa3,4,∗	popa3,4,∗	PROPN
ejpam-6519	1	56	1	1	NUM
ejpam-6519	1	57	department	department	NOUN
ejpam-6519	1	58	of	of	ADP
ejpam-6519	1	59	mathematics	mathematic	NOUN
ejpam-6519	1	60	,	,	PUNCT
ejpam-6519	1	61	quaid	quaid	PROPN
ejpam-6519	1	62	-	-	PUNCT
ejpam-6519	1	63	i	i	PROPN
ejpam-6519	1	64	-	-	PUNCT
ejpam-6519	1	65	azam	azam	PROPN
ejpam-6519	1	66	university	university	PROPN
ejpam-6519	1	67	,	,	PUNCT
ejpam-6519	1	68	islamabad	islamabad	PROPN
ejpam-6519	1	69	45320	45320	NUM
ejpam-6519	1	70	,	,	PUNCT
ejpam-6519	1	71	pakistan	pakistan	PROPN
ejpam-6519	1	72	2	2	NUM
ejpam-6519	1	73	department	department	NOUN
ejpam-6519	1	74	of	of	ADP
ejpam-6519	1	75	mathematics	mathematic	NOUN
ejpam-6519	1	76	,	,	PUNCT
ejpam-6519	1	77	capital	capital	NOUN
ejpam-6519	1	78	university	university	PROPN
ejpam-6519	1	79	of	of	ADP
ejpam-6519	1	80	science	science	NOUN
ejpam-6519	1	81	and	and	CCONJ
ejpam-6519	1	82	technology	technology	NOUN
ejpam-6519	1	83	,	,	PUNCT
ejpam-6519	1	84	islamabad	islamabad	PROPN
ejpam-6519	1	85	,	,	PUNCT
ejpam-6519	1	86	pakistan	pakistan	PROPN
ejpam-6519	1	87	3	3	NUM
ejpam-6519	1	88	department	department	NOUN
ejpam-6519	1	89	of	of	ADP
ejpam-6519	1	90	computing	computing	NOUN
ejpam-6519	1	91	,	,	PUNCT
ejpam-6519	1	92	mathematics	mathematic	NOUN
ejpam-6519	1	93	and	and	CCONJ
ejpam-6519	1	94	electronics	electronic	NOUN
ejpam-6519	1	95	,	,	PUNCT
ejpam-6519	1	96	“	"	PUNCT
ejpam-6519	1	97	1	1	NUM
ejpam-6519	1	98	decembrie	decembrie	NOUN
ejpam-6519	1	99	1918	1918	NUM
ejpam-6519	1	100	”	"	PUNCT
ejpam-6519	1	101	university	university	PROPN
ejpam-6519	1	102	of	of	ADP
ejpam-6519	1	103	alba	alba	PROPN
ejpam-6519	1	104	iulia	iulia	PROPN
ejpam-6519	1	105	,	,	PUNCT
ejpam-6519	1	106	510009	510009	NUM
ejpam-6519	1	107	alba	alba	NOUN
ejpam-6519	1	108	iulia	iulia	PROPN
ejpam-6519	1	109	,	,	PUNCT
ejpam-6519	1	110	romania	romania	PROPN
ejpam-6519	1	111	4	4	NUM
ejpam-6519	1	112	faculty	faculty	NOUN
ejpam-6519	1	113	of	of	ADP
ejpam-6519	1	114	mathematics	mathematic	NOUN
ejpam-6519	1	115	and	and	CCONJ
ejpam-6519	1	116	computer	computer	NOUN
ejpam-6519	1	117	science	science	NOUN
ejpam-6519	1	118	,	,	PUNCT
ejpam-6519	1	119	transilvania	transilvania	PROPN
ejpam-6519	1	120	university	university	PROPN
ejpam-6519	1	121	of	of	ADP
ejpam-6519	1	122	brasov	brasov	NOUN
ejpam-6519	1	123	,	,	PUNCT
ejpam-6519	1	124	iuliu	iuliu	PROPN
ejpam-6519	1	125	maniu	maniu	PROPN
ejpam-6519	1	126	street	street	PROPN
ejpam-6519	1	127	50	50	NUM
ejpam-6519	1	128	,	,	PUNCT
ejpam-6519	1	129	500091	500091	NUM
ejpam-6519	1	130	brasov	brasov	NOUN
ejpam-6519	1	131	,	,	PUNCT
ejpam-6519	1	132	romania	romania	PROPN
ejpam-6519	1	133	abstract	abstract	NOUN
ejpam-6519	1	134	.	.	PUNCT
ejpam-6519	2	1	we	we	PRON
ejpam-6519	2	2	will	will	AUX
ejpam-6519	2	3	define	define	VERB
ejpam-6519	2	4	the	the	DET
ejpam-6519	2	5	idea	idea	NOUN
ejpam-6519	2	6	of	of	ADP
ejpam-6519	2	7	anisotropic	anisotropic	NOUN
ejpam-6519	2	8	herz	herz	ADJ
ejpam-6519	2	9	-	-	PUNCT
ejpam-6519	2	10	slice	slice	NOUN
ejpam-6519	2	11	spaces	space	NOUN
ejpam-6519	2	12	and	and	CCONJ
ejpam-6519	2	13	prove	prove	VERB
ejpam-6519	2	14	some	some	DET
ejpam-6519	2	15	properties	property	NOUN
ejpam-6519	2	16	of	of	ADP
ejpam-6519	2	17	these	these	DET
ejpam-6519	2	18	spaces	space	NOUN
ejpam-6519	2	19	.	.	PUNCT
ejpam-6519	3	1	as	as	ADP
ejpam-6519	3	2	an	an	DET
ejpam-6519	3	3	application	application	NOUN
ejpam-6519	3	4	we	we	PRON
ejpam-6519	3	5	obtain	obtain	VERB
ejpam-6519	3	6	the	the	DET
ejpam-6519	3	7	bounds	bound	NOUN
ejpam-6519	3	8	for	for	ADP
ejpam-6519	3	9	sublinear	sublinear	NOUN
ejpam-6519	3	10	operator	operator	NOUN
ejpam-6519	3	11	on	on	ADP
ejpam-6519	3	12	anisotropic	anisotropic	NOUN
ejpam-6519	3	13	herz	herz	ADJ
ejpam-6519	3	14	-	-	PUNCT
ejpam-6519	3	15	slice	slice	NOUN
ejpam-6519	3	16	spaces	space	NOUN
ejpam-6519	3	17	.	.	PUNCT
ejpam-6519	4	1	2020	2020	NUM
ejpam-6519	4	2	mathematics	mathematic	NOUN
ejpam-6519	4	3	subject	subject	NOUN
ejpam-6519	4	4	classifications	classification	NOUN
ejpam-6519	4	5	:	:	PUNCT
ejpam-6519	4	6	42b35	42b35	NUM
ejpam-6519	4	7	,	,	PUNCT
ejpam-6519	4	8	47b38	47b38	NUM
ejpam-6519	4	9	key	key	ADJ
ejpam-6519	4	10	words	word	NOUN
ejpam-6519	4	11	and	and	CCONJ
ejpam-6519	4	12	phrases	phrase	NOUN
ejpam-6519	4	13	:	:	PUNCT
ejpam-6519	4	14	herz	herz	PROPN
ejpam-6519	4	15	spaces	space	NOUN
ejpam-6519	4	16	,	,	PUNCT
ejpam-6519	4	17	slice	slice	NOUN
ejpam-6519	4	18	spaces	space	NOUN
ejpam-6519	4	19	,	,	PUNCT
ejpam-6519	4	20	herz	herz	ADJ
ejpam-6519	4	21	-	-	PUNCT
ejpam-6519	4	22	slice	slice	NOUN
ejpam-6519	4	23	spaces	space	NOUN
ejpam-6519	4	24	,	,	PUNCT
ejpam-6519	4	25	integral	integral	ADJ
ejpam-6519	4	26	operators	operator	NOUN
ejpam-6519	4	27	,	,	PUNCT
ejpam-6519	4	28	atomic	atomic	ADJ
ejpam-6519	4	29	decomposition	decomposition	NOUN
ejpam-6519	4	30	,	,	PUNCT
ejpam-6519	4	31	boundedness	boundedness	NOUN
ejpam-6519	4	32	1	1	NUM
ejpam-6519	4	33	.	.	PUNCT
ejpam-6519	4	34	introduction	introduction	NOUN
ejpam-6519	4	35	let	let	VERB
ejpam-6519	4	36	p	p	PROPN
ejpam-6519	4	37	∈	∈	PROPN
ejpam-6519	4	38	(	(	PUNCT
ejpam-6519	4	39	0,∞	0,∞	NOUN
ejpam-6519	4	40	)	)	PUNCT
ejpam-6519	4	41	,	,	PUNCT
ejpam-6519	4	42	the	the	DET
ejpam-6519	4	43	lebesgue	lebesgue	NOUN
ejpam-6519	4	44	space	space	NOUN
ejpam-6519	4	45	is	be	AUX
ejpam-6519	4	46	defined	define	VERB
ejpam-6519	4	47	as	as	ADP
ejpam-6519	4	48	lp(e	lp(e	NOUN
ejpam-6519	4	49	)	)	PUNCT
ejpam-6519	4	50	:	:	PUNCT
ejpam-6519	5	1	=	=	X
ejpam-6519	5	2	{	{	PUNCT
ejpam-6519	5	3	f	f	PROPN
ejpam-6519	5	4	is	be	AUX
ejpam-6519	5	5	measurable	measurable	ADJ
ejpam-6519	5	6	:	:	PUNCT
ejpam-6519	5	7	ip	ip	PROPN
ejpam-6519	5	8	(	(	PUNCT
ejpam-6519	5	9	f	f	PROPN
ejpam-6519	5	10	γ	γ	PROPN
ejpam-6519	5	11	)	)	PUNCT
ejpam-6519	5	12	<	<	X
ejpam-6519	5	13	∞	∞	PROPN
ejpam-6519	5	14	for	for	ADP
ejpam-6519	5	15	some	some	DET
ejpam-6519	5	16	constant	constant	ADJ
ejpam-6519	5	17	γ	γ	X
ejpam-6519	5	18	>	>	X
ejpam-6519	5	19	0	0	NUM
ejpam-6519	5	20	}	}	PUNCT
ejpam-6519	5	21	where	where	SCONJ
ejpam-6519	5	22	ip(f	ip(f	NUM
ejpam-6519	5	23	)	)	PUNCT
ejpam-6519	5	24	:	:	PUNCT
ejpam-6519	6	1	=	=	SYM
ejpam-6519	6	2	∫	∫	PROPN
ejpam-6519	6	3	e	e	X
ejpam-6519	6	4	|g(x)|pdx	|g(x)|pdx	X
ejpam-6519	6	5	and	and	CCONJ
ejpam-6519	6	6	‖f‖lp(e	‖f‖lp(e	ADJ
ejpam-6519	6	7	)	)	PUNCT
ejpam-6519	6	8	:	:	PUNCT
ejpam-6519	7	1	=	=	SYM
ejpam-6519	7	2	inf	inf	PROPN
ejpam-6519	7	3	{	{	PUNCT
ejpam-6519	7	4	γ	γ	X
ejpam-6519	7	5	>	>	X
ejpam-6519	7	6	0	0	NUM
ejpam-6519	7	7	:	:	PUNCT
ejpam-6519	7	8	ip	ip	PROPN
ejpam-6519	7	9	(	(	PUNCT
ejpam-6519	7	10	f	f	PROPN
ejpam-6519	7	11	γ	γ	PROPN
ejpam-6519	7	12	)	)	PUNCT
ejpam-6519	7	13	6	6	NUM
ejpam-6519	7	14	1	1	NUM
ejpam-6519	7	15	}	}	PUNCT
ejpam-6519	7	16	.	.	PUNCT
ejpam-6519	8	1	∗corresponding	∗corresponde	VERB
ejpam-6519	8	2	author	author	NOUN
ejpam-6519	8	3	.	.	PUNCT
ejpam-6519	9	1	∗corresponding	∗corresponde	VERB
ejpam-6519	9	2	author	author	NOUN
ejpam-6519	9	3	.	.	PUNCT
ejpam-6519	10	1	doi	doi	NOUN
ejpam-6519	10	2	:	:	PUNCT
ejpam-6519	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6519	https://doi.org/10.29020/nybg.ejpam.v18i4.6519	ADJ
ejpam-6519	10	4	email	email	NOUN
ejpam-6519	10	5	addresses	address	VERB
ejpam-6519	10	6	:	:	PUNCT
ejpam-6519	10	7	babarsultan40@yahoo.com	babarsultan40@yahoo.com	X
ejpam-6519	10	8	(	(	PUNCT
ejpam-6519	10	9	b.	b.	PROPN
ejpam-6519	10	10	sultan	sultan	PROPN
ejpam-6519	10	11	)	)	PUNCT
ejpam-6519	10	12	,	,	PUNCT
ejpam-6519	10	13	a.hussain@qau.edu.pk	a.hussain@qau.edu.pk	PROPN
ejpam-6519	10	14	(	(	PUNCT
ejpam-6519	10	15	a.	a.	NOUN
ejpam-6519	10	16	hussain	hussain	PROPN
ejpam-6519	10	17	)	)	PUNCT
ejpam-6519	10	18	,	,	PUNCT
ejpam-6519	10	19	mehvishsultanbaz@gmail.com	mehvishsultanbaz@gmail.com	X
ejpam-6519	10	20	(	(	PUNCT
ejpam-6519	10	21	m.	m.	NOUN
ejpam-6519	10	22	sultan	sultan	PROPN
ejpam-6519	10	23	)	)	PUNCT
ejpam-6519	10	24	,	,	PUNCT
ejpam-6519	10	25	lucian.popa@uab.ro	lucian.popa@uab.ro	NOUN
ejpam-6519	10	26	(	(	PUNCT
ejpam-6519	10	27	i.-l	i.-l	NOUN
ejpam-6519	10	28	.	.	PUNCT
ejpam-6519	11	1	popa	popa	ADJ
ejpam-6519	11	2	)	)	PUNCT
ejpam-6519	11	3	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6519	12	1	1	1	NUM
ejpam-6519	12	2	copyright	copyright	NOUN
ejpam-6519	12	3	:	:	PUNCT
ejpam-6519	12	4	©	©	PROPN
ejpam-6519	12	5	2025	2025	NUM
ejpam-6519	12	6	the	the	DET
ejpam-6519	12	7	author(s	author(s	NOUN
ejpam-6519	12	8	)	)	PUNCT
ejpam-6519	12	9	.	.	PUNCT
ejpam-6519	13	1	(	(	PUNCT
ejpam-6519	13	2	cc	cc	NOUN
ejpam-6519	13	3	by	by	ADP
ejpam-6519	13	4	-	-	PUNCT
ejpam-6519	13	5	nc	nc	PROPN
ejpam-6519	13	6	4.0	4.0	NUM
ejpam-6519	13	7	)	)	PUNCT
ejpam-6519	13	8	b.	b.	PROPN
ejpam-6519	13	9	sultan	sultan	PROPN
ejpam-6519	13	10	et	et	PROPN
ejpam-6519	13	11	al	al	PROPN
ejpam-6519	13	12	.	.	PUNCT
ejpam-6519	13	13	/	/	SYM
ejpam-6519	13	14	eur	eur	PROPN
ejpam-6519	13	15	.	.	PUNCT
ejpam-6519	14	1	j.	j.	PROPN
ejpam-6519	14	2	pure	pure	PROPN
ejpam-6519	14	3	appl	appl	PROPN
ejpam-6519	14	4	.	.	PROPN
ejpam-6519	14	5	math	math	PROPN
ejpam-6519	14	6	,	,	PUNCT
ejpam-6519	14	7	18	18	NUM
ejpam-6519	14	8	(	(	PUNCT
ejpam-6519	14	9	4	4	NUM
ejpam-6519	14	10	)	)	PUNCT
ejpam-6519	14	11	(	(	PUNCT
ejpam-6519	14	12	2025	2025	NUM
ejpam-6519	14	13	)	)	PUNCT
ejpam-6519	14	14	,	,	PUNCT
ejpam-6519	14	15	6519	6519	NUM
ejpam-6519	14	16	2	2	NUM
ejpam-6519	14	17	of	of	ADP
ejpam-6519	14	18	11	11	NUM
ejpam-6519	14	19	afterward	afterward	ADV
ejpam-6519	14	20	,	,	PUNCT
ejpam-6519	14	21	lp(e	lp(e	PUNCT
ejpam-6519	14	22	)	)	PUNCT
ejpam-6519	14	23	is	be	AUX
ejpam-6519	14	24	a	a	DET
ejpam-6519	14	25	banach	banach	NOUN
ejpam-6519	14	26	space	space	NOUN
ejpam-6519	14	27	,	,	PUNCT
ejpam-6519	14	28	and	and	CCONJ
ejpam-6519	14	29	‖	‖	PROPN
ejpam-6519	14	30	·	·	PUNCT
ejpam-6519	14	31	‖lp(e	‖lp(e	PUNCT
ejpam-6519	14	32	)	)	PUNCT
ejpam-6519	14	33	is	be	AUX
ejpam-6519	14	34	its	its	PRON
ejpam-6519	14	35	norm	norm	NOUN
ejpam-6519	14	36	.	.	PUNCT
ejpam-6519	15	1	slice	slice	NOUN
ejpam-6519	15	2	spaces	space	NOUN
ejpam-6519	15	3	were	be	AUX
ejpam-6519	15	4	initially	initially	ADV
ejpam-6519	15	5	presented	present	VERB
ejpam-6519	15	6	in	in	ADP
ejpam-6519	15	7	[	[	X
ejpam-6519	15	8	1	1	NUM
ejpam-6519	15	9	]	]	PUNCT
ejpam-6519	15	10	to	to	PART
ejpam-6519	15	11	study	study	VERB
ejpam-6519	15	12	weak	weak	ADJ
ejpam-6519	15	13	solutions	solution	NOUN
ejpam-6519	15	14	of	of	ADP
ejpam-6519	15	15	boundary	boundary	ADJ
ejpam-6519	15	16	value	value	NOUN
ejpam-6519	15	17	problems	problem	NOUN
ejpam-6519	15	18	for	for	ADP
ejpam-6519	15	19	time	time	NOUN
ejpam-6519	15	20	-	-	PUNCT
ejpam-6519	15	21	independent	independent	ADJ
ejpam-6519	15	22	elliptic	elliptic	ADJ
ejpam-6519	15	23	systems	system	NOUN
ejpam-6519	15	24	in	in	ADP
ejpam-6519	15	25	the	the	DET
ejpam-6519	15	26	upper	upper	ADJ
ejpam-6519	15	27	half	half	ADJ
ejpam-6519	15	28	-	-	PUNCT
ejpam-6519	15	29	plane	plane	NOUN
ejpam-6519	15	30	.	.	PUNCT
ejpam-6519	16	1	this	this	DET
ejpam-6519	16	2	concept	concept	NOUN
ejpam-6519	16	3	was	be	AUX
ejpam-6519	16	4	later	later	ADV
ejpam-6519	16	5	expanded	expand	VERB
ejpam-6519	16	6	upon	upon	SCONJ
ejpam-6519	16	7	in	in	ADP
ejpam-6519	16	8	[	[	X
ejpam-6519	16	9	2	2	NUM
ejpam-6519	16	10	]	]	PUNCT
ejpam-6519	16	11	,	,	PUNCT
ejpam-6519	16	12	where	where	SCONJ
ejpam-6519	16	13	generalized	generalized	ADJ
ejpam-6519	16	14	slice	slice	NOUN
ejpam-6519	16	15	spaces	space	NOUN
ejpam-6519	16	16	were	be	AUX
ejpam-6519	16	17	used	use	VERB
ejpam-6519	16	18	to	to	PART
ejpam-6519	16	19	study	study	VERB
ejpam-6519	16	20	the	the	DET
ejpam-6519	16	21	mapping	mapping	NOUN
ejpam-6519	16	22	properties	property	NOUN
ejpam-6519	16	23	of	of	ADP
ejpam-6519	16	24	sublinear	sublinear	NOUN
ejpam-6519	16	25	operators	operator	NOUN
ejpam-6519	16	26	on	on	ADP
ejpam-6519	16	27	tent	tent	NOUN
ejpam-6519	16	28	spaces	space	NOUN
ejpam-6519	16	29	,	,	PUNCT
ejpam-6519	16	30	the	the	DET
ejpam-6519	16	31	hardy	hardy	ADJ
ejpam-6519	16	32	-	-	PUNCT
ejpam-6519	16	33	littlewood	littlewood	NOUN
ejpam-6519	16	34	maximal	maximal	ADJ
ejpam-6519	16	35	operator	operator	NOUN
ejpam-6519	16	36	m	m	PROPN
ejpam-6519	16	37	,	,	PUNCT
ejpam-6519	16	38	and	and	CCONJ
ejpam-6519	16	39	the	the	DET
ejpam-6519	16	40	calderón	calderón	NOUN
ejpam-6519	16	41	-	-	PUNCT
ejpam-6519	16	42	zygmund	zygmund	ADJ
ejpam-6519	16	43	operators	operator	NOUN
ejpam-6519	16	44	.	.	PUNCT
ejpam-6519	17	1	let	let	VERB
ejpam-6519	17	2	u	u	PRON
ejpam-6519	17	3	∈	∈	PROPN
ejpam-6519	17	4	(	(	PUNCT
ejpam-6519	17	5	0,∞	0,∞	NOUN
ejpam-6519	17	6	)	)	PUNCT
ejpam-6519	17	7	,	,	PUNCT
ejpam-6519	17	8	p	p	PROPN
ejpam-6519	17	9	∈	∈	PROPN
ejpam-6519	18	1	[	[	X
ejpam-6519	18	2	1,∞	1,∞	NUM
ejpam-6519	18	3	)	)	PUNCT
ejpam-6519	18	4	and	and	CCONJ
ejpam-6519	18	5	r	r	NOUN
ejpam-6519	18	6	∈	∈	PROPN
ejpam-6519	18	7	(	(	PUNCT
ejpam-6519	18	8	1,∞	1,∞	NUM
ejpam-6519	18	9	)	)	PUNCT
ejpam-6519	18	10	,	,	PUNCT
ejpam-6519	18	11	the	the	DET
ejpam-6519	18	12	slice	slice	NOUN
ejpam-6519	18	13	space	space	NOUN
ejpam-6519	18	14	(	(	PUNCT
ejpam-6519	18	15	ep	ep	PROPN
ejpam-6519	18	16	r	r	NOUN
ejpam-6519	18	17	)	)	PUNCT
ejpam-6519	18	18	u	u	NOUN
ejpam-6519	18	19	is	be	AUX
ejpam-6519	18	20	defined	define	VERB
ejpam-6519	18	21	as	as	ADP
ejpam-6519	18	22	the	the	DET
ejpam-6519	18	23	set	set	NOUN
ejpam-6519	18	24	of	of	ADP
ejpam-6519	18	25	all	all	DET
ejpam-6519	18	26	measurable	measurable	ADJ
ejpam-6519	18	27	functions	function	NOUN
ejpam-6519	18	28	g	g	ADP
ejpam-6519	18	29	such	such	ADJ
ejpam-6519	18	30	that	that	DET
ejpam-6519	18	31	‖f‖(ep	‖f‖(ep	PROPN
ejpam-6519	18	32	r	r	NOUN
ejpam-6519	18	33	)	)	PUNCT
ejpam-6519	18	34	u	u	NOUN
ejpam-6519	18	35	:	:	PUNCT
ejpam-6519	18	36	=	=	SYM
ejpam-6519	18	37	∥∥∥∥∥∥∥	∥∥∥∥∥∥∥	PROPN
ejpam-6519	18	38			X
ejpam-6519	18	39	1	1	NUM
ejpam-6519	18	40	|b	|b	ADJ
ejpam-6519	18	41	(	(	PUNCT
ejpam-6519	18	42	·	·	PUNCT
ejpam-6519	18	43	,	,	PUNCT
ejpam-6519	18	44	u)|	u)|	NOUN
ejpam-6519	18	45	∫	∫	PROPN
ejpam-6519	18	46	b(·,u	b(·,u	NOUN
ejpam-6519	18	47	)	)	PUNCT
ejpam-6519	19	1	|f(y)|r	|f(y)|r	PROPN
ejpam-6519	19	2	dy	dy	NOUN
ejpam-6519	19	3			PROPN
ejpam-6519	19	4	∥∥∥∥∥∥∥	∥∥∥∥∥∥∥	PROPN
ejpam-6519	20	1	lp	lp	ADP
ejpam-6519	20	2	<	<	X
ejpam-6519	20	3	∞.	∞.	PROPN
ejpam-6519	20	4	more	more	ADV
ejpam-6519	20	5	recently	recently	ADV
ejpam-6519	20	6	,	,	PUNCT
ejpam-6519	20	7	great	great	ADJ
ejpam-6519	20	8	attention	attention	NOUN
ejpam-6519	20	9	was	be	AUX
ejpam-6519	20	10	paid	pay	VERB
ejpam-6519	20	11	to	to	ADP
ejpam-6519	20	12	the	the	DET
ejpam-6519	20	13	study	study	NOUN
ejpam-6519	20	14	on	on	ADP
ejpam-6519	20	15	the	the	DET
ejpam-6519	20	16	herz	herz	PROPN
ejpam-6519	20	17	spaces	space	NOUN
ejpam-6519	20	18	since	since	SCONJ
ejpam-6519	20	19	there	there	PRON
ejpam-6519	20	20	are	be	VERB
ejpam-6519	20	21	several	several	ADJ
ejpam-6519	20	22	remarkable	remarkable	ADJ
ejpam-6519	20	23	works	work	NOUN
ejpam-6519	20	24	to	to	PART
ejpam-6519	20	25	push	push	VERB
ejpam-6519	20	26	forward	forward	ADV
ejpam-6519	20	27	the	the	DET
ejpam-6519	20	28	study	study	NOUN
ejpam-6519	20	29	on	on	ADP
ejpam-6519	20	30	the	the	DET
ejpam-6519	20	31	herz	herz	PROPN
ejpam-6519	20	32	spaces	space	NOUN
ejpam-6519	20	33	.	.	PUNCT
ejpam-6519	21	1	conversely	conversely	ADV
ejpam-6519	21	2	,	,	PUNCT
ejpam-6519	21	3	herz	herz	PROPN
ejpam-6519	21	4	spaces	space	NOUN
ejpam-6519	21	5	,	,	PUNCT
ejpam-6519	21	6	a	a	DET
ejpam-6519	21	7	class	class	NOUN
ejpam-6519	21	8	of	of	ADP
ejpam-6519	21	9	function	function	NOUN
ejpam-6519	21	10	spaces	space	NOUN
ejpam-6519	21	11	,	,	PUNCT
ejpam-6519	21	12	have	have	AUX
ejpam-6519	21	13	been	be	AUX
ejpam-6519	21	14	pivotal	pivotal	ADJ
ejpam-6519	21	15	in	in	ADP
ejpam-6519	21	16	real	real	ADJ
ejpam-6519	21	17	analysis	analysis	NOUN
ejpam-6519	21	18	due	due	ADP
ejpam-6519	21	19	to	to	ADP
ejpam-6519	21	20	their	their	PRON
ejpam-6519	21	21	norms	norm	NOUN
ejpam-6519	21	22	,	,	PUNCT
ejpam-6519	21	23	which	which	PRON
ejpam-6519	21	24	explicitly	explicitly	ADV
ejpam-6519	21	25	incorporate	incorporate	VERB
ejpam-6519	21	26	both	both	CCONJ
ejpam-6519	21	27	local	local	ADJ
ejpam-6519	21	28	and	and	CCONJ
ejpam-6519	21	29	global	global	ADJ
ejpam-6519	21	30	information	information	NOUN
ejpam-6519	21	31	of	of	ADP
ejpam-6519	21	32	functions	function	NOUN
ejpam-6519	21	33	.	.	PUNCT
ejpam-6519	22	1	for	for	ADP
ejpam-6519	22	2	more	more	ADJ
ejpam-6519	22	3	results	result	NOUN
ejpam-6519	22	4	generalized	generalized	ADJ
ejpam-6519	22	5	versions	version	NOUN
ejpam-6519	22	6	of	of	ADP
ejpam-6519	22	7	herz	herz	ADJ
ejpam-6519	22	8	space	space	NOUN
ejpam-6519	22	9	like	like	ADP
ejpam-6519	22	10	boundedness	boundedness	NOUN
ejpam-6519	22	11	of	of	ADP
ejpam-6519	22	12	sublinear	sublinear	NOUN
ejpam-6519	22	13	operators	operator	NOUN
ejpam-6519	22	14	,	,	PUNCT
ejpam-6519	22	15	fractional	fractional	ADJ
ejpam-6519	22	16	integrals	integral	NOUN
ejpam-6519	22	17	,	,	PUNCT
ejpam-6519	22	18	the	the	DET
ejpam-6519	22	19	commutator	commutator	NOUN
ejpam-6519	22	20	of	of	ADP
ejpam-6519	22	21	singular	singular	ADJ
ejpam-6519	22	22	integrals	integral	NOUN
ejpam-6519	22	23	with	with	ADP
ejpam-6519	22	24	bmo	bmo	NOUN
ejpam-6519	22	25	functions	function	NOUN
ejpam-6519	22	26	,	,	PUNCT
ejpam-6519	22	27	and	and	CCONJ
ejpam-6519	22	28	the	the	DET
ejpam-6519	22	29	commutator	commutator	NOUN
ejpam-6519	22	30	of	of	ADP
ejpam-6519	22	31	fractional	fractional	ADJ
ejpam-6519	22	32	integrals	integral	NOUN
ejpam-6519	22	33	with	with	ADP
ejpam-6519	22	34	bmo	bmo	NOUN
ejpam-6519	22	35	functions	function	NOUN
ejpam-6519	22	36	see	see	VERB
ejpam-6519	22	37	[	[	X
ejpam-6519	22	38	3–25	3–25	VERB
ejpam-6519	22	39	]	]	PUNCT
ejpam-6519	22	40	.	.	PUNCT
ejpam-6519	23	1	let	let	VERB
ejpam-6519	23	2	α	α	PRON
ejpam-6519	23	3	∈	∈	PROPN
ejpam-6519	23	4	r	r	NOUN
ejpam-6519	23	5	,	,	PUNCT
ejpam-6519	23	6	q	q	NOUN
ejpam-6519	23	7	∈	∈	PROPN
ejpam-6519	23	8	(	(	PUNCT
ejpam-6519	23	9	0,∞	0,∞	NOUN
ejpam-6519	23	10	]	]	PUNCT
ejpam-6519	23	11	,	,	PUNCT
ejpam-6519	23	12	and	and	CCONJ
ejpam-6519	23	13	0	0	NUM
ejpam-6519	23	14	<	<	X
ejpam-6519	23	15	p	p	X
ejpam-6519	23	16	≤	≤	NUM
ejpam-6519	23	17	∞	∞	PROPN
ejpam-6519	23	18	,	,	PUNCT
ejpam-6519	23	19	then	then	ADV
ejpam-6519	23	20	the	the	DET
ejpam-6519	23	21	homogeneous	homogeneous	ADJ
ejpam-6519	23	22	version	version	NOUN
ejpam-6519	23	23	of	of	ADP
ejpam-6519	23	24	herz	herz	PROPN
ejpam-6519	23	25	spaces	space	NOUN
ejpam-6519	23	26	k̇α	k̇α	PROPN
ejpam-6519	23	27	,	,	PUNCT
ejpam-6519	23	28	q	q	PROPN
ejpam-6519	23	29	p	p	NOUN
ejpam-6519	23	30	are	be	AUX
ejpam-6519	23	31	defined	define	VERB
ejpam-6519	23	32	by	by	ADP
ejpam-6519	23	33	k̇α	k̇α	PROPN
ejpam-6519	23	34	,	,	PUNCT
ejpam-6519	23	35	q	q	NOUN
ejpam-6519	23	36	p	p	NOUN
ejpam-6519	24	1	=	=	X
ejpam-6519	24	2	{	{	PUNCT
ejpam-6519	24	3	g	g	PROPN
ejpam-6519	24	4	∈	∈	PROPN
ejpam-6519	24	5	lp	lp	NOUN
ejpam-6519	24	6	loc(r	loc(r	PROPN
ejpam-6519	24	7	n	n	CCONJ
ejpam-6519	24	8	\	\	NOUN
ejpam-6519	24	9	{	{	PUNCT
ejpam-6519	24	10	0	0	NUM
ejpam-6519	24	11	}	}	PUNCT
ejpam-6519	24	12	)	)	PUNCT
ejpam-6519	24	13	:	:	PUNCT
ejpam-6519	25	1	‖g‖k̇α	‖g‖k̇α	ADJ
ejpam-6519	25	2	,	,	PUNCT
ejpam-6519	25	3	q	q	X
ejpam-6519	26	1	p	p	X
ejpam-6519	26	2	<	<	X
ejpam-6519	26	3	∞	∞	NUM
ejpam-6519	26	4	}	}	PUNCT
ejpam-6519	26	5	,	,	PUNCT
ejpam-6519	26	6	where	where	SCONJ
ejpam-6519	26	7	‖g‖k̇α	‖g‖k̇α	NOUN
ejpam-6519	26	8	,	,	PUNCT
ejpam-6519	26	9	q	q	NOUN
ejpam-6519	26	10	p	p	NOUN
ejpam-6519	26	11	=	=	X
ejpam-6519	26	12	(	(	PUNCT
ejpam-6519	26	13	∞∑	∞∑	NUM
ejpam-6519	26	14	`	`	PUNCT
ejpam-6519	26	15	=	=	NOUN
ejpam-6519	26	16	−∞	−∞	NOUN
ejpam-6519	26	17	2`αq‖gχ`‖qlp	2`αq‖gχ`‖qlp	NOUN
ejpam-6519	26	18	)	)	PUNCT
ejpam-6519	26	19	1	1	NUM
ejpam-6519	26	20	q	q	NOUN
ejpam-6519	26	21	.	.	PUNCT
ejpam-6519	27	1	firstly	firstly	ADV
ejpam-6519	27	2	,	,	PUNCT
ejpam-6519	27	3	we	we	PRON
ejpam-6519	27	4	define	define	VERB
ejpam-6519	27	5	the	the	DET
ejpam-6519	27	6	idea	idea	NOUN
ejpam-6519	27	7	of	of	ADP
ejpam-6519	27	8	anisotropic	anisotropic	NOUN
ejpam-6519	27	9	herz	herz	ADJ
ejpam-6519	27	10	-	-	PUNCT
ejpam-6519	27	11	slice	slice	NOUN
ejpam-6519	27	12	spaces	space	NOUN
ejpam-6519	27	13	by	by	ADP
ejpam-6519	27	14	using	use	VERB
ejpam-6519	27	15	anisotropic	anisotropic	NOUN
ejpam-6519	27	16	herz	herz	ADJ
ejpam-6519	27	17	spaces	space	NOUN
ejpam-6519	27	18	and	and	CCONJ
ejpam-6519	27	19	slice	slice	NOUN
ejpam-6519	27	20	spaces	space	NOUN
ejpam-6519	27	21	.	.	PUNCT
ejpam-6519	28	1	we	we	PRON
ejpam-6519	28	2	will	will	AUX
ejpam-6519	28	3	establish	establish	VERB
ejpam-6519	28	4	the	the	DET
ejpam-6519	28	5	atomic	atomic	ADJ
ejpam-6519	28	6	decomposition	decomposition	NOUN
ejpam-6519	28	7	in	in	ADP
ejpam-6519	28	8	these	these	DET
ejpam-6519	28	9	spaces	space	NOUN
ejpam-6519	28	10	.	.	PUNCT
ejpam-6519	29	1	then	then	ADV
ejpam-6519	29	2	,	,	PUNCT
ejpam-6519	29	3	we	we	PRON
ejpam-6519	29	4	obtain	obtain	VERB
ejpam-6519	29	5	boundedness	boundedness	NOUN
ejpam-6519	29	6	for	for	ADP
ejpam-6519	29	7	sublinear	sublinear	NOUN
ejpam-6519	29	8	in	in	ADP
ejpam-6519	29	9	these	these	DET
ejpam-6519	29	10	spaces	space	NOUN
ejpam-6519	29	11	.	.	PUNCT
ejpam-6519	30	1	2	2	X
ejpam-6519	30	2	.	.	X
ejpam-6519	30	3	preliminaries	preliminary	NOUN
ejpam-6519	30	4	now	now	ADV
ejpam-6519	30	5	we	we	PRON
ejpam-6519	30	6	give	give	VERB
ejpam-6519	30	7	some	some	DET
ejpam-6519	30	8	notations	notation	NOUN
ejpam-6519	30	9	.	.	PUNCT
ejpam-6519	31	1	let	let	VERB
ejpam-6519	31	2	l	l	NOUN
ejpam-6519	31	3	∈	∈	PROPN
ejpam-6519	31	4	z	z	NOUN
ejpam-6519	31	5	,	,	PUNCT
ejpam-6519	31	6	define	define	VERB
ejpam-6519	31	7	bl	bl	ADP
ejpam-6519	31	8	:	:	PUNCT
ejpam-6519	31	9	=	=	PRON
ejpam-6519	31	10	{	{	PUNCT
ejpam-6519	31	11	z	z	PROPN
ejpam-6519	31	12	∈	∈	PROPN
ejpam-6519	31	13	rn	rn	PROPN
ejpam-6519	31	14	:	:	PUNCT
ejpam-6519	31	15	|z|	|z|	VERB
ejpam-6519	31	16	6	6	NUM
ejpam-6519	31	17	2l	2l	NOUN
ejpam-6519	31	18	}	}	PUNCT
ejpam-6519	31	19	,	,	PUNCT
ejpam-6519	31	20	rl	rl	ADP
ejpam-6519	31	21	:	:	PUNCT
ejpam-6519	31	22	=	=	PUNCT
ejpam-6519	31	23	bl\bl−1	bl\bl−1	NOUN
ejpam-6519	31	24	,	,	PUNCT
ejpam-6519	31	25	and	and	CCONJ
ejpam-6519	31	26	χl	χl	VERB
ejpam-6519	31	27	:	:	PUNCT
ejpam-6519	31	28	=	=	SYM
ejpam-6519	31	29	χrl	χrl	PROPN
ejpam-6519	31	30	.	.	PUNCT
ejpam-6519	32	1	a	a	DET
ejpam-6519	32	2	n	n	NUM
ejpam-6519	32	3	×	×	NOUN
ejpam-6519	32	4	n	n	CCONJ
ejpam-6519	32	5	real	real	ADJ
ejpam-6519	32	6	matrix	matrix	NOUN
ejpam-6519	32	7	o	o	NOUN
ejpam-6519	32	8	is	be	AUX
ejpam-6519	32	9	called	call	VERB
ejpam-6519	32	10	dilation	dilation	NOUN
ejpam-6519	32	11	or	or	CCONJ
ejpam-6519	32	12	expansive	expansive	ADJ
ejpam-6519	32	13	matrix	matrix	NOUN
ejpam-6519	32	14	if	if	SCONJ
ejpam-6519	32	15	|γ|	|γ|	PROPN
ejpam-6519	32	16	>	>	X
ejpam-6519	32	17	1	1	NUM
ejpam-6519	32	18	,	,	PUNCT
ejpam-6519	32	19	where	where	SCONJ
ejpam-6519	32	20	γ	γ	PROPN
ejpam-6519	32	21	is	be	AUX
ejpam-6519	32	22	the	the	DET
ejpam-6519	32	23	eigenvalue	eigenvalue	NOUN
ejpam-6519	32	24	.	.	PUNCT
ejpam-6519	33	1	let	let	VERB
ejpam-6519	33	2	γ1	γ1	NOUN
ejpam-6519	33	3	,	,	PUNCT
ejpam-6519	33	4	·	·	PUNCT
ejpam-6519	33	5	·	·	PUNCT
ejpam-6519	33	6	·	·	PUNCT
ejpam-6519	33	7	,	,	PUNCT
ejpam-6519	33	8	γn	γn	NUM
ejpam-6519	33	9	are	be	AUX
ejpam-6519	33	10	eigenvalues	eigenvalue	NOUN
ejpam-6519	33	11	of	of	ADP
ejpam-6519	33	12	o	o	NOUN
ejpam-6519	33	13	such	such	ADJ
ejpam-6519	33	14	that	that	SCONJ
ejpam-6519	33	15	1	1	NUM
ejpam-6519	33	16	<	<	X
ejpam-6519	33	17	|γ1|	|γ1|	X
ejpam-6519	33	18	≤	≤	NOUN
ejpam-6519	33	19	·	·	PUNCT
ejpam-6519	34	1	·	·	PUNCT
ejpam-6519	34	2	·	·	PUNCT
ejpam-6519	34	3	≤	≤	NUM
ejpam-6519	34	4	|γn|	|γn|	PROPN
ejpam-6519	34	5	and	and	CCONJ
ejpam-6519	34	6	γ−	γ−	PROPN
ejpam-6519	34	7	,	,	PUNCT
ejpam-6519	34	8	γ+	γ+	NUM
ejpam-6519	34	9	are	be	AUX
ejpam-6519	34	10	two	two	NUM
ejpam-6519	34	11	numbers	number	NOUN
ejpam-6519	34	12	such	such	ADJ
ejpam-6519	34	13	that	that	SCONJ
ejpam-6519	34	14	1	1	NUM
ejpam-6519	34	15	<	<	X
ejpam-6519	34	16	γ−	γ−	PROPN
ejpam-6519	35	1	<	<	X
ejpam-6519	35	2	|γ1|	|γ1|	PROPN
ejpam-6519	35	3	≤	≤	PROPN
ejpam-6519	35	4	|γn|	|γn|	PROPN
ejpam-6519	35	5	<	<	X
ejpam-6519	35	6	γ+	γ+	PROPN
ejpam-6519	35	7	.	.	PUNCT
ejpam-6519	36	1	let	let	VERB
ejpam-6519	36	2	|	|	ADV
ejpam-6519	36	3	·	·	PUNCT
ejpam-6519	36	4	|	|	ADV
ejpam-6519	36	5	is	be	AUX
ejpam-6519	36	6	the	the	DET
ejpam-6519	36	7	euclidean	euclidean	ADJ
ejpam-6519	36	8	norm	norm	NOUN
ejpam-6519	36	9	,	,	PUNCT
ejpam-6519	36	10	p	p	NOUN
ejpam-6519	36	11	is	be	AUX
ejpam-6519	36	12	nondegenerate	nondegenerate	ADJ
ejpam-6519	36	13	matrix	matrix	NOUN
ejpam-6519	36	14	of	of	ADP
ejpam-6519	36	15	order	order	NOUN
ejpam-6519	36	16	n×	n×	CCONJ
ejpam-6519	36	17	n	n	NOUN
ejpam-6519	36	18	and	and	CCONJ
ejpam-6519	36	19	r	r	X
ejpam-6519	36	20	>	>	X
ejpam-6519	36	21	1	1	NUM
ejpam-6519	36	22	,	,	PUNCT
ejpam-6519	36	23	then	then	ADV
ejpam-6519	36	24	the	the	DET
ejpam-6519	36	25	set	set	NOUN
ejpam-6519	36	26	∆	∆	PROPN
ejpam-6519	36	27	⊂	⊂	PROPN
ejpam-6519	36	28	rn	rn	PROPN
ejpam-6519	36	29	is	be	AUX
ejpam-6519	36	30	called	call	VERB
ejpam-6519	36	31	ellipsoid	ellipsoid	NOUN
ejpam-6519	36	32	if	if	SCONJ
ejpam-6519	36	33	∆	∆	PROPN
ejpam-6519	36	34	=	=	PRON
ejpam-6519	36	35	{	{	PUNCT
ejpam-6519	36	36	z	z	PROPN
ejpam-6519	36	37	∈	∈	PROPN
ejpam-6519	36	38	rn	rn	PROPN
ejpam-6519	36	39	:	:	PUNCT
ejpam-6519	36	40	|pz|	|pz|	PROPN
ejpam-6519	36	41	<	<	X
ejpam-6519	36	42	1	1	NUM
ejpam-6519	36	43	}	}	PUNCT
ejpam-6519	36	44	.	.	PUNCT
ejpam-6519	37	1	consider	consider	VERB
ejpam-6519	37	2	an	an	DET
ejpam-6519	37	3	ellipsoid	ellipsoid	NOUN
ejpam-6519	37	4	∆	∆	PROPN
ejpam-6519	37	5	and	and	CCONJ
ejpam-6519	37	6	r	r	X
ejpam-6519	37	7	>	>	X
ejpam-6519	37	8	1	1	NUM
ejpam-6519	37	9	,	,	PUNCT
ejpam-6519	37	10	dilation	dilation	NOUN
ejpam-6519	37	11	o	o	NOUN
ejpam-6519	37	12	,	,	PUNCT
ejpam-6519	37	13	∆	∆	PROPN
ejpam-6519	37	14	⊂	⊂	X
ejpam-6519	37	15	r∆	r∆	VERB
ejpam-6519	37	16	⊂	⊂	X
ejpam-6519	37	17	a∆	a∆	X
ejpam-6519	37	18	and	and	CCONJ
ejpam-6519	37	19	|∆|	|∆|	PROPN
ejpam-6519	37	20	=	=	SYM
ejpam-6519	37	21	1	1	NUM
ejpam-6519	37	22	,	,	PUNCT
ejpam-6519	37	23	|∆|	|∆|	PROPN
ejpam-6519	37	24	is	be	AUX
ejpam-6519	37	25	the	the	DET
ejpam-6519	37	26	lebesgue	lebesgue	ADJ
ejpam-6519	37	27	measure	measure	NOUN
ejpam-6519	37	28	of	of	ADP
ejpam-6519	37	29	∆.	∆.	PROPN
ejpam-6519	37	30	if	if	SCONJ
ejpam-6519	37	31	b	b	X
ejpam-6519	37	32	`	`	PUNCT
ejpam-6519	37	33	=	=	PUNCT
ejpam-6519	37	34	o`∆	o`∆	PUNCT
ejpam-6519	37	35	for	for	ADP
ejpam-6519	37	36	`	`	PUNCT
ejpam-6519	37	37	∈	∈	PROPN
ejpam-6519	37	38	z	z	PROPN
ejpam-6519	37	39	,	,	PUNCT
ejpam-6519	37	40	then	then	ADV
ejpam-6519	37	41	we	we	PRON
ejpam-6519	37	42	get	get	VERB
ejpam-6519	37	43	b	b	NUM
ejpam-6519	37	44	`	`	PUNCT
ejpam-6519	37	45	⊂	⊂	PUNCT
ejpam-6519	37	46	rb	rb	PROPN
ejpam-6519	37	47	`	`	PUNCT
ejpam-6519	37	48	⊂	⊂	PROPN
ejpam-6519	37	49	b`+1	b`+1	PROPN
ejpam-6519	37	50	,	,	PUNCT
ejpam-6519	37	51	and	and	CCONJ
ejpam-6519	37	52	|b`|	|b`|	PROPN
ejpam-6519	37	53	=	=	SYM
ejpam-6519	37	54	b	b	NOUN
ejpam-6519	37	55	`	`	PUNCT
ejpam-6519	37	56	such	such	ADJ
ejpam-6519	37	57	that	that	DET
ejpam-6519	37	58	b	b	X
ejpam-6519	37	59	=	=	PRON
ejpam-6519	37	60	∏n	∏n	ADJ
ejpam-6519	37	61	i=1	i=1	PROPN
ejpam-6519	37	62	|γi|	|γi|	NOUN
ejpam-6519	37	63	=	=	SYM
ejpam-6519	37	64	|deto|	|deto|	NOUN
ejpam-6519	37	65	>	>	SYM
ejpam-6519	37	66	1	1	X
ejpam-6519	37	67	.	.	PUNCT
ejpam-6519	37	68	assume	assume	VERB
ejpam-6519	37	69	that	that	SCONJ
ejpam-6519	37	70	w	w	NOUN
ejpam-6519	37	71	is	be	AUX
ejpam-6519	37	72	b.	b.	PROPN
ejpam-6519	37	73	sultan	sultan	PROPN
ejpam-6519	37	74	et	et	PROPN
ejpam-6519	37	75	al	al	PROPN
ejpam-6519	37	76	.	.	PUNCT
ejpam-6519	37	77	/	/	SYM
ejpam-6519	37	78	eur	eur	PROPN
ejpam-6519	37	79	.	.	PUNCT
ejpam-6519	38	1	j.	j.	PROPN
ejpam-6519	38	2	pure	pure	PROPN
ejpam-6519	38	3	appl	appl	PROPN
ejpam-6519	38	4	.	.	PROPN
ejpam-6519	38	5	math	math	PROPN
ejpam-6519	38	6	,	,	PUNCT
ejpam-6519	38	7	18	18	NUM
ejpam-6519	38	8	(	(	PUNCT
ejpam-6519	38	9	4	4	NUM
ejpam-6519	38	10	)	)	PUNCT
ejpam-6519	38	11	(	(	PUNCT
ejpam-6519	38	12	2025	2025	NUM
ejpam-6519	38	13	)	)	PUNCT
ejpam-6519	38	14	,	,	PUNCT
ejpam-6519	38	15	6519	6519	NUM
ejpam-6519	38	16	3	3	NUM
ejpam-6519	38	17	of	of	ADP
ejpam-6519	38	18	11	11	NUM
ejpam-6519	38	19	the	the	DET
ejpam-6519	38	20	smallest	small	ADJ
ejpam-6519	38	21	integer	integer	NOUN
ejpam-6519	39	1	such	such	ADJ
ejpam-6519	39	2	that	that	SCONJ
ejpam-6519	39	3	2b0	2b0	NUM
ejpam-6519	39	4	⊂	⊂	PROPN
ejpam-6519	39	5	owb0	owb0	PROPN
ejpam-6519	39	6	=	=	PUNCT
ejpam-6519	39	7	bw	bw	PROPN
ejpam-6519	39	8	.	.	PUNCT
ejpam-6519	40	1	a	a	DET
ejpam-6519	40	2	quaisi	quaisi	ADJ
ejpam-6519	40	3	-	-	PUNCT
ejpam-6519	40	4	norm	norm	NOUN
ejpam-6519	40	5	with	with	ADP
ejpam-6519	40	6	expansive	expansive	ADJ
ejpam-6519	40	7	matrix	matrix	NOUN
ejpam-6519	40	8	o	o	NOUN
ejpam-6519	40	9	is	be	AUX
ejpam-6519	40	10	a	a	DET
ejpam-6519	40	11	measurable	measurable	ADJ
ejpam-6519	40	12	mapping	mapping	NOUN
ejpam-6519	40	13	τo	τo	VERB
ejpam-6519	40	14	:	:	PUNCT
ejpam-6519	40	15	rn	rn	PROPN
ejpam-6519	40	16	→	→	PROPN
ejpam-6519	40	17	[	[	X
ejpam-6519	40	18	0,∞	0,∞	NUM
ejpam-6519	40	19	)	)	PUNCT
ejpam-6519	41	1	such	such	ADJ
ejpam-6519	41	2	that	that	SCONJ
ejpam-6519	41	3	τo(y	τo(y	PUNCT
ejpam-6519	41	4	)	)	PUNCT
ejpam-6519	41	5	>	>	X
ejpam-6519	41	6	0	0	PUNCT
ejpam-6519	42	1	for	for	ADP
ejpam-6519	42	2	y	y	PROPN
ejpam-6519	42	3	6=	6=	ADP
ejpam-6519	42	4	0	0	NUM
ejpam-6519	42	5	,	,	PUNCT
ejpam-6519	42	6	τo(ay	τo(ay	PROPN
ejpam-6519	42	7	)	)	PUNCT
ejpam-6519	42	8	=	=	PUNCT
ejpam-6519	42	9	|deta|τ(y	|deta|τ(y	NOUN
ejpam-6519	42	10	)	)	PUNCT
ejpam-6519	42	11	for	for	ADP
ejpam-6519	42	12	y	y	PROPN
ejpam-6519	42	13	∈	∈	PROPN
ejpam-6519	42	14	rn	rn	PROPN
ejpam-6519	42	15	,	,	PUNCT
ejpam-6519	42	16	τo(x+	τo(x+	X
ejpam-6519	42	17	y	y	X
ejpam-6519	42	18	)	)	PUNCT
ejpam-6519	42	19	≤	≤	NUM
ejpam-6519	42	20	c	c	X
ejpam-6519	42	21	(	(	PUNCT
ejpam-6519	42	22	τo(x	τo(x	PUNCT
ejpam-6519	42	23	)	)	PUNCT
ejpam-6519	42	24	+	+	CCONJ
ejpam-6519	42	25	τo(y	τo(y	X
ejpam-6519	42	26	)	)	PUNCT
ejpam-6519	42	27	)	)	PUNCT
ejpam-6519	43	1	for	for	ADP
ejpam-6519	43	2	x	x	SYM
ejpam-6519	43	3	,	,	PUNCT
ejpam-6519	43	4	y	y	PROPN
ejpam-6519	43	5	∈	∈	PROPN
ejpam-6519	43	6	rn	rn	PROPN
ejpam-6519	43	7	,	,	PUNCT
ejpam-6519	43	8	where	where	SCONJ
ejpam-6519	43	9	c	c	PROPN
ejpam-6519	43	10	≥	≥	NUM
ejpam-6519	43	11	1	1	NUM
ejpam-6519	43	12	.	.	PUNCT
ejpam-6519	44	1	the	the	DET
ejpam-6519	44	2	step	step	NOUN
ejpam-6519	44	3	homogeneous	homogeneous	ADJ
ejpam-6519	44	4	quasi	quasi	NOUN
ejpam-6519	44	5	-	-	NOUN
ejpam-6519	44	6	norm	norm	ADJ
ejpam-6519	44	7	τ	τ	PROPN
ejpam-6519	44	8	on	on	ADP
ejpam-6519	44	9	rn	rn	PROPN
ejpam-6519	44	10	defined	define	VERB
ejpam-6519	44	11	by	by	ADP
ejpam-6519	44	12	dilation	dilation	NOUN
ejpam-6519	44	13	o	o	NOUN
ejpam-6519	44	14	is	be	AUX
ejpam-6519	44	15	given	give	VERB
ejpam-6519	44	16	as	as	ADP
ejpam-6519	44	17	(	(	PUNCT
ejpam-6519	44	18	τ(x	τ(x	NOUN
ejpam-6519	44	19	)	)	PUNCT
ejpam-6519	44	20	=	=	PUNCT
ejpam-6519	44	21	bj	bj	VERB
ejpam-6519	44	22	for	for	ADP
ejpam-6519	44	23	x	x	PROPN
ejpam-6519	44	24	∈	∈	PROPN
ejpam-6519	44	25	bj+1	bj+1	PROPN
ejpam-6519	44	26	\	\	PROPN
ejpam-6519	44	27	bj	bj	NOUN
ejpam-6519	44	28	)	)	PUNCT
ejpam-6519	44	29	and	and	CCONJ
ejpam-6519	44	30	(	(	PUNCT
ejpam-6519	44	31	0	0	NUM
ejpam-6519	44	32	for	for	ADP
ejpam-6519	44	33	x	x	PUNCT
ejpam-6519	44	34	=	=	NOUN
ejpam-6519	44	35	0	0	NUM
ejpam-6519	44	36	)	)	PUNCT
ejpam-6519	44	37	.	.	PUNCT
ejpam-6519	45	1	if	if	SCONJ
ejpam-6519	45	2	x	x	X
ejpam-6519	45	3	,	,	PUNCT
ejpam-6519	45	4	y	y	PROPN
ejpam-6519	45	5	∈	∈	PROPN
ejpam-6519	45	6	rn	rn	PROPN
ejpam-6519	45	7	,	,	PUNCT
ejpam-6519	45	8	then	then	ADV
ejpam-6519	45	9	we	we	PRON
ejpam-6519	45	10	have	have	VERB
ejpam-6519	45	11	τ(x+	τ(x+	ADV
ejpam-6519	45	12	y	y	NOUN
ejpam-6519	45	13	)	)	PUNCT
ejpam-6519	45	14	≤	≤	NOUN
ejpam-6519	45	15	bw	bw	PROPN
ejpam-6519	45	16	(	(	PUNCT
ejpam-6519	45	17	τ(x	τ(x	ADJ
ejpam-6519	45	18	)	)	PUNCT
ejpam-6519	45	19	+	+	CCONJ
ejpam-6519	45	20	τ(y	τ(y	NOUN
ejpam-6519	45	21	)	)	PUNCT
ejpam-6519	45	22	)	)	PUNCT
ejpam-6519	45	23	.	.	PUNCT
ejpam-6519	46	1	(	(	PUNCT
ejpam-6519	46	2	2.1	2.1	NUM
ejpam-6519	46	3	)	)	PUNCT
ejpam-6519	46	4	definition	definition	NOUN
ejpam-6519	46	5	1	1	NUM
ejpam-6519	46	6	.	.	PUNCT
ejpam-6519	47	1	if	if	SCONJ
ejpam-6519	47	2	α	α	PROPN
ejpam-6519	47	3	∈	∈	PROPN
ejpam-6519	47	4	r	r	X
ejpam-6519	47	5	,	,	PUNCT
ejpam-6519	47	6	u	u	PROPN
ejpam-6519	47	7	∈	∈	PROPN
ejpam-6519	47	8	(	(	PUNCT
ejpam-6519	47	9	0,∞	0,∞	NOUN
ejpam-6519	47	10	)	)	PUNCT
ejpam-6519	47	11	,	,	PUNCT
ejpam-6519	47	12	p	p	X
ejpam-6519	47	13	,	,	PUNCT
ejpam-6519	47	14	q	q	NOUN
ejpam-6519	47	15	∈	∈	PROPN
ejpam-6519	47	16	[	[	X
ejpam-6519	47	17	1,∞	1,∞	NUM
ejpam-6519	47	18	)	)	PUNCT
ejpam-6519	47	19	and	and	CCONJ
ejpam-6519	47	20	r	r	NOUN
ejpam-6519	47	21	∈	∈	PROPN
ejpam-6519	47	22	(	(	PUNCT
ejpam-6519	47	23	1,∞	1,∞	NUM
ejpam-6519	47	24	)	)	PUNCT
ejpam-6519	47	25	,	,	PUNCT
ejpam-6519	47	26	then	then	ADV
ejpam-6519	47	27	the	the	DET
ejpam-6519	47	28	homogeneous	homogeneous	ADJ
ejpam-6519	47	29	version	version	NOUN
ejpam-6519	47	30	of	of	ADP
ejpam-6519	47	31	anisotropic	anisotropic	NOUN
ejpam-6519	47	32	herz	herz	ADJ
ejpam-6519	47	33	-	-	PUNCT
ejpam-6519	47	34	slice	slice	NOUN
ejpam-6519	47	35	spaces	space	NOUN
ejpam-6519	47	36	(	(	PUNCT
ejpam-6519	47	37	k̇eα	k̇eα	NOUN
ejpam-6519	47	38	,	,	PUNCT
ejpam-6519	47	39	p	p	NOUN
ejpam-6519	47	40	q	q	NOUN
ejpam-6519	47	41	,	,	PUNCT
ejpam-6519	47	42	r	r	NOUN
ejpam-6519	47	43	)	)	PUNCT
ejpam-6519	47	44	u	u	NOUN
ejpam-6519	47	45	(	(	PUNCT
ejpam-6519	47	46	o;rn	o;rn	NOUN
ejpam-6519	47	47	)	)	PUNCT
ejpam-6519	47	48	are	be	AUX
ejpam-6519	47	49	defined	define	VERB
ejpam-6519	47	50	by	by	ADP
ejpam-6519	47	51	(	(	PUNCT
ejpam-6519	47	52	k̇eα	k̇eα	NOUN
ejpam-6519	47	53	,	,	PUNCT
ejpam-6519	47	54	p	p	NOUN
ejpam-6519	47	55	q	q	NOUN
ejpam-6519	47	56	,	,	PUNCT
ejpam-6519	47	57	r	r	NOUN
ejpam-6519	47	58	)	)	PUNCT
ejpam-6519	47	59	u	u	NOUN
ejpam-6519	47	60	(	(	PUNCT
ejpam-6519	47	61	o;rn	o;rn	PROPN
ejpam-6519	47	62	)	)	PUNCT
ejpam-6519	47	63	=	=	PRON
ejpam-6519	47	64	{	{	PUNCT
ejpam-6519	47	65	g	g	PROPN
ejpam-6519	47	66	∈	∈	PROPN
ejpam-6519	47	67	(	(	PUNCT
ejpam-6519	47	68	ep	ep	PROPN
ejpam-6519	47	69	r	r	NOUN
ejpam-6519	47	70	)	)	PUNCT
ejpam-6519	47	71	u	u	NOUN
ejpam-6519	47	72	:	:	PUNCT
ejpam-6519	47	73	‖g‖	‖g‖	VERB
ejpam-6519	47	74	(	(	PUNCT
ejpam-6519	47	75	k̇eα	k̇eα	NOUN
ejpam-6519	47	76	,	,	PUNCT
ejpam-6519	47	77	p	p	NOUN
ejpam-6519	47	78	q	q	NOUN
ejpam-6519	47	79	,	,	PUNCT
ejpam-6519	47	80	r	r	NOUN
ejpam-6519	47	81	)	)	PUNCT
ejpam-6519	47	82	u	u	NOUN
ejpam-6519	47	83	(	(	PUNCT
ejpam-6519	47	84	o;rn	o;rn	PROPN
ejpam-6519	47	85	)	)	PUNCT
ejpam-6519	47	86	<	<	X
ejpam-6519	47	87	∞	∞	PROPN
ejpam-6519	47	88	}	}	PUNCT
ejpam-6519	47	89	,	,	PUNCT
ejpam-6519	47	90	where	where	SCONJ
ejpam-6519	47	91	‖g‖	‖g‖	VERB
ejpam-6519	47	92	(	(	PUNCT
ejpam-6519	47	93	k̇eα	k̇eα	NOUN
ejpam-6519	47	94	,	,	PUNCT
ejpam-6519	47	95	p	p	NOUN
ejpam-6519	47	96	q	q	NOUN
ejpam-6519	47	97	,	,	PUNCT
ejpam-6519	47	98	r	r	NOUN
ejpam-6519	47	99	)	)	PUNCT
ejpam-6519	47	100	u	u	NOUN
ejpam-6519	47	101	(	(	PUNCT
ejpam-6519	47	102	o;rn	o;rn	PROPN
ejpam-6519	47	103	)	)	PUNCT
ejpam-6519	47	104	=	=	PUNCT
ejpam-6519	47	105	(	(	PUNCT
ejpam-6519	47	106	∞∑	∞∑	NUM
ejpam-6519	47	107	`	`	PUNCT
ejpam-6519	47	108	=	=	SYM
ejpam-6519	47	109	−∞	−∞	NOUN
ejpam-6519	47	110	b`αq‖gχ`‖q(ep	b`αq‖gχ`‖q(ep	ADJ
ejpam-6519	47	111	r	r	NOUN
ejpam-6519	47	112	)	)	PUNCT
ejpam-6519	47	113	u	u	NOUN
ejpam-6519	47	114	)	)	PUNCT
ejpam-6519	47	115	1	1	NUM
ejpam-6519	47	116	q	q	NOUN
ejpam-6519	47	117	.	.	PUNCT
ejpam-6519	48	1	now	now	ADV
ejpam-6519	48	2	we	we	PRON
ejpam-6519	48	3	state	state	VERB
ejpam-6519	48	4	the	the	DET
ejpam-6519	48	5	hölder	hölder	NOUN
ejpam-6519	48	6	’s	’s	PART
ejpam-6519	48	7	inequality	inequality	NOUN
ejpam-6519	48	8	for	for	ADP
ejpam-6519	48	9	slice	slice	NOUN
ejpam-6519	48	10	space	space	NOUN
ejpam-6519	48	11	.	.	PUNCT
ejpam-6519	49	1	lemma	lemma	PROPN
ejpam-6519	49	2	2	2	NUM
ejpam-6519	49	3	.	.	PUNCT
ejpam-6519	50	1	[	[	X
ejpam-6519	50	2	26	26	NUM
ejpam-6519	50	3	]	]	PUNCT
ejpam-6519	50	4	let	let	VERB
ejpam-6519	50	5	1	1	NUM
ejpam-6519	50	6	≤	≤	NOUN
ejpam-6519	50	7	p	p	NOUN
ejpam-6519	50	8	≤	≤	NUM
ejpam-6519	50	9	∞	∞	PROPN
ejpam-6519	50	10	,	,	PUNCT
ejpam-6519	50	11	0	0	NUM
ejpam-6519	50	12	<	<	X
ejpam-6519	50	13	u	u	X
ejpam-6519	50	14	<	<	X
ejpam-6519	50	15	∞	∞	NUM
ejpam-6519	50	16	and	and	CCONJ
ejpam-6519	50	17	1	1	NUM
ejpam-6519	50	18	<	<	X
ejpam-6519	50	19	r	r	NOUN
ejpam-6519	50	20	<	<	X
ejpam-6519	50	21	∞	∞	PROPN
ejpam-6519	50	22	,	,	PUNCT
ejpam-6519	50	23	‖fg‖l1(rn	‖fg‖l1(rn	ADJ
ejpam-6519	50	24	)	)	PUNCT
ejpam-6519	50	25	≤	≤	NOUN
ejpam-6519	50	26	‖f‖(ep	‖f‖(ep	PROPN
ejpam-6519	50	27	r	r	NOUN
ejpam-6519	50	28	)	)	PUNCT
ejpam-6519	50	29	u	u	NOUN
ejpam-6519	50	30	‖g‖	‖g‖	PROPN
ejpam-6519	50	31	(	(	PUNCT
ejpam-6519	50	32	ep′	ep′	X
ejpam-6519	50	33	r′	r′	PROPN
ejpam-6519	50	34	)	)	PUNCT
ejpam-6519	50	35	u	u	NOUN
ejpam-6519	50	36	where	where	SCONJ
ejpam-6519	50	37	1	1	NUM
ejpam-6519	50	38	p	p	NOUN
ejpam-6519	50	39	+	+	NOUN
ejpam-6519	50	40	1	1	NUM
ejpam-6519	50	41	p′	p′	NOUN
ejpam-6519	50	42	=	=	SYM
ejpam-6519	50	43	1	1	NUM
ejpam-6519	50	44	r	r	NOUN
ejpam-6519	50	45	+	+	NUM
ejpam-6519	50	46	1	1	NUM
ejpam-6519	50	47	r′	r′	NOUN
ejpam-6519	50	48	=	=	SYM
ejpam-6519	50	49	1	1	X
ejpam-6519	50	50	.	.	PUNCT
ejpam-6519	51	1	lemma	lemma	PROPN
ejpam-6519	51	2	3	3	X
ejpam-6519	51	3	.	.	PUNCT
ejpam-6519	52	1	[	[	X
ejpam-6519	52	2	27	27	NUM
ejpam-6519	52	3	]	]	PUNCT
ejpam-6519	52	4	let	let	VERB
ejpam-6519	52	5	u	u	PRON
ejpam-6519	52	6	∈	∈	PROPN
ejpam-6519	52	7	(	(	PUNCT
ejpam-6519	52	8	0,∞	0,∞	NOUN
ejpam-6519	52	9	)	)	PUNCT
ejpam-6519	52	10	,	,	PUNCT
ejpam-6519	52	11	p	p	X
ejpam-6519	52	12	,	,	PUNCT
ejpam-6519	52	13	r	r	NOUN
ejpam-6519	52	14	∈	∈	PROPN
ejpam-6519	52	15	(	(	PUNCT
ejpam-6519	52	16	1,∞	1,∞	NUM
ejpam-6519	52	17	)	)	PUNCT
ejpam-6519	52	18	,	,	PUNCT
ejpam-6519	52	19	if	if	SCONJ
ejpam-6519	52	20	x0	x0	PROPN
ejpam-6519	52	21	∈	∈	PROPN
ejpam-6519	52	22	rn	rn	PROPN
ejpam-6519	52	23	,	,	PUNCT
ejpam-6519	52	24	and	and	CCONJ
ejpam-6519	52	25	1	1	NUM
ejpam-6519	52	26	<	<	X
ejpam-6519	52	27	r0	r0	NOUN
ejpam-6519	52	28	<	<	X
ejpam-6519	52	29	∞	∞	PROPN
ejpam-6519	52	30	,	,	PUNCT
ejpam-6519	52	31	then	then	ADV
ejpam-6519	52	32	the	the	DET
ejpam-6519	52	33	characteristic	characteristic	ADJ
ejpam-6519	52	34	function	function	NOUN
ejpam-6519	52	35	on	on	ADP
ejpam-6519	52	36	b	b	PROPN
ejpam-6519	52	37	(	(	PUNCT
ejpam-6519	52	38	x0	x0	PROPN
ejpam-6519	52	39	,	,	PUNCT
ejpam-6519	52	40	r0	r0	NOUN
ejpam-6519	52	41	)	)	PUNCT
ejpam-6519	52	42	fulfills∥∥χb(x0,r0	fulfills∥∥χb(x0,r0	NOUN
ejpam-6519	52	43	)	)	PUNCT
ejpam-6519	52	44	∥∥	∥∥	PROPN
ejpam-6519	52	45	(	(	PUNCT
ejpam-6519	52	46	ep	ep	PROPN
ejpam-6519	52	47	r	r	NOUN
ejpam-6519	52	48	)	)	PUNCT
ejpam-6519	52	49	u	u	NOUN
ejpam-6519	52	50	≤	≤	NOUN
ejpam-6519	52	51	cr	cr	PROPN
ejpam-6519	52	52	n	n	PROPN
ejpam-6519	52	53	/	/	SYM
ejpam-6519	52	54	p	p	NOUN
ejpam-6519	52	55	0	0	PROPN
ejpam-6519	52	56	.	.	PUNCT
ejpam-6519	53	1	remark	remark	PROPN
ejpam-6519	53	2	4	4	NUM
ejpam-6519	53	3	.	.	PUNCT
ejpam-6519	54	1	[	[	X
ejpam-6519	54	2	27	27	NUM
ejpam-6519	54	3	]	]	PUNCT
ejpam-6519	54	4	let	let	VERB
ejpam-6519	54	5	u	u	PRON
ejpam-6519	54	6	∈	∈	PROPN
ejpam-6519	54	7	(	(	PUNCT
ejpam-6519	54	8	0,∞	0,∞	NOUN
ejpam-6519	54	9	)	)	PUNCT
ejpam-6519	54	10	,	,	PUNCT
ejpam-6519	54	11	p.r	p.r	PROPN
ejpam-6519	54	12	∈	∈	PROPN
ejpam-6519	54	13	(	(	PUNCT
ejpam-6519	54	14	1,∞	1,∞	NUM
ejpam-6519	54	15	)	)	PUNCT
ejpam-6519	54	16	,	,	PUNCT
ejpam-6519	54	17	`	`	PUNCT
ejpam-6519	54	18	∈	∈	PROPN
ejpam-6519	54	19	z	z	NOUN
ejpam-6519	54	20	,	,	PUNCT
ejpam-6519	54	21	then	then	ADV
ejpam-6519	54	22	the	the	DET
ejpam-6519	54	23	characteristic	characteristic	ADJ
ejpam-6519	54	24	function	function	NOUN
ejpam-6519	54	25	on	on	ADP
ejpam-6519	54	26	r	r	NOUN
ejpam-6519	54	27	`	`	PUNCT
ejpam-6519	54	28	fulfills	fulfill	VERB
ejpam-6519	54	29	‖χr	‖χr	NUM
ejpam-6519	54	30	`	`	PUNCT
ejpam-6519	54	31	‖(ep	‖(ep	ADJ
ejpam-6519	54	32	r	r	NOUN
ejpam-6519	54	33	)	)	PUNCT
ejpam-6519	54	34	u	u	NOUN
ejpam-6519	54	35	≤	≤	PROPN
ejpam-6519	54	36	‖χb	‖χb	PROPN
ejpam-6519	54	37	`	`	PUNCT
ejpam-6519	54	38	‖	‖	PROPN
ejpam-6519	54	39	(	(	PUNCT
ejpam-6519	54	40	ep	ep	PROPN
ejpam-6519	54	41	r	r	NOUN
ejpam-6519	54	42	)	)	PUNCT
ejpam-6519	54	43	u	u	NOUN
ejpam-6519	54	44	)	)	PUNCT
ejpam-6519	54	45	≤	≤	ADJ
ejpam-6519	54	46	cb`n	cb`n	NOUN
ejpam-6519	54	47	/	/	SYM
ejpam-6519	54	48	p.	p.	NOUN
ejpam-6519	54	49	b.	b.	PROPN
ejpam-6519	55	1	sultan	sultan	PROPN
ejpam-6519	55	2	et	et	PROPN
ejpam-6519	55	3	al	al	PROPN
ejpam-6519	55	4	.	.	PUNCT
ejpam-6519	55	5	/	/	SYM
ejpam-6519	55	6	eur	eur	PROPN
ejpam-6519	55	7	.	.	PUNCT
ejpam-6519	56	1	j.	j.	PROPN
ejpam-6519	56	2	pure	pure	PROPN
ejpam-6519	56	3	appl	appl	PROPN
ejpam-6519	56	4	.	.	PROPN
ejpam-6519	56	5	math	math	PROPN
ejpam-6519	56	6	,	,	PUNCT
ejpam-6519	56	7	18	18	NUM
ejpam-6519	56	8	(	(	PUNCT
ejpam-6519	56	9	4	4	NUM
ejpam-6519	56	10	)	)	PUNCT
ejpam-6519	56	11	(	(	PUNCT
ejpam-6519	56	12	2025	2025	NUM
ejpam-6519	56	13	)	)	PUNCT
ejpam-6519	56	14	,	,	PUNCT
ejpam-6519	56	15	6519	6519	NUM
ejpam-6519	56	16	4	4	NUM
ejpam-6519	56	17	of	of	ADP
ejpam-6519	56	18	11	11	NUM
ejpam-6519	56	19	3	3	NUM
ejpam-6519	56	20	.	.	PUNCT
ejpam-6519	56	21	atomic	atomic	ADJ
ejpam-6519	56	22	decomposition	decomposition	NOUN
ejpam-6519	56	23	of	of	ADP
ejpam-6519	56	24	anisotropic	anisotropic	NOUN
ejpam-6519	56	25	herz	herz	ADJ
ejpam-6519	56	26	-	-	PUNCT
ejpam-6519	56	27	slice	slice	NOUN
ejpam-6519	56	28	spaces	space	NOUN
ejpam-6519	56	29	definition	definition	NOUN
ejpam-6519	56	30	5	5	NUM
ejpam-6519	56	31	.	.	PUNCT
ejpam-6519	57	1	let	let	VERB
ejpam-6519	57	2	α	α	PRON
ejpam-6519	57	3	∈	∈	PROPN
ejpam-6519	57	4	r	r	NOUN
ejpam-6519	57	5	,	,	PUNCT
ejpam-6519	57	6	and	and	CCONJ
ejpam-6519	57	7	p	p	X
ejpam-6519	57	8	,	,	PUNCT
ejpam-6519	57	9	q	q	ADJ
ejpam-6519	57	10	,	,	PUNCT
ejpam-6519	57	11	r	r	NOUN
ejpam-6519	57	12	,	,	PUNCT
ejpam-6519	57	13	u	u	NOUN
ejpam-6519	57	14	∈	∈	PROPN
ejpam-6519	57	15	(	(	PUNCT
ejpam-6519	57	16	0,∞	0,∞	NOUN
ejpam-6519	57	17	]	]	PUNCT
ejpam-6519	57	18	.	.	PUNCT
ejpam-6519	58	1	then	then	ADV
ejpam-6519	58	2	(	(	PUNCT
ejpam-6519	58	3	i	i	NOUN
ejpam-6519	58	4	)	)	PUNCT
ejpam-6519	58	5	a	a	DET
ejpam-6519	58	6	measurable	measurable	ADJ
ejpam-6519	58	7	function	function	NOUN
ejpam-6519	58	8	a(y	a(y	PROPN
ejpam-6519	58	9	)	)	PUNCT
ejpam-6519	58	10	is	be	AUX
ejpam-6519	58	11	called	call	VERB
ejpam-6519	58	12	central	central	ADJ
ejpam-6519	58	13	(	(	PUNCT
ejpam-6519	58	14	α	α	NOUN
ejpam-6519	58	15	,	,	PUNCT
ejpam-6519	58	16	p	p	X
ejpam-6519	58	17	,	,	PUNCT
ejpam-6519	58	18	r	r	NOUN
ejpam-6519	58	19	,	,	PUNCT
ejpam-6519	58	20	u)-block	u)-block	NOUN
ejpam-6519	58	21	if	if	SCONJ
ejpam-6519	58	22	supp	supp	PROPN
ejpam-6519	58	23	a	a	DET
ejpam-6519	58	24	⊂	⊂	X
ejpam-6519	58	25	bl	bl	PROPN
ejpam-6519	58	26	and	and	CCONJ
ejpam-6519	58	27	‖a‖(ep	‖a‖(ep	NOUN
ejpam-6519	58	28	r	r	NOUN
ejpam-6519	58	29	)	)	PUNCT
ejpam-6519	58	30	u	u	NOUN
ejpam-6519	58	31	≤	≤	NOUN
ejpam-6519	58	32	b−lα	b−lα	NOUN
ejpam-6519	58	33	.	.	PUNCT
ejpam-6519	59	1	(	(	PUNCT
ejpam-6519	59	2	ii	ii	NOUN
ejpam-6519	59	3	)	)	PUNCT
ejpam-6519	59	4	a	a	DET
ejpam-6519	59	5	measurable	measurable	ADJ
ejpam-6519	59	6	function	function	NOUN
ejpam-6519	59	7	a(y	a(y	PROPN
ejpam-6519	59	8	)	)	PUNCT
ejpam-6519	59	9	is	be	AUX
ejpam-6519	59	10	called	call	VERB
ejpam-6519	59	11	central	central	ADJ
ejpam-6519	59	12	(	(	PUNCT
ejpam-6519	59	13	α	α	NOUN
ejpam-6519	59	14	,	,	PUNCT
ejpam-6519	59	15	p	p	X
ejpam-6519	59	16	,	,	PUNCT
ejpam-6519	59	17	r	r	NOUN
ejpam-6519	59	18	,	,	PUNCT
ejpam-6519	59	19	u)-block	u)-block	NOUN
ejpam-6519	59	20	if	if	SCONJ
ejpam-6519	59	21	supp	supp	PROPN
ejpam-6519	59	22	a	a	PRON
ejpam-6519	59	23	⊂	⊂	PROPN
ejpam-6519	59	24	bl	bl	AUX
ejpam-6519	59	25	.	.	PUNCT
ejpam-6519	59	26	theorem	theorem	PROPN
ejpam-6519	59	27	3.1	3.1	NUM
ejpam-6519	59	28	.	.	PUNCT
ejpam-6519	60	1	let	let	VERB
ejpam-6519	60	2	α	α	PRON
ejpam-6519	60	3	∈	∈	PROPN
ejpam-6519	60	4	r	r	NOUN
ejpam-6519	60	5	,	,	PUNCT
ejpam-6519	60	6	and	and	CCONJ
ejpam-6519	60	7	p	p	X
ejpam-6519	60	8	,	,	PUNCT
ejpam-6519	60	9	q	q	ADJ
ejpam-6519	60	10	,	,	PUNCT
ejpam-6519	60	11	r	r	NOUN
ejpam-6519	60	12	,	,	PUNCT
ejpam-6519	60	13	u	u	NOUN
ejpam-6519	60	14	∈	∈	PROPN
ejpam-6519	60	15	(	(	PUNCT
ejpam-6519	60	16	0,∞	0,∞	NOUN
ejpam-6519	60	17	]	]	PUNCT
ejpam-6519	60	18	.	.	PUNCT
ejpam-6519	61	1	let	let	VERB
ejpam-6519	61	2	b	b	AUX
ejpam-6519	61	3	`	`	PUNCT
ejpam-6519	61	4	be	be	AUX
ejpam-6519	61	5	a	a	DET
ejpam-6519	61	6	central	central	ADJ
ejpam-6519	61	7	(	(	PUNCT
ejpam-6519	61	8	α	α	NOUN
ejpam-6519	61	9	,	,	PUNCT
ejpam-6519	61	10	p	p	X
ejpam-6519	61	11	,	,	PUNCT
ejpam-6519	61	12	r	r	NOUN
ejpam-6519	61	13	,	,	PUNCT
ejpam-6519	61	14	u)-block	u)-block	NOUN
ejpam-6519	61	15	with	with	ADP
ejpam-6519	61	16	support	support	NOUN
ejpam-6519	61	17	d	d	NOUN
ejpam-6519	61	18	in	in	ADP
ejpam-6519	61	19	b	b	PROPN
ejpam-6519	61	20	`	`	PUNCT
ejpam-6519	61	21	and	and	CCONJ
ejpam-6519	61	22	∑∞	∑∞	X
ejpam-6519	61	23	`	`	PUNCT
ejpam-6519	61	24	=	=	NOUN
ejpam-6519	61	25	−∞	−∞	ADP
ejpam-6519	61	26	|γ`|q	|γ`|q	PROPN
ejpam-6519	61	27	<	<	X
ejpam-6519	61	28	∞.	∞.	PROPN
ejpam-6519	61	29	then	then	ADV
ejpam-6519	61	30	the	the	DET
ejpam-6519	61	31	following	follow	VERB
ejpam-6519	61	32	two	two	NUM
ejpam-6519	61	33	statements	statement	NOUN
ejpam-6519	61	34	are	be	AUX
ejpam-6519	61	35	equivalent	equivalent	ADJ
ejpam-6519	61	36	:	:	PUNCT
ejpam-6519	61	37	(	(	PUNCT
ejpam-6519	61	38	i	i	NOUN
ejpam-6519	61	39	)	)	PUNCT
ejpam-6519	61	40	g	g	PROPN
ejpam-6519	61	41	∈	∈	PROPN
ejpam-6519	61	42	(	(	PUNCT
ejpam-6519	61	43	k̇eα	k̇eα	NOUN
ejpam-6519	61	44	,	,	PUNCT
ejpam-6519	61	45	p	p	NOUN
ejpam-6519	61	46	q	q	NOUN
ejpam-6519	61	47	,	,	PUNCT
ejpam-6519	61	48	r	r	NOUN
ejpam-6519	61	49	)	)	PUNCT
ejpam-6519	61	50	u	u	NOUN
ejpam-6519	61	51	(	(	PUNCT
ejpam-6519	61	52	o;rn	o;rn	PROPN
ejpam-6519	61	53	)	)	PUNCT
ejpam-6519	61	54	.	.	PUNCT
ejpam-6519	62	1	(	(	PUNCT
ejpam-6519	62	2	ii	ii	NOUN
ejpam-6519	62	3	)	)	PUNCT
ejpam-6519	62	4	g	g	NOUN
ejpam-6519	62	5	are	be	AUX
ejpam-6519	62	6	given	give	VERB
ejpam-6519	62	7	as	as	ADP
ejpam-6519	62	8	g(y	g(y	NOUN
ejpam-6519	62	9	)	)	PUNCT
ejpam-6519	62	10	=	=	PUNCT
ejpam-6519	63	1	∞∑	∞∑	NUM
ejpam-6519	63	2	`	`	PUNCT
ejpam-6519	63	3	=	=	NOUN
ejpam-6519	63	4	−∞	−∞	X
ejpam-6519	63	5	γ`b`(y	γ`b`(y	NUM
ejpam-6519	63	6	)	)	PUNCT
ejpam-6519	63	7	.	.	PUNCT
ejpam-6519	64	1	(	(	PUNCT
ejpam-6519	64	2	2.1	2.1	NUM
ejpam-6519	64	3	)	)	PUNCT
ejpam-6519	64	4	proof	proof	NOUN
ejpam-6519	64	5	.	.	PUNCT
ejpam-6519	65	1	we	we	PRON
ejpam-6519	65	2	first	first	ADV
ejpam-6519	65	3	prove	prove	VERB
ejpam-6519	65	4	(	(	PUNCT
ejpam-6519	65	5	i	i	NOUN
ejpam-6519	65	6	)	)	PUNCT
ejpam-6519	65	7	implies	imply	VERB
ejpam-6519	65	8	(	(	PUNCT
ejpam-6519	65	9	ii	ii	NOUN
ejpam-6519	65	10	)	)	PUNCT
ejpam-6519	65	11	.	.	PUNCT
ejpam-6519	66	1	for	for	ADP
ejpam-6519	66	2	every	every	DET
ejpam-6519	66	3	g	g	PROPN
ejpam-6519	66	4	∈	∈	PROPN
ejpam-6519	66	5	(	(	PUNCT
ejpam-6519	66	6	k̇eα	k̇eα	NOUN
ejpam-6519	66	7	,	,	PUNCT
ejpam-6519	66	8	p	p	NOUN
ejpam-6519	66	9	q	q	NOUN
ejpam-6519	66	10	,	,	PUNCT
ejpam-6519	66	11	r	r	NOUN
ejpam-6519	66	12	)	)	PUNCT
ejpam-6519	66	13	u	u	NOUN
ejpam-6519	66	14	(	(	PUNCT
ejpam-6519	66	15	o;rn	o;rn	PROPN
ejpam-6519	66	16	)	)	PUNCT
ejpam-6519	66	17	,	,	PUNCT
ejpam-6519	66	18	write	write	VERB
ejpam-6519	66	19	g(y	g(y	NOUN
ejpam-6519	66	20	)	)	PUNCT
ejpam-6519	66	21	=	=	PUNCT
ejpam-6519	67	1	∞∑	∞∑	NUM
ejpam-6519	67	2	`	`	PUNCT
ejpam-6519	67	3	=	=	SYM
ejpam-6519	67	4	−∞	−∞	NOUN
ejpam-6519	67	5	g(y)χ`(y	g(y)χ`(y	NOUN
ejpam-6519	67	6	)	)	PUNCT
ejpam-6519	67	7	=	=	PUNCT
ejpam-6519	68	1	∞∑	∞∑	NUM
ejpam-6519	68	2	`	`	PUNCT
ejpam-6519	68	3	=	=	NOUN
ejpam-6519	68	4	−∞	−∞	NOUN
ejpam-6519	68	5	b`α	b`α	PROPN
ejpam-6519	68	6	‖gχ`‖(ep	‖gχ`‖(ep	PROPN
ejpam-6519	68	7	r	r	NOUN
ejpam-6519	68	8	)	)	PUNCT
ejpam-6519	68	9	u	u	NOUN
ejpam-6519	68	10	g(y)χ`(y	g(y)χ`(y	NOUN
ejpam-6519	68	11	)	)	PUNCT
ejpam-6519	68	12	b`α	b`α	PROPN
ejpam-6519	68	13	‖χ`‖(ep	‖χ`‖(ep	NOUN
ejpam-6519	68	14	r	r	NOUN
ejpam-6519	68	15	)	)	PUNCT
ejpam-6519	68	16	u	u	NOUN
ejpam-6519	68	17	=	=	NOUN
ejpam-6519	68	18	∞∑	∞∑	NUM
ejpam-6519	68	19	`	`	PUNCT
ejpam-6519	68	20	=	=	NOUN
ejpam-6519	68	21	−∞	−∞	X
ejpam-6519	68	22	γ`b`(x	γ`b`(x	NUM
ejpam-6519	68	23	)	)	PUNCT
ejpam-6519	68	24	,	,	PUNCT
ejpam-6519	68	25	where	where	SCONJ
ejpam-6519	68	26	γ	γ	X
ejpam-6519	68	27	`	`	PUNCT
ejpam-6519	68	28	=	=	PUNCT
ejpam-6519	68	29	b`α	b`α	PROPN
ejpam-6519	68	30	‖gχ`‖(ep	‖gχ`‖(ep	NOUN
ejpam-6519	68	31	r	r	X
ejpam-6519	68	32	)	)	PUNCT
ejpam-6519	68	33	u	u	NOUN
ejpam-6519	68	34	and	and	CCONJ
ejpam-6519	68	35	b`(x	b`(x	ADJ
ejpam-6519	68	36	)	)	PUNCT
ejpam-6519	68	37	=	=	SYM
ejpam-6519	68	38	g(y)χ`(y	g(y)χ`(y	NOUN
ejpam-6519	68	39	)	)	PUNCT
ejpam-6519	69	1	b`α‖χ`‖(ep	b`α‖χ`‖(ep	PROPN
ejpam-6519	69	2	r	r	NOUN
ejpam-6519	69	3	)	)	PUNCT
ejpam-6519	69	4	u	u	NOUN
ejpam-6519	69	5	.	.	PUNCT
ejpam-6519	70	1	it	it	PRON
ejpam-6519	70	2	is	be	AUX
ejpam-6519	70	3	easy	easy	ADJ
ejpam-6519	70	4	to	to	PART
ejpam-6519	70	5	note	note	VERB
ejpam-6519	70	6	that	that	SCONJ
ejpam-6519	70	7	supp	supp	PROPN
ejpam-6519	70	8	b	b	PROPN
ejpam-6519	70	9	`	`	PUNCT
ejpam-6519	70	10	⊂	⊂	PROPN
ejpam-6519	70	11	b	b	X
ejpam-6519	70	12	`	`	PUNCT
ejpam-6519	70	13	and	and	CCONJ
ejpam-6519	70	14	‖b`‖(ep	‖b`‖(ep	NOUN
ejpam-6519	70	15	r	r	NOUN
ejpam-6519	70	16	)	)	PUNCT
ejpam-6519	70	17	u	u	NOUN
ejpam-6519	70	18	=	=	PROPN
ejpam-6519	70	19	|b`|−α	|b`|−α	PROPN
ejpam-6519	70	20	/	/	SYM
ejpam-6519	70	21	n.	n.	PROPN
ejpam-6519	71	1	so	so	ADV
ejpam-6519	71	2	every	every	DET
ejpam-6519	71	3	b	b	NOUN
ejpam-6519	71	4	`	`	PUNCT
ejpam-6519	71	5	is	be	AUX
ejpam-6519	71	6	a	a	DET
ejpam-6519	71	7	central	central	ADJ
ejpam-6519	71	8	(	(	PUNCT
ejpam-6519	71	9	α	α	NOUN
ejpam-6519	71	10	,	,	PUNCT
ejpam-6519	71	11	p	p	X
ejpam-6519	71	12	,	,	PUNCT
ejpam-6519	71	13	r	r	NOUN
ejpam-6519	71	14	,	,	PUNCT
ejpam-6519	71	15	u)-block	u)-block	NOUN
ejpam-6519	71	16	with	with	ADP
ejpam-6519	71	17	support	support	NOUN
ejpam-6519	71	18	contained	contain	VERB
ejpam-6519	71	19	in	in	ADP
ejpam-6519	71	20	b	b	PROPN
ejpam-6519	71	21	`	`	PUNCT
ejpam-6519	71	22	∞∑	∞∑	NUM
ejpam-6519	71	23	`	`	PUNCT
ejpam-6519	71	24	=	=	NOUN
ejpam-6519	71	25	−∞	−∞	NOUN
ejpam-6519	71	26	|γ`|q	|γ`|q	NOUN
ejpam-6519	71	27	=	=	NOUN
ejpam-6519	72	1	∞∑	∞∑	NUM
ejpam-6519	72	2	`	`	PUNCT
ejpam-6519	72	3	=	=	NOUN
ejpam-6519	72	4	−∞	−∞	NOUN
ejpam-6519	72	5	b`α	b`α	PROPN
ejpam-6519	72	6	‖gχ`‖q(ep	‖gχ`‖q(ep	PROPN
ejpam-6519	72	7	r	r	NOUN
ejpam-6519	72	8	)	)	PUNCT
ejpam-6519	72	9	u	u	NOUN
ejpam-6519	72	10	=	=	NOUN
ejpam-6519	72	11	‖g‖q	‖g‖q	PROPN
ejpam-6519	72	12	(	(	PUNCT
ejpam-6519	72	13	k̇eα	k̇eα	NOUN
ejpam-6519	72	14	,	,	PUNCT
ejpam-6519	72	15	p	p	NOUN
ejpam-6519	72	16	q	q	NOUN
ejpam-6519	72	17	,	,	PUNCT
ejpam-6519	72	18	r	r	NOUN
ejpam-6519	72	19	)	)	PUNCT
ejpam-6519	72	20	u	u	NOUN
ejpam-6519	72	21	(	(	PUNCT
ejpam-6519	72	22	o;rn	o;rn	PROPN
ejpam-6519	72	23	)	)	PUNCT
ejpam-6519	72	24	<	<	X
ejpam-6519	73	1	∞.	∞.	PROPN
ejpam-6519	73	2	now	now	ADV
ejpam-6519	73	3	we	we	PRON
ejpam-6519	73	4	prove	prove	VERB
ejpam-6519	73	5	(	(	PUNCT
ejpam-6519	73	6	ii	ii	NOUN
ejpam-6519	73	7	)	)	PUNCT
ejpam-6519	73	8	implies	imply	VERB
ejpam-6519	73	9	(	(	PUNCT
ejpam-6519	73	10	i	i	NOUN
ejpam-6519	73	11	)	)	PUNCT
ejpam-6519	73	12	.	.	PUNCT
ejpam-6519	74	1	let	let	VERB
ejpam-6519	74	2	g(y	g(y	PRON
ejpam-6519	74	3	)	)	PUNCT
ejpam-6519	74	4	=	=	PUNCT
ejpam-6519	75	1	∑∞	∑∞	NOUN
ejpam-6519	75	2	`	`	PUNCT
ejpam-6519	75	3	=	=	NOUN
ejpam-6519	75	4	−∞	−∞	X
ejpam-6519	75	5	γ`b`(y	γ`b`(y	NUM
ejpam-6519	75	6	)	)	PUNCT
ejpam-6519	75	7	,	,	PUNCT
ejpam-6519	75	8	we	we	PRON
ejpam-6519	75	9	get	get	VERB
ejpam-6519	75	10	‖gχj‖(ep	‖gχj‖(ep	PUNCT
ejpam-6519	75	11	r	r	NOUN
ejpam-6519	75	12	)	)	PUNCT
ejpam-6519	75	13	u	u	NOUN
ejpam-6519	75	14	≤	≤	VERB
ejpam-6519	75	15	∞∑	∞∑	NUM
ejpam-6519	75	16	`	`	PUNCT
ejpam-6519	75	17	=	=	PRON
ejpam-6519	75	18	j	j	X
ejpam-6519	75	19	|γ`|	|γ`|	X
ejpam-6519	75	20	‖b`‖(ep	‖b`‖(ep	NOUN
ejpam-6519	75	21	r	r	NOUN
ejpam-6519	75	22	)	)	PUNCT
ejpam-6519	75	23	u	u	NOUN
ejpam-6519	75	24	.	.	PUNCT
ejpam-6519	76	1	(	(	PUNCT
ejpam-6519	76	2	3.1	3.1	NUM
ejpam-6519	76	3	)	)	PUNCT
ejpam-6519	76	4	if	if	SCONJ
ejpam-6519	76	5	0	0	NUM
ejpam-6519	76	6	<	<	X
ejpam-6519	76	7	q	q	X
ejpam-6519	76	8	≤	≤	NUM
ejpam-6519	76	9	1	1	NUM
ejpam-6519	76	10	.	.	PUNCT
ejpam-6519	76	11	from	from	ADP
ejpam-6519	76	12	(	(	PUNCT
ejpam-6519	76	13	3.1	3.1	NUM
ejpam-6519	76	14	)	)	PUNCT
ejpam-6519	76	15	it	it	PRON
ejpam-6519	76	16	follows	follow	VERB
ejpam-6519	76	17	that	that	DET
ejpam-6519	76	18	‖g‖q	‖g‖q	NOUN
ejpam-6519	76	19	(	(	PUNCT
ejpam-6519	76	20	k̇eα	k̇eα	NOUN
ejpam-6519	76	21	,	,	PUNCT
ejpam-6519	76	22	p	p	NOUN
ejpam-6519	76	23	q	q	NOUN
ejpam-6519	76	24	,	,	PUNCT
ejpam-6519	76	25	r	r	NOUN
ejpam-6519	76	26	)	)	PUNCT
ejpam-6519	76	27	u	u	NOUN
ejpam-6519	76	28	(	(	PUNCT
ejpam-6519	76	29	o;rn	o;rn	PROPN
ejpam-6519	76	30	)	)	PUNCT
ejpam-6519	76	31	=	=	PUNCT
ejpam-6519	77	1	∞∑	∞∑	NUM
ejpam-6519	77	2	`	`	PUNCT
ejpam-6519	77	3	=	=	SYM
ejpam-6519	77	4	−∞	−∞	NOUN
ejpam-6519	77	5	b`α	b`α	PROPN
ejpam-6519	77	6	‖gχ`‖q(ep	‖gχ`‖q(ep	PROPN
ejpam-6519	77	7	r	r	NOUN
ejpam-6519	77	8	)	)	PUNCT
ejpam-6519	77	9	u	u	PROPN
ejpam-6519	77	10	b.	b.	PROPN
ejpam-6519	77	11	sultan	sultan	PROPN
ejpam-6519	77	12	et	et	PROPN
ejpam-6519	77	13	al	al	PROPN
ejpam-6519	77	14	.	.	PUNCT
ejpam-6519	77	15	/	/	SYM
ejpam-6519	77	16	eur	eur	PROPN
ejpam-6519	77	17	.	.	PUNCT
ejpam-6519	78	1	j.	j.	PROPN
ejpam-6519	78	2	pure	pure	PROPN
ejpam-6519	78	3	appl	appl	PROPN
ejpam-6519	78	4	.	.	PROPN
ejpam-6519	78	5	math	math	PROPN
ejpam-6519	78	6	,	,	PUNCT
ejpam-6519	78	7	18	18	NUM
ejpam-6519	78	8	(	(	PUNCT
ejpam-6519	78	9	4	4	NUM
ejpam-6519	78	10	)	)	PUNCT
ejpam-6519	78	11	(	(	PUNCT
ejpam-6519	78	12	2025	2025	NUM
ejpam-6519	78	13	)	)	PUNCT
ejpam-6519	78	14	,	,	PUNCT
ejpam-6519	78	15	6519	6519	NUM
ejpam-6519	78	16	5	5	NUM
ejpam-6519	78	17	of	of	ADP
ejpam-6519	78	18	11	11	NUM
ejpam-6519	78	19	≤	≤	NOUN
ejpam-6519	79	1	∞∑	∞∑	NUM
ejpam-6519	79	2	`	`	PUNCT
ejpam-6519	79	3	=	=	NOUN
ejpam-6519	79	4	−∞	−∞	NOUN
ejpam-6519	79	5	b`αq	b`αq	NOUN
ejpam-6519	79	6	‖gχ`‖q(ep	‖gχ`‖q(ep	PROPN
ejpam-6519	79	7	r	r	NOUN
ejpam-6519	79	8	)	)	PUNCT
ejpam-6519	79	9	u	u	NOUN
ejpam-6519	79	10	≤	≤	VERB
ejpam-6519	79	11	∞∑	∞∑	NUM
ejpam-6519	79	12	`	`	PUNCT
ejpam-6519	79	13	=	=	NOUN
ejpam-6519	79	14	−∞	−∞	NOUN
ejpam-6519	79	15	b`αq	b`αq	ADP
ejpam-6519	79	16			PROPN
ejpam-6519	79	17	∞∑	∞∑	NUM
ejpam-6519	79	18	j=	j=	NOUN
ejpam-6519	79	19	`	`	PUNCT
ejpam-6519	79	20	|γj	|γj	NOUN
ejpam-6519	79	21	|q	|q	NOUN
ejpam-6519	79	22	‖bj‖q(ep	‖bj‖q(ep	PROPN
ejpam-6519	79	23	r	r	NOUN
ejpam-6519	79	24	)	)	PUNCT
ejpam-6519	79	25	u	u	NOUN
ejpam-6519	79	26			PROPN
ejpam-6519	79	27	.	.	PUNCT
ejpam-6519	80	1	let	let	VERB
ejpam-6519	80	2	i	i	PRON
ejpam-6519	80	3	=	=	PUNCT
ejpam-6519	81	1	∞∑	∞∑	NUM
ejpam-6519	81	2	`	`	PUNCT
ejpam-6519	81	3	=	=	NOUN
ejpam-6519	81	4	−∞	−∞	X
ejpam-6519	81	5	b`αq	b`αq	NOUN
ejpam-6519	81	6	(	(	PUNCT
ejpam-6519	81	7	∑∞	∑∞	NOUN
ejpam-6519	81	8	j=	j=	VERB
ejpam-6519	81	9	`	`	PUNCT
ejpam-6519	81	10	|γj	|γj	PROPN
ejpam-6519	81	11	|	|	NOUN
ejpam-6519	81	12	q	q	NOUN
ejpam-6519	81	13	‖bj‖q(ep	‖bj‖q(ep	PROPN
ejpam-6519	81	14	r	r	NOUN
ejpam-6519	81	15	)	)	PUNCT
ejpam-6519	81	16	u	u	NOUN
ejpam-6519	81	17	)	)	PUNCT
ejpam-6519	81	18	.	.	PUNCT
ejpam-6519	82	1	by	by	ADP
ejpam-6519	82	2	using	use	VERB
ejpam-6519	82	3	the	the	DET
ejpam-6519	82	4	fact	fact	NOUN
ejpam-6519	82	5	0	0	PUNCT
ejpam-6519	82	6	<	<	X
ejpam-6519	82	7	α	α	X
ejpam-6519	82	8	<	<	X
ejpam-6519	82	9	∞	∞	PROPN
ejpam-6519	82	10	,	,	PUNCT
ejpam-6519	82	11	we	we	PRON
ejpam-6519	82	12	get	get	VERB
ejpam-6519	82	13	i	i	PRON
ejpam-6519	82	14	=	=	PUNCT
ejpam-6519	83	1	∞∑	∞∑	NUM
ejpam-6519	83	2	`	`	PUNCT
ejpam-6519	83	3	=	=	NOUN
ejpam-6519	83	4	−∞	−∞	NOUN
ejpam-6519	83	5	b`αq	b`αq	ADP
ejpam-6519	83	6			PROPN
ejpam-6519	83	7	∞∑	∞∑	NUM
ejpam-6519	83	8	j=	j=	NOUN
ejpam-6519	83	9	`	`	PUNCT
ejpam-6519	83	10	|γj	|γj	NOUN
ejpam-6519	83	11	|q	|q	NOUN
ejpam-6519	83	12	‖bj‖q(ep	‖bj‖q(ep	PROPN
ejpam-6519	83	13	r	r	NOUN
ejpam-6519	83	14	)	)	PUNCT
ejpam-6519	83	15	u	u	NOUN
ejpam-6519	83	16			PROPN
ejpam-6519	83	17	.	.	PUNCT
ejpam-6519	84	1	∞∑	∞∑	NUM
ejpam-6519	84	2	`	`	PUNCT
ejpam-6519	84	3	=	=	NOUN
ejpam-6519	84	4	−∞	−∞	NOUN
ejpam-6519	84	5	b`αq	b`αq	ADP
ejpam-6519	84	6	∞∑	∞∑	NUM
ejpam-6519	84	7	j=	j=	NOUN
ejpam-6519	84	8	`	`	PUNCT
ejpam-6519	84	9	|γj	|γj	NOUN
ejpam-6519	84	10	|q	|q	NOUN
ejpam-6519	84	11	b−jαq	b−jαq	NOUN
ejpam-6519	84	12	.	.	PUNCT
ejpam-6519	85	1	∞∑	∞∑	NUM
ejpam-6519	85	2	`	`	PUNCT
ejpam-6519	85	3	=	=	NOUN
ejpam-6519	85	4	−∞	−∞	ADP
ejpam-6519	85	5	∞∑	∞∑	NUM
ejpam-6519	85	6	j=	j=	NOUN
ejpam-6519	85	7	`	`	PUNCT
ejpam-6519	85	8	|γj	|γj	NOUN
ejpam-6519	85	9	|q	|q	NOUN
ejpam-6519	85	10	b(`−j)αq	b(`−j)αq	NOUN
ejpam-6519	85	11	.	.	PUNCT
ejpam-6519	86	1	∞∑	∞∑	NUM
ejpam-6519	86	2	j=−∞	j=−∞	NOUN
ejpam-6519	87	1	j∑	j∑	PROPN
ejpam-6519	87	2	`	`	PUNCT
ejpam-6519	87	3	=	=	NOUN
ejpam-6519	87	4	−∞	−∞	X
ejpam-6519	87	5	|γj	|γj	NOUN
ejpam-6519	87	6	|q	|q	NOUN
ejpam-6519	87	7	b(`−j)αq	b(`−j)αq	NOUN
ejpam-6519	87	8	.	.	PUNCT
ejpam-6519	88	1	∞∑	∞∑	NUM
ejpam-6519	88	2	j=−∞	j=−∞	ADJ
ejpam-6519	88	3	|γj	|γj	NOUN
ejpam-6519	88	4	|q	|q	NOUN
ejpam-6519	88	5	.	.	PUNCT
ejpam-6519	89	1	if	if	SCONJ
ejpam-6519	89	2	1	1	NUM
ejpam-6519	89	3	<	<	X
ejpam-6519	89	4	q	q	X
ejpam-6519	89	5	<	<	X
ejpam-6519	89	6	∞	∞	PROPN
ejpam-6519	89	7	,	,	PUNCT
ejpam-6519	89	8	we	we	PRON
ejpam-6519	89	9	have	have	VERB
ejpam-6519	89	10	for	for	ADP
ejpam-6519	89	11	i	i	PRON
ejpam-6519	89	12	,	,	PUNCT
ejpam-6519	89	13	if	if	SCONJ
ejpam-6519	89	14	0	0	NUM
ejpam-6519	89	15	<	<	X
ejpam-6519	89	16	α	α	X
ejpam-6519	89	17	<	<	X
ejpam-6519	89	18	∞	∞	PROPN
ejpam-6519	89	19	,	,	PUNCT
ejpam-6519	89	20	then	then	ADV
ejpam-6519	89	21	(	(	PUNCT
ejpam-6519	89	22	3.1	3.1	NUM
ejpam-6519	89	23	)	)	PUNCT
ejpam-6519	89	24	and	and	CCONJ
ejpam-6519	89	25	hölder	hölder	PROPN
ejpam-6519	89	26	’s	’s	PART
ejpam-6519	89	27	inequality	inequality	NOUN
ejpam-6519	89	28	yields	yield	VERB
ejpam-6519	89	29	i	i	PRON
ejpam-6519	89	30	.	.	PUNCT
ejpam-6519	90	1	∞∑	∞∑	NUM
ejpam-6519	90	2	`	`	PUNCT
ejpam-6519	90	3	=	=	NOUN
ejpam-6519	90	4	−∞	−∞	NOUN
ejpam-6519	90	5	b`αq	b`αq	ADP
ejpam-6519	90	6			PROPN
ejpam-6519	90	7	∞∑	∞∑	NUM
ejpam-6519	90	8	j=	j=	NOUN
ejpam-6519	90	9	`	`	PUNCT
ejpam-6519	90	10	|γj	|γj	NOUN
ejpam-6519	90	11	|	|	ADV
ejpam-6519	90	12	‖bj‖(ep	‖bj‖(ep	ADJ
ejpam-6519	90	13	r	r	NOUN
ejpam-6519	90	14	)	)	PUNCT
ejpam-6519	90	15	u	u	NOUN
ejpam-6519	90	16			PROPN
ejpam-6519	90	17	.	.	PUNCT
ejpam-6519	91	1	∞∑	∞∑	NUM
ejpam-6519	91	2	`	`	PUNCT
ejpam-6519	91	3	=	=	NOUN
ejpam-6519	91	4	−∞	−∞	ADP
ejpam-6519	91	5			PROPN
ejpam-6519	91	6	∞∑	∞∑	NUM
ejpam-6519	91	7	j=	j=	NOUN
ejpam-6519	91	8	`	`	PUNCT
ejpam-6519	91	9	|γj	|γj	PROPN
ejpam-6519	91	10	|	|	ADV
ejpam-6519	91	11	b(`−j)α	b(`−j)α	PROPN
ejpam-6519	91	12	q	q	INTJ
ejpam-6519	91	13	.	.	PUNCT
ejpam-6519	92	1	∞∑	∞∑	NUM
ejpam-6519	92	2	`	`	PUNCT
ejpam-6519	92	3	=	=	NOUN
ejpam-6519	92	4	−∞	−∞	ADP
ejpam-6519	92	5			PROPN
ejpam-6519	92	6	∞∑	∞∑	NUM
ejpam-6519	92	7	j=	j=	NOUN
ejpam-6519	92	8	`	`	PUNCT
ejpam-6519	92	9	|γj	|γj	NOUN
ejpam-6519	92	10	|q	|q	NOUN
ejpam-6519	92	11	b(`−j)αq/2	b(`−j)αq/2	NOUN
ejpam-6519	92	12			PUNCT
ejpam-6519	92	13	∞∑	∞∑	NUM
ejpam-6519	92	14	j=	j=	NOUN
ejpam-6519	92	15	`	`	PUNCT
ejpam-6519	92	16	b(`−j)αq′/2	b(`−j)αq′/2	NOUN
ejpam-6519	92	17	q	q	PUNCT
ejpam-6519	92	18	/	/	SYM
ejpam-6519	92	19	q′	q′	NOUN
ejpam-6519	92	20	.	.	PUNCT
ejpam-6519	93	1	∞∑	∞∑	NUM
ejpam-6519	93	2	`	`	PUNCT
ejpam-6519	93	3	=	=	NOUN
ejpam-6519	93	4	−∞	−∞	ADP
ejpam-6519	93	5			PROPN
ejpam-6519	93	6	∞∑	∞∑	NUM
ejpam-6519	93	7	j=	j=	NOUN
ejpam-6519	93	8	`	`	PUNCT
ejpam-6519	93	9	|γj	|γj	NOUN
ejpam-6519	93	10	|q	|q	NOUN
ejpam-6519	93	11	b(`−j)αq/2	b(`−j)αq/2	NOUN
ejpam-6519	93	12			PROPN
ejpam-6519	93	13	.	.	PUNCT
ejpam-6519	94	1	∞∑	∞∑	NUM
ejpam-6519	94	2	j=−∞	j=−∞	NOUN
ejpam-6519	95	1	j∑	j∑	PROPN
ejpam-6519	95	2	`	`	PUNCT
ejpam-6519	95	3	=	=	NOUN
ejpam-6519	95	4	−∞	−∞	ADP
ejpam-6519	95	5	|γj	|γj	NOUN
ejpam-6519	95	6	|q	|q	NOUN
ejpam-6519	95	7	b(`−j)αq/2	b(`−j)αq/2	PROPN
ejpam-6519	95	8	b.	b.	PROPN
ejpam-6519	95	9	sultan	sultan	PROPN
ejpam-6519	95	10	et	et	PROPN
ejpam-6519	95	11	al	al	PROPN
ejpam-6519	95	12	.	.	PUNCT
ejpam-6519	95	13	/	/	SYM
ejpam-6519	95	14	eur	eur	PROPN
ejpam-6519	95	15	.	.	PUNCT
ejpam-6519	96	1	j.	j.	PROPN
ejpam-6519	96	2	pure	pure	PROPN
ejpam-6519	96	3	appl	appl	PROPN
ejpam-6519	96	4	.	.	PROPN
ejpam-6519	96	5	math	math	PROPN
ejpam-6519	96	6	,	,	PUNCT
ejpam-6519	96	7	18	18	NUM
ejpam-6519	96	8	(	(	PUNCT
ejpam-6519	96	9	4	4	NUM
ejpam-6519	96	10	)	)	PUNCT
ejpam-6519	96	11	(	(	PUNCT
ejpam-6519	96	12	2025	2025	NUM
ejpam-6519	96	13	)	)	PUNCT
ejpam-6519	96	14	,	,	PUNCT
ejpam-6519	96	15	6519	6519	NUM
ejpam-6519	96	16	6	6	NUM
ejpam-6519	96	17	of	of	ADP
ejpam-6519	96	18	11	11	NUM
ejpam-6519	96	19	.	.	PUNCT
ejpam-6519	97	1	∞∑	∞∑	NUM
ejpam-6519	97	2	j=−∞	j=−∞	ADJ
ejpam-6519	97	3	|γj	|γj	NOUN
ejpam-6519	97	4	|q	|q	NOUN
ejpam-6519	97	5	.	.	PUNCT
ejpam-6519	98	1	thus	thus	ADV
ejpam-6519	98	2	the	the	DET
ejpam-6519	98	3	proof	proof	NOUN
ejpam-6519	98	4	of	of	ADP
ejpam-6519	98	5	the	the	DET
ejpam-6519	98	6	theorem	theorem	NOUN
ejpam-6519	98	7	is	be	AUX
ejpam-6519	98	8	completed	complete	VERB
ejpam-6519	98	9	.	.	PUNCT
ejpam-6519	99	1	non	non	ADJ
ejpam-6519	99	2	-	-	ADJ
ejpam-6519	99	3	homogeneous	homogeneous	ADJ
ejpam-6519	99	4	version	version	NOUN
ejpam-6519	99	5	of	of	ADP
ejpam-6519	99	6	the	the	DET
ejpam-6519	99	7	theorem	theorem	NOUN
ejpam-6519	99	8	is	be	AUX
ejpam-6519	99	9	obtained	obtain	VERB
ejpam-6519	99	10	similarly	similarly	ADV
ejpam-6519	99	11	.	.	PUNCT
ejpam-6519	100	1	remark	remark	PROPN
ejpam-6519	100	2	6	6	NUM
ejpam-6519	100	3	.	.	PUNCT
ejpam-6519	100	4	by	by	ADP
ejpam-6519	100	5	using	use	VERB
ejpam-6519	100	6	the	the	DET
ejpam-6519	100	7	theorem	theorem	NOUN
ejpam-6519	100	8	,	,	PUNCT
ejpam-6519	100	9	note	note	VERB
ejpam-6519	100	10	that	that	SCONJ
ejpam-6519	100	11	if	if	SCONJ
ejpam-6519	100	12	g	g	PROPN
ejpam-6519	100	13	∈	∈	PROPN
ejpam-6519	100	14	(	(	PUNCT
ejpam-6519	100	15	k̇eα	k̇eα	NOUN
ejpam-6519	100	16	,	,	PUNCT
ejpam-6519	100	17	p	p	NOUN
ejpam-6519	100	18	q	q	NOUN
ejpam-6519	100	19	,	,	PUNCT
ejpam-6519	100	20	r	r	NOUN
ejpam-6519	100	21	)	)	PUNCT
ejpam-6519	100	22	u	u	NOUN
ejpam-6519	100	23	(	(	PUNCT
ejpam-6519	100	24	o;rn	o;rn	PROPN
ejpam-6519	100	25	)	)	PUNCT
ejpam-6519	100	26	and	and	CCONJ
ejpam-6519	100	27	g(y	g(y	NOUN
ejpam-6519	100	28	)	)	PUNCT
ejpam-6519	101	1	=	=	NOUN
ejpam-6519	101	2	∑∞	∑∞	NOUN
ejpam-6519	101	3	`	`	PUNCT
ejpam-6519	101	4	=	=	NOUN
ejpam-6519	101	5	−∞	−∞	X
ejpam-6519	101	6	γ`b`(x	γ`b`(x	NUM
ejpam-6519	101	7	)	)	PUNCT
ejpam-6519	101	8	is	be	AUX
ejpam-6519	101	9	a	a	DET
ejpam-6519	101	10	central	central	ADJ
ejpam-6519	101	11	(	(	PUNCT
ejpam-6519	101	12	α	α	NOUN
ejpam-6519	101	13	,	,	PUNCT
ejpam-6519	101	14	p	p	X
ejpam-6519	101	15	,	,	PUNCT
ejpam-6519	101	16	r	r	NOUN
ejpam-6519	101	17	,	,	PUNCT
ejpam-6519	101	18	u)-block	u)-block	ADJ
ejpam-6519	101	19	decomposition	decomposition	NOUN
ejpam-6519	101	20	,	,	PUNCT
ejpam-6519	101	21	then	then	ADV
ejpam-6519	101	22	‖g‖	‖g‖	PROPN
ejpam-6519	101	23	(	(	PUNCT
ejpam-6519	101	24	k̇eα	k̇eα	NOUN
ejpam-6519	101	25	,	,	PUNCT
ejpam-6519	101	26	p	p	NOUN
ejpam-6519	101	27	q	q	NOUN
ejpam-6519	101	28	,	,	PUNCT
ejpam-6519	101	29	r	r	NOUN
ejpam-6519	101	30	)	)	PUNCT
ejpam-6519	101	31	u	u	NOUN
ejpam-6519	101	32	(	(	PUNCT
ejpam-6519	101	33	o;rn	o;rn	PROPN
ejpam-6519	101	34	)	)	PUNCT
ejpam-6519	101	35	≈	≈	PROPN
ejpam-6519	101	36	(	(	PUNCT
ejpam-6519	101	37	∞∑	∞∑	NUM
ejpam-6519	101	38	`	`	PUNCT
ejpam-6519	101	39	=	=	SYM
ejpam-6519	101	40	−∞	−∞	NOUN
ejpam-6519	101	41	|γ`|q	|γ`|q	NOUN
ejpam-6519	101	42	)	)	PUNCT
ejpam-6519	101	43	1	1	X
ejpam-6519	101	44	/	/	SYM
ejpam-6519	101	45	q	q	NOUN
ejpam-6519	101	46	.	.	PUNCT
ejpam-6519	102	1	4	4	X
ejpam-6519	102	2	.	.	X
ejpam-6519	102	3	boundedness	boundedness	NOUN
ejpam-6519	102	4	of	of	ADP
ejpam-6519	102	5	sublinear	sublinear	NOUN
ejpam-6519	102	6	operators	operator	NOUN
ejpam-6519	102	7	on	on	ADP
ejpam-6519	102	8	anisotropic	anisotropic	NOUN
ejpam-6519	102	9	herz	herz	ADJ
ejpam-6519	102	10	-	-	PUNCT
ejpam-6519	102	11	slice	slice	NOUN
ejpam-6519	102	12	spaces	space	NOUN
ejpam-6519	102	13	as	as	ADP
ejpam-6519	102	14	applications	application	NOUN
ejpam-6519	102	15	of	of	ADP
ejpam-6519	102	16	the	the	DET
ejpam-6519	102	17	decomposition	decomposition	NOUN
ejpam-6519	102	18	theorem	theorem	NOUN
ejpam-6519	102	19	,	,	PUNCT
ejpam-6519	102	20	we	we	PRON
ejpam-6519	102	21	will	will	AUX
ejpam-6519	102	22	prove	prove	VERB
ejpam-6519	102	23	the	the	DET
ejpam-6519	102	24	boundedness	boundedness	NOUN
ejpam-6519	102	25	of	of	ADP
ejpam-6519	102	26	sublinear	sublinear	NOUN
ejpam-6519	102	27	operators	operator	NOUN
ejpam-6519	102	28	on	on	ADP
ejpam-6519	102	29	anisotropic	anisotropic	NOUN
ejpam-6519	102	30	herz	herz	ADJ
ejpam-6519	102	31	-	-	PUNCT
ejpam-6519	102	32	slice	slice	NOUN
ejpam-6519	102	33	spaces	space	NOUN
ejpam-6519	102	34	.	.	PUNCT
ejpam-6519	103	1	theorem	theorem	VERB
ejpam-6519	103	2	4.1	4.1	NUM
ejpam-6519	103	3	.	.	PUNCT
ejpam-6519	104	1	let	let	VERB
ejpam-6519	104	2	α	α	PRON
ejpam-6519	104	3	∈	∈	PROPN
ejpam-6519	104	4	r	r	NOUN
ejpam-6519	104	5	,	,	PUNCT
ejpam-6519	104	6	with	with	ADP
ejpam-6519	104	7	0	0	NUM
ejpam-6519	104	8	<	<	X
ejpam-6519	104	9	α	α	X
ejpam-6519	104	10	<	<	X
ejpam-6519	104	11	1	1	NUM
ejpam-6519	104	12	/	/	SYM
ejpam-6519	104	13	p′	p′	NOUN
ejpam-6519	104	14	and	and	CCONJ
ejpam-6519	104	15	p	p	X
ejpam-6519	104	16	,	,	PUNCT
ejpam-6519	104	17	q	q	ADJ
ejpam-6519	104	18	,	,	PUNCT
ejpam-6519	104	19	r	r	NOUN
ejpam-6519	104	20	,	,	PUNCT
ejpam-6519	104	21	u	u	NOUN
ejpam-6519	104	22	∈	∈	PROPN
ejpam-6519	104	23	(	(	PUNCT
ejpam-6519	104	24	0,∞	0,∞	NOUN
ejpam-6519	104	25	]	]	PUNCT
ejpam-6519	104	26	.	.	PUNCT
ejpam-6519	105	1	let	let	VERB
ejpam-6519	105	2	the	the	DET
ejpam-6519	105	3	sublinear	sublinear	NOUN
ejpam-6519	105	4	t	t	PROPN
ejpam-6519	105	5	fulfills	fulfill	VERB
ejpam-6519	105	6	the	the	DET
ejpam-6519	105	7	size	size	NOUN
ejpam-6519	105	8	condition	condition	NOUN
ejpam-6519	105	9	|tg(y)|	|tg(y)|	PROPN
ejpam-6519	105	10	.	.	PUNCT
ejpam-6519	106	1	∫	∫	PROPN
ejpam-6519	106	2	rn	rn	PROPN
ejpam-6519	106	3	|g(y)|	|g(y)|	PROPN
ejpam-6519	106	4	τ(x−	τ(x−	PROPN
ejpam-6519	106	5	y	y	PROPN
ejpam-6519	106	6	)	)	PUNCT
ejpam-6519	106	7	dy	dy	NOUN
ejpam-6519	106	8	,	,	PUNCT
ejpam-6519	106	9	x	x	NOUN
ejpam-6519	106	10	/∈	/∈	PUNCT
ejpam-6519	106	11	supp	supp	PROPN
ejpam-6519	106	12	g	g	PROPN
ejpam-6519	106	13	,	,	PUNCT
ejpam-6519	106	14	(	(	PUNCT
ejpam-6519	106	15	4.1	4.1	NUM
ejpam-6519	106	16	)	)	PUNCT
ejpam-6519	106	17	for	for	ADP
ejpam-6519	106	18	any	any	DET
ejpam-6519	106	19	g	g	PROPN
ejpam-6519	106	20	∈	∈	PROPN
ejpam-6519	106	21	(	(	PUNCT
ejpam-6519	106	22	ep	ep	PROPN
ejpam-6519	106	23	r	r	NOUN
ejpam-6519	106	24	)	)	PUNCT
ejpam-6519	106	25	u	u	NOUN
ejpam-6519	106	26	with	with	ADP
ejpam-6519	106	27	a	a	DET
ejpam-6519	106	28	compact	compact	ADJ
ejpam-6519	106	29	support	support	NOUN
ejpam-6519	106	30	and	and	CCONJ
ejpam-6519	106	31	t	t	PROPN
ejpam-6519	106	32	is	be	AUX
ejpam-6519	106	33	bounded	bound	VERB
ejpam-6519	106	34	on	on	ADP
ejpam-6519	106	35	(	(	PUNCT
ejpam-6519	106	36	ep	ep	PROPN
ejpam-6519	106	37	r	r	NOUN
ejpam-6519	107	1	)	)	PUNCT
ejpam-6519	107	2	u.	u.	PROPN
ejpam-6519	107	3	then	then	ADV
ejpam-6519	107	4	t	t	PROPN
ejpam-6519	107	5	is	be	AUX
ejpam-6519	107	6	bounded	bound	VERB
ejpam-6519	107	7	in	in	ADP
ejpam-6519	107	8	(	(	PUNCT
ejpam-6519	107	9	k̇eα	k̇eα	NOUN
ejpam-6519	107	10	,	,	PUNCT
ejpam-6519	107	11	p	p	NOUN
ejpam-6519	107	12	q	q	NOUN
ejpam-6519	107	13	,	,	PUNCT
ejpam-6519	107	14	r	r	NOUN
ejpam-6519	107	15	)	)	PUNCT
ejpam-6519	107	16	u	u	NOUN
ejpam-6519	107	17	(	(	PUNCT
ejpam-6519	107	18	o;rn	o;rn	NOUN
ejpam-6519	107	19	)	)	PUNCT
ejpam-6519	107	20	.	.	PUNCT
ejpam-6519	108	1	proof	proof	NOUN
ejpam-6519	108	2	.	.	PUNCT
ejpam-6519	109	1	let	let	VERB
ejpam-6519	109	2	g	g	PROPN
ejpam-6519	109	3	∈	∈	PROPN
ejpam-6519	109	4	(	(	PUNCT
ejpam-6519	109	5	k̇eα	k̇eα	NOUN
ejpam-6519	109	6	,	,	PUNCT
ejpam-6519	109	7	p	p	NOUN
ejpam-6519	109	8	q	q	NOUN
ejpam-6519	109	9	,	,	PUNCT
ejpam-6519	109	10	r	r	NOUN
ejpam-6519	109	11	)	)	PUNCT
ejpam-6519	109	12	u	u	NOUN
ejpam-6519	109	13	(	(	PUNCT
ejpam-6519	109	14	o;rn)/	o;rn)/	VERB
ejpam-6519	109	15	such	such	ADJ
ejpam-6519	109	16	that	that	SCONJ
ejpam-6519	109	17	g(y	g(y	NOUN
ejpam-6519	109	18	)	)	PUNCT
ejpam-6519	109	19	=	=	SYM
ejpam-6519	109	20	∑∞	∑∞	NOUN
ejpam-6519	109	21	a0=−∞	a0=−∞	ADJ
ejpam-6519	109	22	γa0ba0(x	γa0ba0(x	NOUN
ejpam-6519	109	23	)	)	PUNCT
ejpam-6519	109	24	where	where	SCONJ
ejpam-6519	109	25	ba0	ba0	NOUN
ejpam-6519	109	26	is	be	AUX
ejpam-6519	109	27	a	a	DET
ejpam-6519	109	28	central	central	ADJ
ejpam-6519	109	29	(	(	PUNCT
ejpam-6519	109	30	α	α	PROPN
ejpam-6519	109	31	,	,	PUNCT
ejpam-6519	109	32	p.r	p.r	PROPN
ejpam-6519	109	33	,	,	PUNCT
ejpam-6519	109	34	u)-block	u)-block	NOUN
ejpam-6519	109	35	with	with	ADP
ejpam-6519	109	36	support	support	NOUN
ejpam-6519	109	37	contained	contain	VERB
ejpam-6519	109	38	in	in	ADP
ejpam-6519	109	39	ba0	ba0	NOUN
ejpam-6519	109	40	,	,	PUNCT
ejpam-6519	109	41	by	by	ADP
ejpam-6519	109	42	applying	apply	VERB
ejpam-6519	109	43	the	the	DET
ejpam-6519	109	44	decomposition	decomposition	NOUN
ejpam-6519	109	45	theorem	theorem	NOUN
ejpam-6519	109	46	,	,	PUNCT
ejpam-6519	109	47	we	we	PRON
ejpam-6519	109	48	get	get	VERB
ejpam-6519	109	49	‖g‖	‖g‖	NOUN
ejpam-6519	109	50	(	(	PUNCT
ejpam-6519	109	51	k̇eα	k̇eα	NOUN
ejpam-6519	109	52	,	,	PUNCT
ejpam-6519	109	53	p	p	NOUN
ejpam-6519	109	54	q	q	NOUN
ejpam-6519	109	55	,	,	PUNCT
ejpam-6519	109	56	r	r	NOUN
ejpam-6519	109	57	)	)	PUNCT
ejpam-6519	109	58	u	u	NOUN
ejpam-6519	109	59	(	(	PUNCT
ejpam-6519	109	60	o;rn	o;rn	PROPN
ejpam-6519	109	61	)	)	PUNCT
ejpam-6519	110	1	≈	≈	PROPN
ejpam-6519	110	2	(	(	PUNCT
ejpam-6519	110	3	∞∑	∞∑	NUM
ejpam-6519	110	4	a0=−∞	a0=−∞	NOUN
ejpam-6519	110	5	|γa0	|γa0	PRON
ejpam-6519	110	6	|	|	NOUN
ejpam-6519	110	7	q	q	NOUN
ejpam-6519	110	8	)	)	PUNCT
ejpam-6519	110	9	1	1	NUM
ejpam-6519	110	10	/	/	SYM
ejpam-6519	110	11	q	q	NOUN
ejpam-6519	110	12	.	.	PUNCT
ejpam-6519	111	1	therefore	therefore	ADV
ejpam-6519	111	2	,	,	PUNCT
ejpam-6519	111	3	we	we	PRON
ejpam-6519	111	4	get	get	VERB
ejpam-6519	111	5	‖tg‖q	‖tg‖q	PROPN
ejpam-6519	111	6	(	(	PUNCT
ejpam-6519	111	7	k̇eα	k̇eα	NOUN
ejpam-6519	111	8	,	,	PUNCT
ejpam-6519	111	9	p	p	NOUN
ejpam-6519	111	10	q	q	NOUN
ejpam-6519	111	11	,	,	PUNCT
ejpam-6519	111	12	r	r	NOUN
ejpam-6519	111	13	)	)	PUNCT
ejpam-6519	111	14	u	u	NOUN
ejpam-6519	111	15	(	(	PUNCT
ejpam-6519	111	16	o;rn	o;rn	PROPN
ejpam-6519	111	17	)	)	PUNCT
ejpam-6519	111	18	=	=	PUNCT
ejpam-6519	112	1	∞∑	∞∑	NUM
ejpam-6519	112	2	`	`	PUNCT
ejpam-6519	112	3	=	=	NOUN
ejpam-6519	112	4	−∞	−∞	X
ejpam-6519	112	5	b`αq	b`αq	NOUN
ejpam-6519	112	6	‖(tg)χ`‖q(ep	‖(tg)χ`‖q(ep	PROPN
ejpam-6519	112	7	r	r	NOUN
ejpam-6519	112	8	)	)	PUNCT
ejpam-6519	112	9	u	u	NOUN
ejpam-6519	112	10	.	.	PUNCT
ejpam-6519	113	1	∞∑	∞∑	NUM
ejpam-6519	113	2	`	`	PUNCT
ejpam-6519	113	3	=	=	NOUN
ejpam-6519	113	4	−∞	−∞	X
ejpam-6519	113	5	b`αq	b`αq	NOUN
ejpam-6519	113	6	‖(tg)χ`‖q(ep	‖(tg)χ`‖q(ep	PROPN
ejpam-6519	113	7	r	r	NOUN
ejpam-6519	113	8	)	)	PUNCT
ejpam-6519	113	9	u	u	NOUN
ejpam-6519	113	10	.	.	PUNCT
ejpam-6519	114	1	∞∑	∞∑	NUM
ejpam-6519	114	2	`	`	PUNCT
ejpam-6519	114	3	=	=	NOUN
ejpam-6519	114	4	−∞	−∞	X
ejpam-6519	114	5	b`αq	b`αq	NOUN
ejpam-6519	114	6	(	(	PUNCT
ejpam-6519	114	7	`	`	PUNCT
ejpam-6519	114	8	−w−1∑	−w−1∑	X
ejpam-6519	114	9	a0=−∞	a0=−∞	NOUN
ejpam-6519	114	10	|γa0	|γa0	PROPN
ejpam-6519	114	11	|	|	ADV
ejpam-6519	114	12	‖(tba0)χ`‖(ep	‖(tba0)χ`‖(ep	PROPN
ejpam-6519	114	13	r	r	NOUN
ejpam-6519	114	14	)	)	PUNCT
ejpam-6519	114	15	u	u	NOUN
ejpam-6519	114	16	)	)	PUNCT
ejpam-6519	114	17	q	q	PROPN
ejpam-6519	114	18	b.	b.	PROPN
ejpam-6519	114	19	sultan	sultan	PROPN
ejpam-6519	114	20	et	et	PROPN
ejpam-6519	114	21	al	al	PROPN
ejpam-6519	114	22	.	.	PUNCT
ejpam-6519	114	23	/	/	SYM
ejpam-6519	114	24	eur	eur	PROPN
ejpam-6519	114	25	.	.	PUNCT
ejpam-6519	115	1	j.	j.	PROPN
ejpam-6519	115	2	pure	pure	PROPN
ejpam-6519	115	3	appl	appl	PROPN
ejpam-6519	115	4	.	.	PROPN
ejpam-6519	115	5	math	math	PROPN
ejpam-6519	115	6	,	,	PUNCT
ejpam-6519	115	7	18	18	NUM
ejpam-6519	115	8	(	(	PUNCT
ejpam-6519	115	9	4	4	NUM
ejpam-6519	115	10	)	)	PUNCT
ejpam-6519	115	11	(	(	PUNCT
ejpam-6519	115	12	2025	2025	NUM
ejpam-6519	115	13	)	)	PUNCT
ejpam-6519	115	14	,	,	PUNCT
ejpam-6519	115	15	6519	6519	NUM
ejpam-6519	115	16	7	7	NUM
ejpam-6519	115	17	of	of	ADP
ejpam-6519	115	18	11	11	NUM
ejpam-6519	115	19	+	+	CCONJ
ejpam-6519	115	20	∞∑	∞∑	NUM
ejpam-6519	115	21	`	`	PUNCT
ejpam-6519	115	22	=	=	NOUN
ejpam-6519	115	23	−∞	−∞	NOUN
ejpam-6519	115	24	b`αq	b`αq	ADP
ejpam-6519	115	25			PROPN
ejpam-6519	115	26	∞∑	∞∑	PROPN
ejpam-6519	115	27	a0=`−w	a0=`−w	ADV
ejpam-6519	115	28	|γa0	|γa0	DET
ejpam-6519	115	29	|	|	ADV
ejpam-6519	115	30	‖(tba0)χ`‖(ep	‖(tba0)χ`‖(ep	PROPN
ejpam-6519	115	31	r	r	NOUN
ejpam-6519	115	32	)	)	PUNCT
ejpam-6519	115	33	u	u	NOUN
ejpam-6519	115	34	q	q	PROPN
ejpam-6519	116	1	=	=	SYM
ejpam-6519	116	2	i1	i1	PROPN
ejpam-6519	116	3	+	+	CCONJ
ejpam-6519	116	4	i2	i2	PROPN
ejpam-6519	116	5	.	.	PUNCT
ejpam-6519	117	1	to	to	PART
ejpam-6519	117	2	find	find	VERB
ejpam-6519	117	3	the	the	DET
ejpam-6519	117	4	estimate	estimate	NOUN
ejpam-6519	117	5	of	of	ADP
ejpam-6519	117	6	i1	i1	PROPN
ejpam-6519	117	7	.	.	PUNCT
ejpam-6519	118	1	let	let	VERB
ejpam-6519	118	2	x	x	SYM
ejpam-6519	118	3	∈	∈	PROPN
ejpam-6519	118	4	c	c	X
ejpam-6519	118	5	`	`	PUNCT
ejpam-6519	118	6	,	,	PUNCT
ejpam-6519	118	7	y	y	PROPN
ejpam-6519	118	8	∈	∈	PROPN
ejpam-6519	118	9	ba0	ba0	CCONJ
ejpam-6519	118	10	such	such	ADJ
ejpam-6519	118	11	that	that	DET
ejpam-6519	118	12	a0	a0	PROPN
ejpam-6519	118	13	≤	≤	PROPN
ejpam-6519	118	14	`	`	PUNCT
ejpam-6519	118	15	−	−	PROPN
ejpam-6519	118	16	w	w	NOUN
ejpam-6519	118	17	−	−	PROPN
ejpam-6519	118	18	1	1	NUM
ejpam-6519	118	19	,	,	PUNCT
ejpam-6519	118	20	,	,	PUNCT
ejpam-6519	118	21	then	then	ADV
ejpam-6519	118	22	(	(	PUNCT
ejpam-6519	118	23	2.1	2.1	NUM
ejpam-6519	118	24	)	)	PUNCT
ejpam-6519	118	25	yields	yield	NOUN
ejpam-6519	118	26	b−w(1−	b−w(1−	ADJ
ejpam-6519	118	27	1	1	NUM
ejpam-6519	118	28	/	/	SYM
ejpam-6519	118	29	b)τ(x	b)τ(x	NOUN
ejpam-6519	118	30	)	)	PUNCT
ejpam-6519	118	31	=	=	VERB
ejpam-6519	118	32	b−wτ(x)−	b−wτ(x)−	PROPN
ejpam-6519	118	33	b−w−1τ(x	b−w−1τ(x	PROPN
ejpam-6519	118	34	)	)	PUNCT
ejpam-6519	118	35	≤	≤	PROPN
ejpam-6519	118	36	b−wτ(x)−	b−wτ(x)−	NOUN
ejpam-6519	118	37	τ(y	τ(y	PROPN
ejpam-6519	118	38	)	)	PUNCT
ejpam-6519	118	39	≤	≤	NOUN
ejpam-6519	118	40	τ(x−	τ(x−	DET
ejpam-6519	118	41	y	y	NOUN
ejpam-6519	118	42	)	)	PUNCT
ejpam-6519	118	43	.	.	PUNCT
ejpam-6519	119	1	hence	hence	ADV
ejpam-6519	119	2	(	(	PUNCT
ejpam-6519	119	3	4.1	4.1	NUM
ejpam-6519	119	4	)	)	PUNCT
ejpam-6519	119	5	and	and	CCONJ
ejpam-6519	119	6	hölder	hölder	PROPN
ejpam-6519	119	7	’s	’s	PART
ejpam-6519	119	8	inequality	inequality	NOUN
ejpam-6519	119	9	yields	yield	NOUN
ejpam-6519	119	10	|tba0(x)|	|tba0(x)|	VERB
ejpam-6519	119	11	≤	≤	NUM
ejpam-6519	119	12	cτ(x)−1	cτ(x)−1	NOUN
ejpam-6519	119	13	∫	∫	PROPN
ejpam-6519	119	14	ba0	ba0	PROPN
ejpam-6519	119	15	|ba0(y)|	|ba0(y)|	PROPN
ejpam-6519	119	16	dy	dy	VERB
ejpam-6519	119	17	≤	≤	NUM
ejpam-6519	119	18	cb−	cb−	PROPN
ejpam-6519	119	19	`	`	PUNCT
ejpam-6519	119	20	‖ba0‖(ep	‖ba0‖(ep	PROPN
ejpam-6519	119	21	r	r	NOUN
ejpam-6519	119	22	)	)	PUNCT
ejpam-6519	119	23	u	u	NOUN
ejpam-6519	119	24	∥∥χba0	∥∥χba0	PUNCT
ejpam-6519	119	25	∥∥	∥∥	X
ejpam-6519	119	26	(	(	PUNCT
ejpam-6519	119	27	ep′	ep′	X
ejpam-6519	119	28	r′	r′	PROPN
ejpam-6519	119	29	)	)	PUNCT
ejpam-6519	119	30	u	u	NOUN
ejpam-6519	119	31	.	.	PUNCT
ejpam-6519	120	1	applying	apply	VERB
ejpam-6519	120	2	lemmas	lemmas	PROPN
ejpam-6519	120	3	2	2	NUM
ejpam-6519	120	4	and	and	CCONJ
ejpam-6519	120	5	4	4	NUM
ejpam-6519	120	6	,	,	PUNCT
ejpam-6519	120	7	we	we	PRON
ejpam-6519	120	8	get	get	VERB
ejpam-6519	120	9	‖(tba0)χ`‖(ep	‖(tba0)χ`‖(ep	PROPN
ejpam-6519	120	10	r	r	NOUN
ejpam-6519	120	11	)	)	PUNCT
ejpam-6519	120	12	u	u	NOUN
ejpam-6519	120	13	.	.	PUNCT
ejpam-6519	121	1	b−	b−	PROPN
ejpam-6519	121	2	`	`	PUNCT
ejpam-6519	121	3	‖ba0‖(ep	‖ba0‖(ep	PROPN
ejpam-6519	121	4	r	r	NOUN
ejpam-6519	121	5	)	)	PUNCT
ejpam-6519	121	6	u	u	NOUN
ejpam-6519	121	7	∥∥χba0	∥∥χba0	PUNCT
ejpam-6519	121	8	∥∥	∥∥	X
ejpam-6519	121	9	(	(	PUNCT
ejpam-6519	121	10	ep′	ep′	X
ejpam-6519	121	11	r′	r′	PROPN
ejpam-6519	121	12	)	)	PUNCT
ejpam-6519	121	13	u	u	NOUN
ejpam-6519	121	14	‖χb	‖χb	NOUN
ejpam-6519	121	15	`	`	PUNCT
ejpam-6519	121	16	‖(ep	‖(ep	ADJ
ejpam-6519	121	17	r	r	NOUN
ejpam-6519	121	18	)	)	PUNCT
ejpam-6519	121	19	u	u	NOUN
ejpam-6519	121	20	.	.	PUNCT
ejpam-6519	122	1	b−	b−	PROPN
ejpam-6519	122	2	`	`	PUNCT
ejpam-6519	122	3	‖ba0‖(ep	‖ba0‖(ep	PROPN
ejpam-6519	122	4	r	r	NOUN
ejpam-6519	122	5	)	)	PUNCT
ejpam-6519	122	6	u	u	NOUN
ejpam-6519	122	7	(	(	PUNCT
ejpam-6519	122	8	|b`|	|b`|	PROPN
ejpam-6519	122	9	‖χb	‖χb	NOUN
ejpam-6519	122	10	`	`	PUNCT
ejpam-6519	122	11	‖−1	‖−1	NOUN
ejpam-6519	122	12	(	(	PUNCT
ejpam-6519	122	13	ep′	ep′	X
ejpam-6519	122	14	r′	r′	PROPN
ejpam-6519	122	15	)	)	PUNCT
ejpam-6519	122	16	u	u	NOUN
ejpam-6519	122	17	)	)	PUNCT
ejpam-6519	122	18	∥∥χba0	∥∥χba0	PUNCT
ejpam-6519	122	19	∥∥	∥∥	PROPN
ejpam-6519	122	20	(	(	PUNCT
ejpam-6519	122	21	ep′	ep′	X
ejpam-6519	122	22	r′	r′	PROPN
ejpam-6519	122	23	)	)	PUNCT
ejpam-6519	122	24	u	u	NOUN
ejpam-6519	122	25	.	.	PUNCT
ejpam-6519	123	1	‖ba0‖(ep	‖ba0‖(ep	PROPN
ejpam-6519	123	2	r	r	NOUN
ejpam-6519	123	3	)	)	PUNCT
ejpam-6519	123	4	u	u	NOUN
ejpam-6519	123	5	∥∥χba0	∥∥χba0	PUNCT
ejpam-6519	123	6	∥∥	∥∥	X
ejpam-6519	123	7	(	(	PUNCT
ejpam-6519	123	8	ep′	ep′	X
ejpam-6519	123	9	r′	r′	PROPN
ejpam-6519	123	10	)	)	PUNCT
ejpam-6519	123	11	u	u	PROPN
ejpam-6519	123	12	‖χb	‖χb	PROPN
ejpam-6519	123	13	`	`	PUNCT
ejpam-6519	123	14	‖	‖	PROPN
ejpam-6519	123	15	(	(	PUNCT
ejpam-6519	123	16	ep′	ep′	X
ejpam-6519	123	17	r′	r′	PROPN
ejpam-6519	123	18	)	)	PUNCT
ejpam-6519	123	19	u	u	NOUN
ejpam-6519	123	20	.	.	PUNCT
ejpam-6519	124	1	b(a0−`)/p′	b(a0−`)/p′	X
ejpam-6519	125	1	‖ba0‖(ep	‖ba0‖(ep	PROPN
ejpam-6519	125	2	r	r	NOUN
ejpam-6519	125	3	)	)	PUNCT
ejpam-6519	125	4	u	u	NOUN
ejpam-6519	125	5	.	.	PUNCT
ejpam-6519	126	1	therefore	therefore	ADV
ejpam-6519	126	2	,	,	PUNCT
ejpam-6519	126	3	for	for	ADP
ejpam-6519	126	4	0	0	NUM
ejpam-6519	126	5	<	<	X
ejpam-6519	126	6	q	q	X
ejpam-6519	126	7	≤	≤	NUM
ejpam-6519	126	8	1	1	NUM
ejpam-6519	126	9	,	,	PUNCT
ejpam-6519	126	10	and	and	CCONJ
ejpam-6519	126	11	0	0	NUM
ejpam-6519	126	12	<	<	X
ejpam-6519	126	13	α	α	X
ejpam-6519	126	14	<	<	X
ejpam-6519	126	15	1	1	NUM
ejpam-6519	126	16	/	/	SYM
ejpam-6519	126	17	p′	p′	NOUN
ejpam-6519	126	18	,	,	PUNCT
ejpam-6519	126	19	we	we	PRON
ejpam-6519	126	20	have	have	VERB
ejpam-6519	126	21	i1	i1	NOUN
ejpam-6519	126	22	=	=	PROPN
ejpam-6519	127	1	∞∑	∞∑	NUM
ejpam-6519	127	2	`	`	PUNCT
ejpam-6519	127	3	=	=	NOUN
ejpam-6519	127	4	−∞	−∞	NOUN
ejpam-6519	127	5	b`αq	b`αq	NOUN
ejpam-6519	127	6	(	(	PUNCT
ejpam-6519	127	7	`	`	PUNCT
ejpam-6519	127	8	−w−1∑	−w−1∑	X
ejpam-6519	127	9	a0=−∞	a0=−∞	NOUN
ejpam-6519	127	10	|γa0	|γa0	PROPN
ejpam-6519	127	11	|	|	ADV
ejpam-6519	127	12	‖(tba0)χ`‖(ep	‖(tba0)χ`‖(ep	PROPN
ejpam-6519	127	13	r	r	NOUN
ejpam-6519	127	14	)	)	PUNCT
ejpam-6519	127	15	u	u	NOUN
ejpam-6519	127	16	)	)	PUNCT
ejpam-6519	127	17	q	q	NOUN
ejpam-6519	127	18	.	.	PUNCT
ejpam-6519	128	1	∞∑	∞∑	NUM
ejpam-6519	128	2	`	`	PUNCT
ejpam-6519	128	3	=	=	NOUN
ejpam-6519	128	4	−∞	−∞	X
ejpam-6519	128	5	b`αq	b`αq	NOUN
ejpam-6519	128	6	(	(	PUNCT
ejpam-6519	128	7	`	`	PUNCT
ejpam-6519	128	8	−w−1∑	−w−1∑	X
ejpam-6519	128	9	a0=−∞	a0=−∞	NOUN
ejpam-6519	128	10	|γa0	|γa0	PROPN
ejpam-6519	128	11	|	|	ADV
ejpam-6519	128	12	q	q	X
ejpam-6519	128	13	b[(a0−`)/p′−a0α]q	b[(a0−`)/p′−a0α]q	PROPN
ejpam-6519	128	14	)	)	PUNCT
ejpam-6519	128	15	.	.	PUNCT
ejpam-6519	129	1	−w−2∑	−w−2∑	PROPN
ejpam-6519	130	1	a0=−∞	a0=−∞	NOUN
ejpam-6519	131	1	|γa0	|γa0	PRON
ejpam-6519	132	1	|	|	ADV
ejpam-6519	132	2	q	q	X
ejpam-6519	132	3	∞∑	∞∑	NUM
ejpam-6519	132	4	`	`	PUNCT
ejpam-6519	132	5	=	=	NOUN
ejpam-6519	132	6	a0+w+1	a0+w+1	X
ejpam-6519	132	7	b(a0−`)[1	b(a0−`)[1	NOUN
ejpam-6519	132	8	/	/	SYM
ejpam-6519	132	9	p′−α]q	p′−α]q	PROPN
ejpam-6519	132	10	.	.	PUNCT
ejpam-6519	133	1	−w−2∑	−w−2∑	PROPN
ejpam-6519	133	2	a0=−∞	a0=−∞	NOUN
ejpam-6519	134	1	|γa0	|γa0	PRON
ejpam-6519	134	2	|	|	ADV
ejpam-6519	134	3	q	q	PROPN
ejpam-6519	134	4	b.	b.	PROPN
ejpam-6519	134	5	sultan	sultan	PROPN
ejpam-6519	134	6	et	et	PROPN
ejpam-6519	134	7	al	al	PROPN
ejpam-6519	134	8	.	.	PUNCT
ejpam-6519	134	9	/	/	SYM
ejpam-6519	134	10	eur	eur	PROPN
ejpam-6519	134	11	.	.	PUNCT
ejpam-6519	135	1	j.	j.	PROPN
ejpam-6519	135	2	pure	pure	PROPN
ejpam-6519	135	3	appl	appl	PROPN
ejpam-6519	135	4	.	.	PROPN
ejpam-6519	135	5	math	math	PROPN
ejpam-6519	135	6	,	,	PUNCT
ejpam-6519	135	7	18	18	NUM
ejpam-6519	135	8	(	(	PUNCT
ejpam-6519	135	9	4	4	NUM
ejpam-6519	135	10	)	)	PUNCT
ejpam-6519	135	11	(	(	PUNCT
ejpam-6519	135	12	2025	2025	NUM
ejpam-6519	135	13	)	)	PUNCT
ejpam-6519	135	14	,	,	PUNCT
ejpam-6519	135	15	6519	6519	NUM
ejpam-6519	135	16	8	8	NUM
ejpam-6519	135	17	of	of	ADP
ejpam-6519	135	18	11	11	NUM
ejpam-6519	135	19	.	.	PUNCT
ejpam-6519	136	1	‖g‖q	‖g‖q	PROPN
ejpam-6519	136	2	(	(	PUNCT
ejpam-6519	136	3	k̇eα	k̇eα	NOUN
ejpam-6519	136	4	,	,	PUNCT
ejpam-6519	136	5	p	p	NOUN
ejpam-6519	136	6	q	q	NOUN
ejpam-6519	136	7	,	,	PUNCT
ejpam-6519	136	8	r	r	NOUN
ejpam-6519	136	9	)	)	PUNCT
ejpam-6519	136	10	u	u	NOUN
ejpam-6519	136	11	(	(	PUNCT
ejpam-6519	136	12	o;rn	o;rn	PROPN
ejpam-6519	136	13	)	)	PUNCT
ejpam-6519	136	14	.	.	PUNCT
ejpam-6519	137	1	when	when	SCONJ
ejpam-6519	137	2	1	1	NUM
ejpam-6519	137	3	<	<	X
ejpam-6519	137	4	q	q	X
ejpam-6519	137	5	<	<	X
ejpam-6519	137	6	∞	∞	PROPN
ejpam-6519	137	7	,	,	PUNCT
ejpam-6519	137	8	0	0	NUM
ejpam-6519	137	9	<	<	X
ejpam-6519	137	10	α	α	X
ejpam-6519	137	11	<	<	X
ejpam-6519	137	12	1	1	NUM
ejpam-6519	137	13	/	/	SYM
ejpam-6519	137	14	p′	p′	NOUN
ejpam-6519	137	15	,	,	PUNCT
ejpam-6519	137	16	and	and	CCONJ
ejpam-6519	137	17	the	the	DET
ejpam-6519	137	18	hölder	hölder	NOUN
ejpam-6519	137	19	inequality	inequality	NOUN
ejpam-6519	137	20	yields	yield	VERB
ejpam-6519	137	21	i1	i1	PROPN
ejpam-6519	137	22	.	.	PUNCT
ejpam-6519	138	1	∞∑	∞∑	NUM
ejpam-6519	138	2	`	`	PUNCT
ejpam-6519	138	3	=	=	NOUN
ejpam-6519	138	4	−∞	−∞	X
ejpam-6519	138	5	b`αq	b`αq	NOUN
ejpam-6519	138	6	(	(	PUNCT
ejpam-6519	138	7	`	`	PUNCT
ejpam-6519	138	8	−w−1∑	−w−1∑	X
ejpam-6519	138	9	a0=−∞	a0=−∞	NOUN
ejpam-6519	138	10	|γa0	|γa0	ADP
ejpam-6519	138	11	|	|	NOUN
ejpam-6519	138	12	b(a0−`)/p′−a0α	b(a0−`)/p′−a0α	NOUN
ejpam-6519	138	13	)	)	PUNCT
ejpam-6519	138	14	q	q	X
ejpam-6519	138	15	.	.	PUNCT
ejpam-6519	139	1	∞∑	∞∑	NUM
ejpam-6519	139	2	`	`	PUNCT
ejpam-6519	139	3	=	=	NOUN
ejpam-6519	139	4	−∞	−∞	X
ejpam-6519	139	5	(	(	PUNCT
ejpam-6519	139	6	`	`	PUNCT
ejpam-6519	139	7	−w−1∑	−w−1∑	X
ejpam-6519	139	8	a0=−∞	a0=−∞	NOUN
ejpam-6519	139	9	|γa0	|γa0	PROPN
ejpam-6519	139	10	|	|	ADV
ejpam-6519	139	11	q	q	NOUN
ejpam-6519	139	12	b(a0−`)[1	b(a0−`)[1	NOUN
ejpam-6519	139	13	/	/	SYM
ejpam-6519	139	14	p′−α]q/2	p′−α]q/2	NOUN
ejpam-6519	139	15	)	)	PUNCT
ejpam-6519	139	16	(	(	PUNCT
ejpam-6519	139	17	`	`	PUNCT
ejpam-6519	139	18	−w−1∑	−w−1∑	X
ejpam-6519	139	19	a0=−∞	a0=−∞	ADJ
ejpam-6519	139	20	b(a0−`)[1	b(a0−`)[1	NOUN
ejpam-6519	139	21	/	/	SYM
ejpam-6519	139	22	p′−α]q′/2	p′−α]q′/2	NOUN
ejpam-6519	139	23	)	)	PUNCT
ejpam-6519	139	24	q	q	X
ejpam-6519	139	25	/	/	SYM
ejpam-6519	139	26	q′	q′	NOUN
ejpam-6519	139	27	.	.	PUNCT
ejpam-6519	140	1	∞∑	∞∑	NUM
ejpam-6519	140	2	`	`	PUNCT
ejpam-6519	140	3	=	=	NOUN
ejpam-6519	140	4	−∞	−∞	X
ejpam-6519	140	5	(	(	PUNCT
ejpam-6519	140	6	`	`	PUNCT
ejpam-6519	140	7	−w−1∑	−w−1∑	X
ejpam-6519	140	8	a0=−∞	a0=−∞	NOUN
ejpam-6519	140	9	|γa0	|γa0	PROPN
ejpam-6519	140	10	|	|	ADV
ejpam-6519	140	11	q	q	NOUN
ejpam-6519	140	12	b(a0−`)[1	b(a0−`)[1	NOUN
ejpam-6519	140	13	/	/	SYM
ejpam-6519	140	14	p′−α]q/2	p′−α]q/2	PROPN
ejpam-6519	140	15	)	)	PUNCT
ejpam-6519	140	16	.	.	PUNCT
ejpam-6519	141	1	−w−2∑	−w−2∑	PROPN
ejpam-6519	142	1	a0=−∞	a0=−∞	NOUN
ejpam-6519	143	1	|γa0	|γa0	PRON
ejpam-6519	144	1	|	|	ADV
ejpam-6519	144	2	q	q	X
ejpam-6519	144	3	−1∑	−1∑	NOUN
ejpam-6519	144	4	`	`	PUNCT
ejpam-6519	144	5	=	=	NOUN
ejpam-6519	144	6	a0+w+1	a0+w+1	X
ejpam-6519	144	7	b(a0−`)[1	b(a0−`)[1	NOUN
ejpam-6519	144	8	/	/	SYM
ejpam-6519	144	9	p′−α]q/2	p′−α]q/2	NOUN
ejpam-6519	144	10	.	.	PUNCT
ejpam-6519	145	1	−w−2∑	−w−2∑	PROPN
ejpam-6519	145	2	a0=−∞	a0=−∞	NOUN
ejpam-6519	146	1	|γa0	|γa0	PRON
ejpam-6519	146	2	|	|	ADV
ejpam-6519	146	3	q	q	NOUN
ejpam-6519	146	4	.	.	PUNCT
ejpam-6519	147	1	‖g‖q	‖g‖q	PROPN
ejpam-6519	147	2	(	(	PUNCT
ejpam-6519	147	3	k̇eα	k̇eα	NOUN
ejpam-6519	147	4	,	,	PUNCT
ejpam-6519	147	5	p	p	NOUN
ejpam-6519	147	6	q	q	NOUN
ejpam-6519	147	7	,	,	PUNCT
ejpam-6519	147	8	r	r	NOUN
ejpam-6519	147	9	)	)	PUNCT
ejpam-6519	147	10	u	u	NOUN
ejpam-6519	147	11	(	(	PUNCT
ejpam-6519	147	12	o;rn	o;rn	PROPN
ejpam-6519	147	13	)	)	PUNCT
ejpam-6519	147	14	.	.	PUNCT
ejpam-6519	148	1	next	next	ADV
ejpam-6519	148	2	we	we	PRON
ejpam-6519	148	3	find	find	VERB
ejpam-6519	148	4	the	the	DET
ejpam-6519	148	5	estimate	estimate	NOUN
ejpam-6519	148	6	of	of	ADP
ejpam-6519	148	7	i2	i2	PROPN
ejpam-6519	148	8	.	.	PUNCT
ejpam-6519	149	1	if	if	SCONJ
ejpam-6519	149	2	0	0	NUM
ejpam-6519	149	3	<	<	X
ejpam-6519	149	4	q	q	X
ejpam-6519	149	5	≤	≤	NUM
ejpam-6519	149	6	1	1	NUM
ejpam-6519	149	7	,	,	PUNCT
ejpam-6519	149	8	by	by	ADP
ejpam-6519	149	9	(	(	PUNCT
ejpam-6519	149	10	ep	ep	PROPN
ejpam-6519	149	11	r	r	NOUN
ejpam-6519	149	12	)	)	PUNCT
ejpam-6519	149	13	u	u	NOUN
ejpam-6519	149	14	boundedness	boundedness	NOUN
ejpam-6519	149	15	of	of	ADP
ejpam-6519	149	16	t	t	PROPN
ejpam-6519	149	17	,	,	PUNCT
ejpam-6519	149	18	we	we	PRON
ejpam-6519	149	19	get	get	VERB
ejpam-6519	149	20	i2	i2	NOUN
ejpam-6519	149	21	=	=	PUNCT
ejpam-6519	150	1	∞∑	∞∑	PRON
ejpam-6519	150	2	`	`	PUNCT
ejpam-6519	150	3	=	=	NOUN
ejpam-6519	150	4	−∞	−∞	NOUN
ejpam-6519	150	5	b`αq	b`αq	ADP
ejpam-6519	150	6			PROPN
ejpam-6519	150	7	∞∑	∞∑	PROPN
ejpam-6519	150	8	a0=`−w	a0=`−w	ADV
ejpam-6519	150	9	|γa0	|γa0	DET
ejpam-6519	150	10	|	|	ADV
ejpam-6519	150	11	‖(tba0)χ`‖(ep	‖(tba0)χ`‖(ep	PROPN
ejpam-6519	150	12	r	r	NOUN
ejpam-6519	150	13	)	)	PUNCT
ejpam-6519	150	14	u	u	NOUN
ejpam-6519	150	15	q	q	NOUN
ejpam-6519	150	16	.	.	PUNCT
ejpam-6519	151	1	∞∑	∞∑	NUM
ejpam-6519	151	2	`	`	PUNCT
ejpam-6519	151	3	=	=	NOUN
ejpam-6519	151	4	−∞	−∞	X
ejpam-6519	151	5	b`αq	b`αq	ADP
ejpam-6519	151	6			PROPN
ejpam-6519	151	7	∞∑	∞∑	PROPN
ejpam-6519	151	8	a0=`−w	a0=`−w	ADV
ejpam-6519	151	9	|γa0	|γa0	ADV
ejpam-6519	151	10	|	|	ADV
ejpam-6519	151	11	q	q	NOUN
ejpam-6519	151	12	‖	‖	ADJ
ejpam-6519	151	13	ba0	ba0	NOUN
ejpam-6519	152	1	|	|	ADV
ejpam-6519	152	2	q	q	NOUN
ejpam-6519	152	3	(	(	PUNCT
ejpam-6519	152	4	ep	ep	PROPN
ejpam-6519	152	5	r	r	NOUN
ejpam-6519	152	6	)	)	PUNCT
ejpam-6519	152	7	u	u	NOUN
ejpam-6519	152	8			PROPN
ejpam-6519	152	9	.	.	PUNCT
ejpam-6519	153	1	∞∑	∞∑	NUM
ejpam-6519	153	2	`	`	PUNCT
ejpam-6519	153	3	=	=	NOUN
ejpam-6519	153	4	−∞	−∞	X
ejpam-6519	153	5	b`αq	b`αq	ADP
ejpam-6519	153	6			PROPN
ejpam-6519	153	7	∞∑	∞∑	PROPN
ejpam-6519	153	8	a0=`−w	a0=`−w	ADV
ejpam-6519	153	9	|γa0	|γa0	ADV
ejpam-6519	153	10	|	|	ADV
ejpam-6519	153	11	q	q	X
ejpam-6519	153	12	b−a0αq	b−a0αq	NOUN
ejpam-6519	153	13			PROPN
ejpam-6519	153	14	.	.	PUNCT
ejpam-6519	154	1	∞∑	∞∑	NUM
ejpam-6519	154	2	`	`	PUNCT
ejpam-6519	154	3	=	=	NOUN
ejpam-6519	154	4	−∞	−∞	X
ejpam-6519	154	5	∞∑	∞∑	NUM
ejpam-6519	154	6	a0=`−w	a0=`−w	ADV
ejpam-6519	154	7	|γa0	|γa0	ADV
ejpam-6519	154	8	|	|	ADV
ejpam-6519	154	9	q	q	NOUN
ejpam-6519	154	10	b(`−a0)αq	b(`−a0)αq	NOUN
ejpam-6519	154	11	.	.	PUNCT
ejpam-6519	155	1	∞∑	∞∑	NUM
ejpam-6519	155	2	a0=−∞	a0=−∞	ADJ
ejpam-6519	155	3	|γa0	|γa0	ADP
ejpam-6519	155	4	|	|	ADV
ejpam-6519	155	5	q	q	X
ejpam-6519	155	6	a0+w∑	a0+w∑	PUNCT
ejpam-6519	155	7	`	`	PUNCT
ejpam-6519	155	8	=	=	NOUN
ejpam-6519	155	9	−∞	−∞	X
ejpam-6519	155	10	b(`−a0)αq	b(`−a0)αq	NOUN
ejpam-6519	155	11	.	.	PUNCT
ejpam-6519	156	1	∞∑	∞∑	NUM
ejpam-6519	156	2	a0=−∞	a0=−∞	ADJ
ejpam-6519	156	3	|γa0	|γa0	ADP
ejpam-6519	156	4	|	|	ADV
ejpam-6519	156	5	q	q	NOUN
ejpam-6519	156	6	.	.	PUNCT
ejpam-6519	157	1	‖g‖q	‖g‖q	PROPN
ejpam-6519	157	2	(	(	PUNCT
ejpam-6519	157	3	k̇eα	k̇eα	NOUN
ejpam-6519	157	4	,	,	PUNCT
ejpam-6519	157	5	p	p	NOUN
ejpam-6519	157	6	q	q	NOUN
ejpam-6519	157	7	,	,	PUNCT
ejpam-6519	157	8	r	r	NOUN
ejpam-6519	157	9	)	)	PUNCT
ejpam-6519	157	10	u	u	NOUN
ejpam-6519	157	11	(	(	PUNCT
ejpam-6519	157	12	o;rn	o;rn	PROPN
ejpam-6519	157	13	)	)	PUNCT
ejpam-6519	157	14	.	.	PUNCT
ejpam-6519	158	1	b.	b.	PROPN
ejpam-6519	158	2	sultan	sultan	PROPN
ejpam-6519	158	3	et	et	PROPN
ejpam-6519	158	4	al	al	PROPN
ejpam-6519	158	5	.	.	PUNCT
ejpam-6519	158	6	/	/	SYM
ejpam-6519	158	7	eur	eur	PROPN
ejpam-6519	158	8	.	.	PUNCT
ejpam-6519	159	1	j.	j.	PROPN
ejpam-6519	159	2	pure	pure	PROPN
ejpam-6519	159	3	appl	appl	PROPN
ejpam-6519	159	4	.	.	PROPN
ejpam-6519	159	5	math	math	PROPN
ejpam-6519	159	6	,	,	PUNCT
ejpam-6519	159	7	18	18	NUM
ejpam-6519	159	8	(	(	PUNCT
ejpam-6519	159	9	4	4	NUM
ejpam-6519	159	10	)	)	PUNCT
ejpam-6519	159	11	(	(	PUNCT
ejpam-6519	159	12	2025	2025	NUM
ejpam-6519	159	13	)	)	PUNCT
ejpam-6519	159	14	,	,	PUNCT
ejpam-6519	159	15	6519	6519	NUM
ejpam-6519	159	16	9	9	NUM
ejpam-6519	159	17	of	of	ADP
ejpam-6519	159	18	11	11	NUM
ejpam-6519	159	19	if	if	SCONJ
ejpam-6519	159	20	1	1	NUM
ejpam-6519	159	21	<	<	X
ejpam-6519	159	22	q	q	X
ejpam-6519	159	23	<	<	X
ejpam-6519	159	24	∞	∞	PROPN
ejpam-6519	159	25	,	,	PUNCT
ejpam-6519	159	26	by	by	ADP
ejpam-6519	159	27	using	use	VERB
ejpam-6519	159	28	(	(	PUNCT
ejpam-6519	159	29	ep	ep	PROPN
ejpam-6519	159	30	r	r	NOUN
ejpam-6519	159	31	)	)	PUNCT
ejpam-6519	159	32	u	u	NOUN
ejpam-6519	159	33	boundedness	boundedness	NOUN
ejpam-6519	159	34	of	of	ADP
ejpam-6519	159	35	t	t	PROPN
ejpam-6519	159	36	and	and	CCONJ
ejpam-6519	159	37	again	again	ADV
ejpam-6519	159	38	hölder	hölder	VERB
ejpam-6519	159	39	inequality	inequality	NOUN
ejpam-6519	159	40	to	to	PART
ejpam-6519	159	41	obtain	obtain	VERB
ejpam-6519	159	42	i2	i2	NOUN
ejpam-6519	159	43	.	.	PUNCT
ejpam-6519	160	1	∞∑	∞∑	NUM
ejpam-6519	160	2	`	`	PUNCT
ejpam-6519	160	3	=	=	NOUN
ejpam-6519	160	4	−∞	−∞	X
ejpam-6519	160	5	b`αq	b`αq	ADP
ejpam-6519	160	6			PROPN
ejpam-6519	160	7	∞∑	∞∑	PROPN
ejpam-6519	160	8	a0=`−w	a0=`−w	ADV
ejpam-6519	160	9	|γa0	|γa0	ADV
ejpam-6519	160	10	|	|	ADV
ejpam-6519	160	11	‖ba0‖(ep	‖ba0‖(ep	PROPN
ejpam-6519	160	12	r	r	NOUN
ejpam-6519	160	13	)	)	PUNCT
ejpam-6519	160	14	u	u	NOUN
ejpam-6519	160	15	q	q	NOUN
ejpam-6519	160	16	.	.	PUNCT
ejpam-6519	161	1	∞∑	∞∑	NUM
ejpam-6519	161	2	`	`	PUNCT
ejpam-6519	161	3	=	=	NOUN
ejpam-6519	161	4	−∞	−∞	ADP
ejpam-6519	161	5			PROPN
ejpam-6519	161	6	∞∑	∞∑	PROPN
ejpam-6519	161	7	a0=`−w	a0=`−w	ADV
ejpam-6519	161	8	|γa0	|γa0	DET
ejpam-6519	161	9	|	|	ADV
ejpam-6519	161	10	b(`−a0)α	b(`−a0)α	NOUN
ejpam-6519	161	11	q	q	PUNCT
ejpam-6519	161	12	.	.	PUNCT
ejpam-6519	162	1	∞∑	∞∑	NUM
ejpam-6519	162	2	`	`	PUNCT
ejpam-6519	162	3	=	=	NOUN
ejpam-6519	162	4	−∞	−∞	ADP
ejpam-6519	162	5			PROPN
ejpam-6519	162	6	∞∑	∞∑	PROPN
ejpam-6519	162	7	a0=`−w	a0=`−w	ADV
ejpam-6519	162	8	|γa0	|γa0	ADV
ejpam-6519	163	1	|	|	NOUN
ejpam-6519	163	2	q	q	NOUN
ejpam-6519	163	3	b(`−a0)αq/2	b(`−a0)αq/2	NOUN
ejpam-6519	163	4			PUNCT
ejpam-6519	164	1	∞∑	∞∑	NUM
ejpam-6519	164	2	a0=`−w	a0=`−w	ADV
ejpam-6519	164	3	b(`−a0)α(q	b(`−a0)α(q	NUM
ejpam-6519	164	4	)	)	PUNCT
ejpam-6519	164	5	′/2	′/2	NUM
ejpam-6519	164	6	q	q	PUNCT
ejpam-6519	164	7	/	/	SYM
ejpam-6519	164	8	q′	q′	NOUN
ejpam-6519	164	9	.	.	PUNCT
ejpam-6519	165	1	∞∑	∞∑	PRON
ejpam-6519	165	2	a0=−∞	a0=−∞	ADJ
ejpam-6519	165	3	|γa0	|γa0	ADP
ejpam-6519	165	4	|	|	ADV
ejpam-6519	165	5	q	q	X
ejpam-6519	165	6	a0+w∑	a0+w∑	PUNCT
ejpam-6519	165	7	`	`	PUNCT
ejpam-6519	165	8	=	=	NOUN
ejpam-6519	165	9	−∞	−∞	NOUN
ejpam-6519	165	10	b(`−a0)αq/2	b(`−a0)αq/2	NOUN
ejpam-6519	165	11	.	.	PUNCT
ejpam-6519	166	1	∞∑	∞∑	NUM
ejpam-6519	166	2	a0=−∞	a0=−∞	ADJ
ejpam-6519	166	3	|γa0	|γa0	ADP
ejpam-6519	166	4	|	|	ADV
ejpam-6519	166	5	q	q	NOUN
ejpam-6519	166	6	.	.	PUNCT
ejpam-6519	167	1	‖g‖q	‖g‖q	PROPN
ejpam-6519	167	2	(	(	PUNCT
ejpam-6519	167	3	k̇eα	k̇eα	NOUN
ejpam-6519	167	4	,	,	PUNCT
ejpam-6519	167	5	p	p	NOUN
ejpam-6519	167	6	q	q	NOUN
ejpam-6519	167	7	,	,	PUNCT
ejpam-6519	167	8	r	r	NOUN
ejpam-6519	167	9	)	)	PUNCT
ejpam-6519	167	10	u	u	NOUN
ejpam-6519	167	11	(	(	PUNCT
ejpam-6519	167	12	o;rn	o;rn	PROPN
ejpam-6519	167	13	)	)	PUNCT
ejpam-6519	167	14	.	.	PUNCT
ejpam-6519	168	1	combining	combine	VERB
ejpam-6519	168	2	these	these	DET
ejpam-6519	168	3	estimates	estimate	NOUN
ejpam-6519	168	4	we	we	PRON
ejpam-6519	168	5	get	get	VERB
ejpam-6519	168	6	‖tg‖	‖tg‖	PROPN
ejpam-6519	168	7	(	(	PUNCT
ejpam-6519	168	8	k̇eα	k̇eα	X
ejpam-6519	168	9	,	,	PUNCT
ejpam-6519	168	10	p	p	NOUN
ejpam-6519	168	11	q	q	NOUN
ejpam-6519	168	12	,	,	PUNCT
ejpam-6519	168	13	r	r	NOUN
ejpam-6519	168	14	)	)	PUNCT
ejpam-6519	168	15	u	u	NOUN
ejpam-6519	168	16	(	(	PUNCT
ejpam-6519	168	17	o;rn	o;rn	PROPN
ejpam-6519	168	18	)	)	PUNCT
ejpam-6519	168	19	.	.	PUNCT
ejpam-6519	169	1	‖g‖	‖g‖	VERB
ejpam-6519	169	2	(	(	PUNCT
ejpam-6519	169	3	k̇eα	k̇eα	NOUN
ejpam-6519	169	4	,	,	PUNCT
ejpam-6519	169	5	p	p	NOUN
ejpam-6519	169	6	q	q	NOUN
ejpam-6519	169	7	,	,	PUNCT
ejpam-6519	169	8	r	r	NOUN
ejpam-6519	169	9	)	)	PUNCT
ejpam-6519	169	10	u	u	NOUN
ejpam-6519	169	11	(	(	PUNCT
ejpam-6519	169	12	o;rn	o;rn	PROPN
ejpam-6519	169	13	)	)	PUNCT
ejpam-6519	169	14	.	.	PUNCT
ejpam-6519	170	1	thus	thus	ADV
ejpam-6519	170	2	,	,	PUNCT
ejpam-6519	170	3	the	the	DET
ejpam-6519	170	4	proof	proof	NOUN
ejpam-6519	170	5	of	of	ADP
ejpam-6519	170	6	the	the	DET
ejpam-6519	170	7	theorem	theorem	NOUN
ejpam-6519	170	8	4.1	4.1	NUM
ejpam-6519	170	9	is	be	AUX
ejpam-6519	170	10	completed	complete	VERB
ejpam-6519	170	11	.	.	PUNCT
ejpam-6519	171	1	5	5	X
ejpam-6519	171	2	.	.	PUNCT
ejpam-6519	171	3	ethics	ethic	NOUN
ejpam-6519	171	4	declarations	declaration	NOUN
ejpam-6519	171	5	conflict	conflict	NOUN
ejpam-6519	171	6	of	of	ADP
ejpam-6519	171	7	interest	interest	NOUN
ejpam-6519	171	8	the	the	DET
ejpam-6519	171	9	authors	author	NOUN
ejpam-6519	171	10	declare	declare	VERB
ejpam-6519	171	11	that	that	SCONJ
ejpam-6519	171	12	they	they	PRON
ejpam-6519	171	13	have	have	VERB
ejpam-6519	171	14	no	no	DET
ejpam-6519	171	15	known	know	VERB
ejpam-6519	171	16	competing	compete	VERB
ejpam-6519	171	17	financial	financial	ADJ
ejpam-6519	171	18	interests	interest	NOUN
ejpam-6519	171	19	or	or	CCONJ
ejpam-6519	171	20	personal	personal	ADJ
ejpam-6519	171	21	relationships	relationship	NOUN
ejpam-6519	171	22	that	that	PRON
ejpam-6519	171	23	could	could	AUX
ejpam-6519	171	24	have	have	AUX
ejpam-6519	171	25	appeared	appear	VERB
ejpam-6519	171	26	to	to	PART
ejpam-6519	171	27	influence	influence	VERB
ejpam-6519	171	28	the	the	DET
ejpam-6519	171	29	work	work	NOUN
ejpam-6519	171	30	reported	report	VERB
ejpam-6519	171	31	in	in	ADP
ejpam-6519	171	32	this	this	DET
ejpam-6519	171	33	paper	paper	NOUN
ejpam-6519	171	34	.	.	PUNCT
ejpam-6519	172	1	ethics	ethic	NOUN
ejpam-6519	172	2	approval	approval	NOUN
ejpam-6519	172	3	and	and	CCONJ
ejpam-6519	172	4	consent	consent	NOUN
ejpam-6519	172	5	to	to	PART
ejpam-6519	172	6	participate	participate	VERB
ejpam-6519	172	7	this	this	DET
ejpam-6519	172	8	manuscript	manuscript	NOUN
ejpam-6519	172	9	has	have	VERB
ejpam-6519	172	10	not	not	PART
ejpam-6519	172	11	and	and	CCONJ
ejpam-6519	172	12	will	will	AUX
ejpam-6519	172	13	not	not	PART
ejpam-6519	172	14	be	be	AUX
ejpam-6519	172	15	submitted	submit	VERB
ejpam-6519	172	16	to	to	ADP
ejpam-6519	172	17	more	more	ADJ
ejpam-6519	172	18	than	than	ADP
ejpam-6519	172	19	one	one	NUM
ejpam-6519	172	20	journal	journal	NOUN
ejpam-6519	172	21	for	for	ADP
ejpam-6519	172	22	simultaneous	simultaneous	ADJ
ejpam-6519	172	23	consideration	consideration	NOUN
ejpam-6519	172	24	.	.	PUNCT
ejpam-6519	173	1	the	the	DET
ejpam-6519	173	2	submitted	submit	VERB
ejpam-6519	173	3	work	work	NOUN
ejpam-6519	173	4	is	be	AUX
ejpam-6519	173	5	original	original	ADJ
ejpam-6519	173	6	and	and	CCONJ
ejpam-6519	173	7	will	will	AUX
ejpam-6519	173	8	not	not	PART
ejpam-6519	173	9	be	be	AUX
ejpam-6519	173	10	published	publish	VERB
ejpam-6519	173	11	elsewhere	elsewhere	ADV
ejpam-6519	173	12	.	.	PUNCT
ejpam-6519	174	1	funding	funding	NOUN
ejpam-6519	174	2	authors	author	NOUN
ejpam-6519	174	3	state	state	VERB
ejpam-6519	174	4	no	no	DET
ejpam-6519	174	5	funding	funding	NOUN
ejpam-6519	174	6	involved	involve	VERB
ejpam-6519	174	7	.	.	PUNCT
ejpam-6519	175	1	b.	b.	PROPN
ejpam-6519	175	2	sultan	sultan	PROPN
ejpam-6519	175	3	et	et	PROPN
ejpam-6519	175	4	al	al	PROPN
ejpam-6519	175	5	.	.	PUNCT
ejpam-6519	175	6	/	/	SYM
ejpam-6519	175	7	eur	eur	PROPN
ejpam-6519	175	8	.	.	PUNCT
ejpam-6519	176	1	j.	j.	PROPN
ejpam-6519	176	2	pure	pure	PROPN
ejpam-6519	176	3	appl	appl	PROPN
ejpam-6519	176	4	.	.	PROPN
ejpam-6519	176	5	math	math	PROPN
ejpam-6519	176	6	,	,	PUNCT
ejpam-6519	176	7	18	18	NUM
ejpam-6519	176	8	(	(	PUNCT
ejpam-6519	176	9	4	4	NUM
ejpam-6519	176	10	)	)	PUNCT
ejpam-6519	176	11	(	(	PUNCT
ejpam-6519	176	12	2025	2025	NUM
ejpam-6519	176	13	)	)	PUNCT
ejpam-6519	176	14	,	,	PUNCT
ejpam-6519	176	15	6519	6519	NUM
ejpam-6519	176	16	10	10	NUM
ejpam-6519	176	17	of	of	ADP
ejpam-6519	176	18	11	11	NUM
ejpam-6519	176	19	availability	availability	NOUN
ejpam-6519	176	20	of	of	ADP
ejpam-6519	176	21	data	datum	NOUN
ejpam-6519	176	22	no	no	DET
ejpam-6519	176	23	data	data	NOUN
ejpam-6519	176	24	is	be	AUX
ejpam-6519	176	25	available	available	ADJ
ejpam-6519	176	26	for	for	ADP
ejpam-6519	176	27	this	this	DET
ejpam-6519	176	28	study	study	NOUN
ejpam-6519	176	29	.	.	PUNCT
ejpam-6519	177	1	references	reference	NOUN
ejpam-6519	177	2	[	[	X
ejpam-6519	177	3	1	1	X
ejpam-6519	177	4	]	]	PUNCT
ejpam-6519	177	5	p.	p.	NOUN
ejpam-6519	177	6	auscher	auscher	PROPN
ejpam-6519	177	7	and	and	CCONJ
ejpam-6519	177	8	m.	m.	NOUN
ejpam-6519	177	9	mourgoglou	mourgoglou	PROPN
ejpam-6519	177	10	.	.	PUNCT
ejpam-6519	178	1	representation	representation	NOUN
ejpam-6519	178	2	and	and	CCONJ
ejpam-6519	178	3	uniqueness	uniqueness	NOUN
ejpam-6519	178	4	for	for	ADP
ejpam-6519	178	5	boundary	boundary	ADJ
ejpam-6519	178	6	value	value	NOUN
ejpam-6519	178	7	elliptic	elliptic	ADJ
ejpam-6519	178	8	problems	problem	NOUN
ejpam-6519	178	9	via	via	ADP
ejpam-6519	178	10	first	first	ADJ
ejpam-6519	178	11	order	order	NOUN
ejpam-6519	178	12	systems	system	NOUN
ejpam-6519	178	13	.	.	PUNCT
ejpam-6519	179	1	revista	revista	PROPN
ejpam-6519	179	2	matemática	matemática	PROPN
ejpam-6519	179	3	iberoamericana	iberoamericana	PROPN
ejpam-6519	179	4	,	,	PUNCT
ejpam-6519	179	5	35:241–315	35:241–315	NUM
ejpam-6519	179	6	,	,	PUNCT
ejpam-6519	179	7	2019	2019	NUM
ejpam-6519	179	8	.	.	PUNCT
ejpam-6519	180	1	[	[	X
ejpam-6519	180	2	2	2	X
ejpam-6519	180	3	]	]	PUNCT
ejpam-6519	180	4	p.	p.	NOUN
ejpam-6519	180	5	auscher	auscher	PROPN
ejpam-6519	180	6	and	and	CCONJ
ejpam-6519	180	7	c.	c.	PROPN
ejpam-6519	180	8	prisuelos	prisuelos	PROPN
ejpam-6519	180	9	-	-	PUNCT
ejpam-6519	180	10	arribas	arribas	PROPN
ejpam-6519	180	11	.	.	PUNCT
ejpam-6519	181	1	tent	tent	NOUN
ejpam-6519	181	2	space	space	NOUN
ejpam-6519	181	3	boundedness	boundedness	NOUN
ejpam-6519	181	4	via	via	ADP
ejpam-6519	181	5	extrapolation	extrapolation	NOUN
ejpam-6519	181	6	.	.	PUNCT
ejpam-6519	182	1	mathematische	mathematische	PROPN
ejpam-6519	182	2	zeitschrift	zeitschrift	PROPN
ejpam-6519	182	3	,	,	PUNCT
ejpam-6519	182	4	286:1575–1604	286:1575–1604	NUM
ejpam-6519	182	5	,	,	PUNCT
ejpam-6519	182	6	2017	2017	NUM
ejpam-6519	182	7	.	.	PUNCT
ejpam-6519	183	1	[	[	X
ejpam-6519	183	2	3	3	X
ejpam-6519	183	3	]	]	PUNCT
ejpam-6519	183	4	m.	m.	NOUN
ejpam-6519	183	5	sultan	sultan	PROPN
ejpam-6519	183	6	and	and	CCONJ
ejpam-6519	183	7	b.	b.	PROPN
ejpam-6519	183	8	sultan	sultan	PROPN
ejpam-6519	183	9	.	.	PUNCT
ejpam-6519	184	1	λ	λ	ADJ
ejpam-6519	184	2	-	-	ADJ
ejpam-6519	184	3	central	central	ADJ
ejpam-6519	184	4	musielak	musielak	NOUN
ejpam-6519	184	5	–	–	PUNCT
ejpam-6519	184	6	orlicz	orlicz	NUM
ejpam-6519	184	7	–	–	PUNCT
ejpam-6519	184	8	morrey	morrey	NOUN
ejpam-6519	184	9	spaces	space	NOUN
ejpam-6519	184	10	.	.	PUNCT
ejpam-6519	185	1	arabian	arabian	ADJ
ejpam-6519	185	2	journal	journal	PROPN
ejpam-6519	185	3	of	of	ADP
ejpam-6519	185	4	mathematics	mathematic	NOUN
ejpam-6519	185	5	,	,	PUNCT
ejpam-6519	185	6	14:357–363	14:357–363	NUM
ejpam-6519	185	7	,	,	PUNCT
ejpam-6519	185	8	2025	2025	NUM
ejpam-6519	185	9	.	.	PUNCT
ejpam-6519	186	1	[	[	X
ejpam-6519	186	2	4	4	NUM
ejpam-6519	186	3	]	]	PUNCT
ejpam-6519	186	4	m.	m.	NOUN
ejpam-6519	186	5	sultan	sultan	PROPN
ejpam-6519	186	6	and	and	CCONJ
ejpam-6519	186	7	b.	b.	PROPN
ejpam-6519	186	8	sultan	sultan	PROPN
ejpam-6519	186	9	.	.	PUNCT
ejpam-6519	187	1	boundedness	boundedness	PROPN
ejpam-6519	187	2	of	of	ADP
ejpam-6519	187	3	sublinear	sublinear	NOUN
ejpam-6519	187	4	operators	operator	NOUN
ejpam-6519	187	5	on	on	ADP
ejpam-6519	187	6	grand	grand	ADJ
ejpam-6519	187	7	central	central	ADJ
ejpam-6519	187	8	orliczmorrey	orliczmorrey	NOUN
ejpam-6519	187	9	spaces	space	NOUN
ejpam-6519	187	10	.	.	PUNCT
ejpam-6519	188	1	bulletin	bulletin	PROPN
ejpam-6519	188	2	des	des	PROPN
ejpam-6519	188	3	sciences	sciences	PROPN
ejpam-6519	188	4	mathématiques	mathématique	NOUN
ejpam-6519	188	5	,	,	PUNCT
ejpam-6519	188	6	205:103704	205:103704	NUM
ejpam-6519	188	7	,	,	PUNCT
ejpam-6519	188	8	2025	2025	NUM
ejpam-6519	188	9	.	.	PUNCT
ejpam-6519	189	1	[	[	X
ejpam-6519	189	2	5	5	NUM
ejpam-6519	189	3	]	]	PUNCT
ejpam-6519	189	4	b.	b.	PROPN
ejpam-6519	189	5	sultan	sultan	PROPN
ejpam-6519	189	6	and	and	CCONJ
ejpam-6519	189	7	m.	m.	PROPN
ejpam-6519	189	8	sultan	sultan	PROPN
ejpam-6519	189	9	.	.	PUNCT
ejpam-6519	190	1	boundedness	boundedness	NOUN
ejpam-6519	190	2	of	of	ADP
ejpam-6519	190	3	higher	high	ADJ
ejpam-6519	190	4	order	order	NOUN
ejpam-6519	190	5	commutators	commutator	NOUN
ejpam-6519	190	6	of	of	ADP
ejpam-6519	190	7	hardy	hardy	ADJ
ejpam-6519	190	8	operators	operator	NOUN
ejpam-6519	190	9	on	on	ADP
ejpam-6519	190	10	grand	grand	ADJ
ejpam-6519	190	11	herz	herz	PROPN
ejpam-6519	190	12	-	-	PUNCT
ejpam-6519	190	13	morrey	morrey	PROPN
ejpam-6519	190	14	spaces	space	NOUN
ejpam-6519	190	15	.	.	PUNCT
ejpam-6519	191	1	bulletin	bulletin	PROPN
ejpam-6519	191	2	des	des	PROPN
ejpam-6519	191	3	sciences	sciences	PROPN
ejpam-6519	191	4	mathématiques	mathématique	NOUN
ejpam-6519	191	5	,	,	PUNCT
ejpam-6519	191	6	190	190	NUM
ejpam-6519	191	7	,	,	PUNCT
ejpam-6519	191	8	2024	2024	NUM
ejpam-6519	191	9	.	.	PUNCT
ejpam-6519	192	1	[	[	X
ejpam-6519	192	2	6	6	NUM
ejpam-6519	192	3	]	]	PUNCT
ejpam-6519	192	4	m.	m.	NOUN
ejpam-6519	192	5	sultan	sultan	PROPN
ejpam-6519	192	6	,	,	PUNCT
ejpam-6519	192	7	b.	b.	PROPN
ejpam-6519	192	8	sultan	sultan	PROPN
ejpam-6519	192	9	,	,	PUNCT
ejpam-6519	192	10	a.	a.	PROPN
ejpam-6519	192	11	khan	khan	PROPN
ejpam-6519	192	12	,	,	PUNCT
ejpam-6519	192	13	and	and	CCONJ
ejpam-6519	192	14	t.	t.	PROPN
ejpam-6519	192	15	abdeljawad	abdeljawad	NOUN
ejpam-6519	192	16	.	.	PUNCT
ejpam-6519	193	1	boundedness	boundedness	NOUN
ejpam-6519	193	2	of	of	ADP
ejpam-6519	193	3	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6519	193	4	integral	integral	ADJ
ejpam-6519	193	5	operator	operator	NOUN
ejpam-6519	193	6	of	of	ADP
ejpam-6519	193	7	variable	variable	ADJ
ejpam-6519	193	8	order	order	NOUN
ejpam-6519	193	9	in	in	ADP
ejpam-6519	193	10	grand	grand	ADJ
ejpam-6519	193	11	herz	herz	PROPN
ejpam-6519	193	12	-	-	PUNCT
ejpam-6519	193	13	morrey	morrey	PROPN
ejpam-6519	193	14	spaces	space	NOUN
ejpam-6519	193	15	.	.	PUNCT
ejpam-6519	194	1	aims	aim	VERB
ejpam-6519	194	2	mathematics	mathematic	NOUN
ejpam-6519	194	3	,	,	PUNCT
ejpam-6519	194	4	8(9):22338–22353	8(9):22338–22353	PROPN
ejpam-6519	194	5	,	,	PUNCT
ejpam-6519	194	6	2023	2023	NUM
ejpam-6519	194	7	.	.	PUNCT
ejpam-6519	195	1	[	[	X
ejpam-6519	195	2	7	7	X
ejpam-6519	195	3	]	]	X
ejpam-6519	195	4	b.	b.	PROPN
ejpam-6519	195	5	sultan	sultan	PROPN
ejpam-6519	195	6	,	,	PUNCT
ejpam-6519	195	7	m.	m.	NOUN
ejpam-6519	195	8	sultan	sultan	PROPN
ejpam-6519	195	9	,	,	PUNCT
ejpam-6519	195	10	and	and	CCONJ
ejpam-6519	195	11	i.	i.	PROPN
ejpam-6519	195	12	khan	khan	PROPN
ejpam-6519	195	13	.	.	PUNCT
ejpam-6519	196	1	on	on	ADP
ejpam-6519	196	2	sobolev	sobolev	PROPN
ejpam-6519	196	3	theorem	theorem	NOUN
ejpam-6519	196	4	for	for	ADP
ejpam-6519	196	5	higher	high	ADJ
ejpam-6519	196	6	commutators	commutator	NOUN
ejpam-6519	196	7	of	of	ADP
ejpam-6519	196	8	fractional	fractional	ADJ
ejpam-6519	196	9	integrals	integral	NOUN
ejpam-6519	196	10	in	in	ADP
ejpam-6519	196	11	grand	grand	ADJ
ejpam-6519	196	12	variable	variable	ADJ
ejpam-6519	196	13	herz	herz	PROPN
ejpam-6519	196	14	spaces	space	NOUN
ejpam-6519	196	15	.	.	PUNCT
ejpam-6519	197	1	communications	communication	NOUN
ejpam-6519	197	2	in	in	ADP
ejpam-6519	197	3	nonlinear	nonlinear	ADJ
ejpam-6519	197	4	science	science	NOUN
ejpam-6519	197	5	and	and	CCONJ
ejpam-6519	197	6	numerical	numerical	PROPN
ejpam-6519	197	7	simulation	simulation	PROPN
ejpam-6519	197	8	,	,	PUNCT
ejpam-6519	197	9	126	126	NUM
ejpam-6519	197	10	,	,	PUNCT
ejpam-6519	197	11	2023	2023	NUM
ejpam-6519	197	12	.	.	PUNCT
ejpam-6519	198	1	[	[	X
ejpam-6519	198	2	8	8	NUM
ejpam-6519	198	3	]	]	X
ejpam-6519	198	4	b.	b.	PROPN
ejpam-6519	198	5	sultan	sultan	PROPN
ejpam-6519	198	6	and	and	CCONJ
ejpam-6519	198	7	m.	m.	PROPN
ejpam-6519	198	8	sultan	sultan	PROPN
ejpam-6519	198	9	.	.	PUNCT
ejpam-6519	199	1	boundedness	boundedness	NOUN
ejpam-6519	199	2	of	of	ADP
ejpam-6519	199	3	commutators	commutator	NOUN
ejpam-6519	199	4	of	of	ADP
ejpam-6519	199	5	rough	rough	ADJ
ejpam-6519	199	6	hardy	hardy	ADJ
ejpam-6519	199	7	operators	operator	NOUN
ejpam-6519	199	8	on	on	ADP
ejpam-6519	199	9	grand	grand	ADJ
ejpam-6519	199	10	variable	variable	ADJ
ejpam-6519	199	11	herz	herz	PROPN
ejpam-6519	199	12	spaces	space	NOUN
ejpam-6519	199	13	.	.	PUNCT
ejpam-6519	200	1	forum	forum	PROPN
ejpam-6519	200	2	mathematicum	mathematicum	PROPN
ejpam-6519	200	3	,	,	PUNCT
ejpam-6519	200	4	2023	2023	NUM
ejpam-6519	200	5	.	.	PUNCT
ejpam-6519	201	1	[	[	X
ejpam-6519	201	2	9	9	NUM
ejpam-6519	201	3	]	]	PUNCT
ejpam-6519	201	4	b.	b.	PROPN
ejpam-6519	201	5	sultan	sultan	PROPN
ejpam-6519	201	6	,	,	PUNCT
ejpam-6519	201	7	m.	m.	NOUN
ejpam-6519	201	8	sultan	sultan	PROPN
ejpam-6519	201	9	,	,	PUNCT
ejpam-6519	201	10	q.	q.	PROPN
ejpam-6519	201	11	q.	q.	PROPN
ejpam-6519	201	12	zhang	zhang	PROPN
ejpam-6519	201	13	,	,	PUNCT
ejpam-6519	201	14	and	and	CCONJ
ejpam-6519	201	15	n.	n.	PROPN
ejpam-6519	201	16	mlaiki	mlaiki	PROPN
ejpam-6519	201	17	.	.	PUNCT
ejpam-6519	202	1	boundedness	boundedness	PROPN
ejpam-6519	202	2	of	of	ADP
ejpam-6519	202	3	hardy	hardy	ADJ
ejpam-6519	202	4	operators	operator	NOUN
ejpam-6519	202	5	on	on	ADP
ejpam-6519	202	6	grand	grand	ADJ
ejpam-6519	202	7	variable	variable	NOUN
ejpam-6519	202	8	weighted	weight	VERB
ejpam-6519	202	9	herz	herz	PROPN
ejpam-6519	202	10	spaces	space	NOUN
ejpam-6519	202	11	.	.	PUNCT
ejpam-6519	203	1	aims	aim	VERB
ejpam-6519	203	2	mathematics	mathematic	NOUN
ejpam-6519	203	3	,	,	PUNCT
ejpam-6519	203	4	8(10):24515–24527	8(10):24515–24527	NUM
ejpam-6519	203	5	,	,	PUNCT
ejpam-6519	203	6	2023	2023	NUM
ejpam-6519	203	7	.	.	PUNCT
ejpam-6519	204	1	[	[	X
ejpam-6519	204	2	10	10	NUM
ejpam-6519	204	3	]	]	X
ejpam-6519	204	4	b.	b.	PROPN
ejpam-6519	204	5	sultan	sultan	PROPN
ejpam-6519	204	6	,	,	PUNCT
ejpam-6519	204	7	f.	f.	PROPN
ejpam-6519	204	8	azmi	azmi	PROPN
ejpam-6519	204	9	,	,	PUNCT
ejpam-6519	204	10	m.	m.	NOUN
ejpam-6519	204	11	sultan	sultan	PROPN
ejpam-6519	204	12	,	,	PUNCT
ejpam-6519	204	13	t.	t.	PROPN
ejpam-6519	204	14	mahmood	mahmood	PROPN
ejpam-6519	204	15	,	,	PUNCT
ejpam-6519	204	16	n.	n.	PROPN
ejpam-6519	204	17	mlaiki	mlaiki	PROPN
ejpam-6519	204	18	,	,	PUNCT
ejpam-6519	204	19	and	and	CCONJ
ejpam-6519	204	20	n.	n.	NOUN
ejpam-6519	204	21	souayah	souayah	NOUN
ejpam-6519	204	22	.	.	PUNCT
ejpam-6519	205	1	boundedness	boundedness	NOUN
ejpam-6519	205	2	of	of	ADP
ejpam-6519	205	3	fractional	fractional	ADJ
ejpam-6519	205	4	integrals	integral	NOUN
ejpam-6519	205	5	on	on	ADP
ejpam-6519	205	6	grand	grand	ADJ
ejpam-6519	205	7	weighted	weight	VERB
ejpam-6519	205	8	herz	herz	PROPN
ejpam-6519	205	9	-	-	PUNCT
ejpam-6519	205	10	morrey	morrey	PROPN
ejpam-6519	205	11	spaces	space	NOUN
ejpam-6519	205	12	with	with	ADP
ejpam-6519	205	13	variable	variable	ADJ
ejpam-6519	205	14	exponent	exponent	NOUN
ejpam-6519	205	15	.	.	PUNCT
ejpam-6519	206	1	fractal	fractal	PROPN
ejpam-6519	206	2	and	and	CCONJ
ejpam-6519	206	3	fractional	fractional	ADJ
ejpam-6519	206	4	,	,	PUNCT
ejpam-6519	206	5	6(11):660–670	6(11):660–670	NUM
ejpam-6519	206	6	,	,	PUNCT
ejpam-6519	206	7	2022	2022	NUM
ejpam-6519	206	8	.	.	PUNCT
ejpam-6519	207	1	[	[	X
ejpam-6519	207	2	11	11	NUM
ejpam-6519	207	3	]	]	PUNCT
ejpam-6519	207	4	b.	b.	PROPN
ejpam-6519	207	5	sultan	sultan	PROPN
ejpam-6519	207	6	,	,	PUNCT
ejpam-6519	207	7	m.	m.	NOUN
ejpam-6519	207	8	sultan	sultan	PROPN
ejpam-6519	207	9	,	,	PUNCT
ejpam-6519	207	10	m.	m.	PROPN
ejpam-6519	207	11	mehmood	mehmood	PROPN
ejpam-6519	207	12	,	,	PUNCT
ejpam-6519	207	13	f.	f.	PROPN
ejpam-6519	207	14	azmi	azmi	PROPN
ejpam-6519	207	15	,	,	PUNCT
ejpam-6519	207	16	m.	m.	NOUN
ejpam-6519	207	17	a.	a.	NOUN
ejpam-6519	207	18	alghafli	alghafli	PROPN
ejpam-6519	207	19	,	,	PUNCT
ejpam-6519	207	20	and	and	CCONJ
ejpam-6519	207	21	n.	n.	PROPN
ejpam-6519	207	22	mlaiki	mlaiki	PROPN
ejpam-6519	207	23	.	.	PUNCT
ejpam-6519	208	1	boundedness	boundedness	PROPN
ejpam-6519	208	2	of	of	ADP
ejpam-6519	208	3	fractional	fractional	ADJ
ejpam-6519	208	4	integrals	integral	NOUN
ejpam-6519	208	5	on	on	ADP
ejpam-6519	208	6	grand	grand	ADJ
ejpam-6519	208	7	weighted	weight	VERB
ejpam-6519	208	8	herz	herz	PROPN
ejpam-6519	208	9	spaces	space	NOUN
ejpam-6519	208	10	with	with	ADP
ejpam-6519	208	11	variable	variable	ADJ
ejpam-6519	208	12	exponent	exponent	NOUN
ejpam-6519	208	13	.	.	PUNCT
ejpam-6519	209	1	aims	aim	VERB
ejpam-6519	209	2	mathematics	mathematic	NOUN
ejpam-6519	209	3	,	,	PUNCT
ejpam-6519	209	4	8(1):752–764	8(1):752–764	NUM
ejpam-6519	209	5	,	,	PUNCT
ejpam-6519	209	6	2023	2023	NUM
ejpam-6519	209	7	.	.	PUNCT
ejpam-6519	210	1	[	[	X
ejpam-6519	210	2	12	12	NUM
ejpam-6519	210	3	]	]	PUNCT
ejpam-6519	210	4	b.	b.	PROPN
ejpam-6519	210	5	sultan	sultan	PROPN
ejpam-6519	210	6	,	,	PUNCT
ejpam-6519	210	7	f.	f.	PROPN
ejpam-6519	210	8	azmi	azmi	PROPN
ejpam-6519	210	9	,	,	PUNCT
ejpam-6519	210	10	m.	m.	NOUN
ejpam-6519	210	11	sultan	sultan	PROPN
ejpam-6519	210	12	,	,	PUNCT
ejpam-6519	210	13	m.	m.	NOUN
ejpam-6519	210	14	mehmood	mehmood	PROPN
ejpam-6519	210	15	,	,	PUNCT
ejpam-6519	210	16	and	and	CCONJ
ejpam-6519	210	17	n.	n.	PROPN
ejpam-6519	210	18	mlaiki	mlaiki	PROPN
ejpam-6519	210	19	.	.	PUNCT
ejpam-6519	211	1	boundedness	boundedness	PROPN
ejpam-6519	211	2	of	of	ADP
ejpam-6519	211	3	riesz	riesz	PROPN
ejpam-6519	211	4	potential	potential	ADJ
ejpam-6519	211	5	operator	operator	NOUN
ejpam-6519	211	6	on	on	ADP
ejpam-6519	211	7	grand	grand	ADJ
ejpam-6519	211	8	herz	herz	PROPN
ejpam-6519	211	9	-	-	PUNCT
ejpam-6519	211	10	morrey	morrey	PROPN
ejpam-6519	211	11	spaces	space	NOUN
ejpam-6519	211	12	.	.	PUNCT
ejpam-6519	212	1	axioms	axiom	NOUN
ejpam-6519	212	2	,	,	PUNCT
ejpam-6519	212	3	11(11):583	11(11):583	NUM
ejpam-6519	212	4	,	,	PUNCT
ejpam-6519	212	5	2022	2022	NUM
ejpam-6519	212	6	.	.	PUNCT
ejpam-6519	213	1	[	[	X
ejpam-6519	213	2	13	13	NUM
ejpam-6519	213	3	]	]	PUNCT
ejpam-6519	213	4	m.	m.	NOUN
ejpam-6519	213	5	sultan	sultan	PROPN
ejpam-6519	213	6	and	and	CCONJ
ejpam-6519	213	7	b.	b.	PROPN
ejpam-6519	213	8	sultan	sultan	PROPN
ejpam-6519	213	9	.	.	PUNCT
ejpam-6519	214	1	a	a	DET
ejpam-6519	214	2	note	note	NOUN
ejpam-6519	214	3	on	on	ADP
ejpam-6519	214	4	the	the	DET
ejpam-6519	214	5	boundedness	boundedness	NOUN
ejpam-6519	214	6	of	of	ADP
ejpam-6519	214	7	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6519	214	8	integral	integral	ADJ
ejpam-6519	214	9	operator	operator	NOUN
ejpam-6519	214	10	on	on	ADP
ejpam-6519	214	11	continual	continual	ADJ
ejpam-6519	214	12	herz	herz	PROPN
ejpam-6519	214	13	-	-	PUNCT
ejpam-6519	214	14	morrey	morrey	PROPN
ejpam-6519	214	15	spaces	space	NOUN
ejpam-6519	214	16	.	.	PUNCT
ejpam-6519	215	1	filomat	filomat	PROPN
ejpam-6519	215	2	,	,	PUNCT
ejpam-6519	215	3	39(6):2017–2027	39(6):2017–2027	PROPN
ejpam-6519	215	4	,	,	PUNCT
ejpam-6519	215	5	2025	2025	NUM
ejpam-6519	215	6	.	.	PUNCT
ejpam-6519	216	1	[	[	X
ejpam-6519	216	2	14	14	NUM
ejpam-6519	216	3	]	]	X
ejpam-6519	216	4	j.	j.	PROPN
ejpam-6519	216	5	younas	younas	PROPN
ejpam-6519	216	6	,	,	PUNCT
ejpam-6519	216	7	a.	a.	NOUN
ejpam-6519	216	8	hussain	hussain	PROPN
ejpam-6519	216	9	,	,	PUNCT
ejpam-6519	216	10	h.	h.	PROPN
ejpam-6519	216	11	alhazmi	alhazmi	PROPN
ejpam-6519	216	12	,	,	PUNCT
ejpam-6519	216	13	a.	a.	PROPN
ejpam-6519	216	14	f.	f.	PROPN
ejpam-6519	216	15	aljohani	aljohani	PROPN
ejpam-6519	216	16	,	,	PUNCT
ejpam-6519	216	17	and	and	CCONJ
ejpam-6519	216	18	i.	i.	PROPN
ejpam-6519	216	19	khan	khan	PROPN
ejpam-6519	216	20	.	.	PUNCT
ejpam-6519	217	1	bmo	bmo	PROPN
ejpam-6519	217	2	estimates	estimate	NOUN
ejpam-6519	217	3	for	for	ADP
ejpam-6519	217	4	commutators	commutator	NOUN
ejpam-6519	217	5	of	of	ADP
ejpam-6519	217	6	the	the	DET
ejpam-6519	217	7	rough	rough	ADJ
ejpam-6519	217	8	fractional	fractional	ADJ
ejpam-6519	217	9	hausdorff	hausdorff	NOUN
ejpam-6519	217	10	operator	operator	NOUN
ejpam-6519	217	11	on	on	ADP
ejpam-6519	217	12	grand	grand	ADJ
ejpam-6519	217	13	-	-	PUNCT
ejpam-6519	217	14	variable	variable	ADJ
ejpam-6519	217	15	-	-	PUNCT
ejpam-6519	217	16	herzmorrey	herzmorrey	NOUN
ejpam-6519	217	17	spaces	space	NOUN
ejpam-6519	217	18	.	.	PUNCT
ejpam-6519	218	1	aims	aim	VERB
ejpam-6519	218	2	mathematics	mathematic	NOUN
ejpam-6519	218	3	,	,	PUNCT
ejpam-6519	218	4	9(9):23434–23448	9(9):23434–23448	NUM
ejpam-6519	218	5	,	,	PUNCT
ejpam-6519	218	6	2024	2024	NUM
ejpam-6519	218	7	.	.	PUNCT
ejpam-6519	219	1	b.	b.	PROPN
ejpam-6519	219	2	sultan	sultan	PROPN
ejpam-6519	219	3	et	et	PROPN
ejpam-6519	219	4	al	al	PROPN
ejpam-6519	219	5	.	.	PUNCT
ejpam-6519	219	6	/	/	SYM
ejpam-6519	219	7	eur	eur	PROPN
ejpam-6519	219	8	.	.	PUNCT
ejpam-6519	220	1	j.	j.	PROPN
ejpam-6519	220	2	pure	pure	PROPN
ejpam-6519	220	3	appl	appl	PROPN
ejpam-6519	220	4	.	.	PROPN
ejpam-6519	220	5	math	math	PROPN
ejpam-6519	220	6	,	,	PUNCT
ejpam-6519	220	7	18	18	NUM
ejpam-6519	220	8	(	(	PUNCT
ejpam-6519	220	9	4	4	NUM
ejpam-6519	220	10	)	)	PUNCT
ejpam-6519	220	11	(	(	PUNCT
ejpam-6519	220	12	2025	2025	NUM
ejpam-6519	220	13	)	)	PUNCT
ejpam-6519	220	14	,	,	PUNCT
ejpam-6519	220	15	6519	6519	NUM
ejpam-6519	220	16	11	11	NUM
ejpam-6519	220	17	of	of	ADP
ejpam-6519	220	18	11	11	NUM
ejpam-6519	221	1	[	[	SYM
ejpam-6519	221	2	15	15	NUM
ejpam-6519	221	3	]	]	PUNCT
ejpam-6519	221	4	a.	a.	NOUN
ejpam-6519	221	5	hussain	hussain	PROPN
ejpam-6519	221	6	,	,	PUNCT
ejpam-6519	221	7	i.	i.	PROPN
ejpam-6519	221	8	khan	khan	PROPN
ejpam-6519	221	9	,	,	PUNCT
ejpam-6519	221	10	and	and	CCONJ
ejpam-6519	221	11	a.	a.	PROPN
ejpam-6519	221	12	mohamed	mohamed	PROPN
ejpam-6519	221	13	.	.	PUNCT
ejpam-6519	222	1	variable	variable	ADJ
ejpam-6519	222	2	her	her	PROPN
ejpam-6519	222	3	-	-	PUNCT
ejpam-6519	222	4	morrey	morrey	PROPN
ejpam-6519	222	5	estimates	estimate	NOUN
ejpam-6519	222	6	for	for	ADP
ejpam-6519	222	7	rough	rough	ADJ
ejpam-6519	222	8	fractional	fractional	ADJ
ejpam-6519	222	9	hausdorff	hausdorff	NOUN
ejpam-6519	222	10	operator	operator	NOUN
ejpam-6519	222	11	.	.	PUNCT
ejpam-6519	223	1	journal	journal	PROPN
ejpam-6519	223	2	of	of	ADP
ejpam-6519	223	3	inequalities	inequality	NOUN
ejpam-6519	223	4	and	and	CCONJ
ejpam-6519	223	5	applications	application	NOUN
ejpam-6519	223	6	,	,	PUNCT
ejpam-6519	223	7	33	33	NUM
ejpam-6519	223	8	,	,	PUNCT
ejpam-6519	223	9	2024	2024	NUM
ejpam-6519	223	10	.	.	PUNCT
ejpam-6519	224	1	[	[	X
ejpam-6519	224	2	16	16	NUM
ejpam-6519	224	3	]	]	PUNCT
ejpam-6519	224	4	a.	a.	NOUN
ejpam-6519	224	5	hussain	hussain	PROPN
ejpam-6519	224	6	and	and	CCONJ
ejpam-6519	224	7	g.	g.	PROPN
ejpam-6519	224	8	gao	gao	PROPN
ejpam-6519	224	9	.	.	PUNCT
ejpam-6519	225	1	multilinear	multilinear	PROPN
ejpam-6519	225	2	singular	singular	PROPN
ejpam-6519	225	3	integrals	integral	NOUN
ejpam-6519	225	4	and	and	CCONJ
ejpam-6519	225	5	commutators	commutator	NOUN
ejpam-6519	225	6	on	on	ADP
ejpam-6519	225	7	herz	herz	ADJ
ejpam-6519	225	8	space	space	NOUN
ejpam-6519	225	9	with	with	ADP
ejpam-6519	225	10	variable	variable	ADJ
ejpam-6519	225	11	exponent	exponent	NOUN
ejpam-6519	225	12	.	.	PUNCT
ejpam-6519	226	1	isrn	isrn	PROPN
ejpam-6519	226	2	mathematical	mathematical	ADJ
ejpam-6519	226	3	analysis	analysis	NOUN
ejpam-6519	226	4	,	,	PUNCT
ejpam-6519	226	5	pages	page	NOUN
ejpam-6519	226	6	1–10	1–10	NOUN
ejpam-6519	226	7	,	,	PUNCT
ejpam-6519	226	8	2014	2014	NUM
ejpam-6519	226	9	.	.	PUNCT
ejpam-6519	227	1	[	[	X
ejpam-6519	227	2	17	17	NUM
ejpam-6519	227	3	]	]	PUNCT
ejpam-6519	227	4	m.	m.	NOUN
ejpam-6519	227	5	sultan	sultan	PROPN
ejpam-6519	227	6	,	,	PUNCT
ejpam-6519	227	7	b.	b.	PROPN
ejpam-6519	227	8	sultan	sultan	PROPN
ejpam-6519	227	9	,	,	PUNCT
ejpam-6519	227	10	and	and	CCONJ
ejpam-6519	227	11	a.	a.	NOUN
ejpam-6519	227	12	hussain	hussain	PROPN
ejpam-6519	227	13	.	.	PUNCT
ejpam-6519	228	1	grand	grand	PROPN
ejpam-6519	228	2	herz	herz	PROPN
ejpam-6519	228	3	–	–	PUNCT
ejpam-6519	228	4	morrey	morrey	PROPN
ejpam-6519	228	5	spaces	space	VERB
ejpam-6519	228	6	with	with	ADP
ejpam-6519	228	7	variable	variable	ADJ
ejpam-6519	228	8	exponent	exponent	NOUN
ejpam-6519	228	9	.	.	PUNCT
ejpam-6519	229	1	mathematical	mathematical	ADJ
ejpam-6519	229	2	notes	note	NOUN
ejpam-6519	229	3	,	,	PUNCT
ejpam-6519	229	4	114(5):957–977	114(5):957–977	NUM
ejpam-6519	229	5	,	,	PUNCT
ejpam-6519	229	6	2023	2023	NUM
ejpam-6519	229	7	.	.	PUNCT
ejpam-6519	230	1	[	[	X
ejpam-6519	230	2	18	18	NUM
ejpam-6519	230	3	]	]	PUNCT
ejpam-6519	230	4	m.	m.	NOUN
ejpam-6519	230	5	sultan	sultan	PROPN
ejpam-6519	230	6	and	and	CCONJ
ejpam-6519	230	7	b.	b.	PROPN
ejpam-6519	230	8	sultan	sultan	PROPN
ejpam-6519	230	9	.	.	PUNCT
ejpam-6519	231	1	a	a	DET
ejpam-6519	231	2	note	note	NOUN
ejpam-6519	231	3	on	on	ADP
ejpam-6519	231	4	the	the	DET
ejpam-6519	231	5	boundedness	boundedness	NOUN
ejpam-6519	231	6	of	of	ADP
ejpam-6519	231	7	higher	high	ADJ
ejpam-6519	231	8	order	order	NOUN
ejpam-6519	231	9	commutators	commutator	NOUN
ejpam-6519	231	10	on	on	ADP
ejpam-6519	231	11	fractional	fractional	ADJ
ejpam-6519	231	12	integrals	integral	NOUN
ejpam-6519	231	13	in	in	ADP
ejpam-6519	231	14	grand	grand	ADJ
ejpam-6519	231	15	variable	variable	ADJ
ejpam-6519	231	16	herz	herz	ADJ
ejpam-6519	231	17	-	-	PUNCT
ejpam-6519	231	18	morrey	morrey	PROPN
ejpam-6519	231	19	spaces	space	NOUN
ejpam-6519	231	20	.	.	PUNCT
ejpam-6519	232	1	kragujevac	kragujevac	PROPN
ejpam-6519	232	2	journal	journal	PROPN
ejpam-6519	232	3	of	of	ADP
ejpam-6519	232	4	mathematics	mathematic	NOUN
ejpam-6519	232	5	,	,	PUNCT
ejpam-6519	232	6	50(7):1063–1080	50(7):1063–1080	NUM
ejpam-6519	232	7	,	,	PUNCT
ejpam-6519	232	8	2026	2026	NUM
ejpam-6519	232	9	.	.	PUNCT
ejpam-6519	233	1	[	[	X
ejpam-6519	233	2	19	19	NUM
ejpam-6519	233	3	]	]	PUNCT
ejpam-6519	233	4	m.	m.	NOUN
ejpam-6519	233	5	sultan	sultan	PROPN
ejpam-6519	233	6	,	,	PUNCT
ejpam-6519	233	7	b.	b.	PROPN
ejpam-6519	233	8	sultan	sultan	PROPN
ejpam-6519	233	9	,	,	PUNCT
ejpam-6519	233	10	and	and	CCONJ
ejpam-6519	233	11	r.	r.	PROPN
ejpam-6519	233	12	e.	e.	PROPN
ejpam-6519	233	13	castillo	castillo	PROPN
ejpam-6519	233	14	.	.	PUNCT
ejpam-6519	234	1	weighted	weight	VERB
ejpam-6519	234	2	composition	composition	NOUN
ejpam-6519	234	3	operator	operator	NOUN
ejpam-6519	234	4	on	on	ADP
ejpam-6519	234	5	gamma	gamma	NOUN
ejpam-6519	234	6	spaces	space	NOUN
ejpam-6519	234	7	with	with	ADP
ejpam-6519	234	8	variable	variable	ADJ
ejpam-6519	234	9	exponent	exponent	NOUN
ejpam-6519	234	10	.	.	PUNCT
ejpam-6519	235	1	journal	journal	PROPN
ejpam-6519	235	2	of	of	ADP
ejpam-6519	235	3	pseudo	pseudo	NOUN
ejpam-6519	235	4	-	-	ADJ
ejpam-6519	235	5	differential	differential	ADJ
ejpam-6519	235	6	operators	operator	NOUN
ejpam-6519	235	7	and	and	CCONJ
ejpam-6519	235	8	applications	application	NOUN
ejpam-6519	235	9	,	,	PUNCT
ejpam-6519	235	10	15:46	15:46	NUM
ejpam-6519	235	11	,	,	PUNCT
ejpam-6519	235	12	2024	2024	NUM
ejpam-6519	235	13	.	.	PUNCT
ejpam-6519	236	1	[	[	X
ejpam-6519	236	2	20	20	NUM
ejpam-6519	236	3	]	]	PUNCT
ejpam-6519	236	4	b.	b.	PROPN
ejpam-6519	236	5	sultan	sultan	PROPN
ejpam-6519	236	6	and	and	CCONJ
ejpam-6519	236	7	m.	m.	PROPN
ejpam-6519	236	8	sultan	sultan	PROPN
ejpam-6519	236	9	.	.	PUNCT
ejpam-6519	237	1	sobolev	sobolev	NOUN
ejpam-6519	237	2	-	-	PUNCT
ejpam-6519	237	3	type	type	NOUN
ejpam-6519	237	4	theorem	theorem	NOUN
ejpam-6519	237	5	for	for	ADP
ejpam-6519	237	6	commutators	commutator	NOUN
ejpam-6519	237	7	of	of	ADP
ejpam-6519	237	8	hardy	hardy	ADJ
ejpam-6519	237	9	operators	operator	NOUN
ejpam-6519	237	10	in	in	ADP
ejpam-6519	237	11	grand	grand	ADJ
ejpam-6519	237	12	herz	herz	PROPN
ejpam-6519	237	13	spaces	space	NOUN
ejpam-6519	237	14	.	.	PUNCT
ejpam-6519	238	1	ukrainian	ukrainian	ADJ
ejpam-6519	238	2	mathematical	mathematical	ADJ
ejpam-6519	238	3	journal	journal	NOUN
ejpam-6519	238	4	,	,	PUNCT
ejpam-6519	238	5	76:1196–1213	76:1196–1213	NUM
ejpam-6519	238	6	,	,	PUNCT
ejpam-6519	238	7	2024	2024	NUM
ejpam-6519	238	8	.	.	PUNCT
ejpam-6519	239	1	[	[	X
ejpam-6519	239	2	21	21	NUM
ejpam-6519	239	3	]	]	PUNCT
ejpam-6519	239	4	b.	b.	PROPN
ejpam-6519	239	5	sultan	sultan	PROPN
ejpam-6519	239	6	,	,	PUNCT
ejpam-6519	239	7	m.	m.	NOUN
ejpam-6519	239	8	sultan	sultan	PROPN
ejpam-6519	239	9	,	,	PUNCT
ejpam-6519	239	10	a.	a.	PROPN
ejpam-6519	239	11	khan	khan	PROPN
ejpam-6519	239	12	,	,	PUNCT
ejpam-6519	239	13	and	and	CCONJ
ejpam-6519	239	14	t.	t.	PROPN
ejpam-6519	239	15	abdeljawad	abdeljawad	NOUN
ejpam-6519	239	16	.	.	PUNCT
ejpam-6519	240	1	boundedness	boundedness	NOUN
ejpam-6519	240	2	of	of	ADP
ejpam-6519	240	3	commutators	commutator	NOUN
ejpam-6519	240	4	of	of	ADP
ejpam-6519	240	5	variable	variable	ADJ
ejpam-6519	240	6	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6519	240	7	fractional	fractional	ADJ
ejpam-6519	240	8	integral	integral	ADJ
ejpam-6519	240	9	operator	operator	NOUN
ejpam-6519	240	10	in	in	ADP
ejpam-6519	240	11	grand	grand	ADJ
ejpam-6519	240	12	variable	variable	ADJ
ejpam-6519	240	13	herz	herz	PROPN
ejpam-6519	240	14	spaces	space	NOUN
ejpam-6519	240	15	.	.	PUNCT
ejpam-6519	241	1	journal	journal	PROPN
ejpam-6519	241	2	of	of	ADP
ejpam-6519	241	3	inequalities	inequality	NOUN
ejpam-6519	241	4	and	and	CCONJ
ejpam-6519	241	5	applications	application	NOUN
ejpam-6519	241	6	,	,	PUNCT
ejpam-6519	241	7	page	page	NOUN
ejpam-6519	241	8	93	93	NUM
ejpam-6519	241	9	,	,	PUNCT
ejpam-6519	241	10	2024	2024	NUM
ejpam-6519	241	11	.	.	PUNCT
ejpam-6519	242	1	[	[	X
ejpam-6519	242	2	22	22	NUM
ejpam-6519	242	3	]	]	PUNCT
ejpam-6519	242	4	b.	b.	PROPN
ejpam-6519	242	5	sultan	sultan	PROPN
ejpam-6519	242	6	,	,	PUNCT
ejpam-6519	242	7	a.	a.	NOUN
ejpam-6519	242	8	hussain	hussain	PROPN
ejpam-6519	242	9	,	,	PUNCT
ejpam-6519	242	10	and	and	CCONJ
ejpam-6519	242	11	m.	m.	NOUN
ejpam-6519	242	12	sultan	sultan	PROPN
ejpam-6519	242	13	.	.	PUNCT
ejpam-6519	243	1	characterization	characterization	NOUN
ejpam-6519	243	2	of	of	ADP
ejpam-6519	243	3	generalized	generalized	ADJ
ejpam-6519	243	4	campanato	campanato	NOUN
ejpam-6519	243	5	spaces	space	NOUN
ejpam-6519	243	6	with	with	ADP
ejpam-6519	243	7	variable	variable	ADJ
ejpam-6519	243	8	exponents	exponent	NOUN
ejpam-6519	243	9	via	via	ADP
ejpam-6519	243	10	fractional	fractional	ADJ
ejpam-6519	243	11	integrals	integral	NOUN
ejpam-6519	243	12	.	.	PUNCT
ejpam-6519	244	1	journal	journal	NOUN
ejpam-6519	244	2	of	of	ADP
ejpam-6519	244	3	pseudo	pseudo	NOUN
ejpam-6519	244	4	-	-	ADJ
ejpam-6519	244	5	differential	differential	ADJ
ejpam-6519	244	6	operators	operator	NOUN
ejpam-6519	244	7	and	and	CCONJ
ejpam-6519	244	8	applications	application	NOUN
ejpam-6519	244	9	,	,	PUNCT
ejpam-6519	244	10	16:22	16:22	NUM
ejpam-6519	244	11	,	,	PUNCT
ejpam-6519	244	12	2025	2025	NUM
ejpam-6519	244	13	.	.	PUNCT
ejpam-6519	245	1	[	[	X
ejpam-6519	245	2	23	23	NUM
ejpam-6519	245	3	]	]	PUNCT
ejpam-6519	245	4	b.	b.	PROPN
ejpam-6519	245	5	sultan	sultan	PROPN
ejpam-6519	245	6	,	,	PUNCT
ejpam-6519	245	7	m.	m.	NOUN
ejpam-6519	245	8	sultan	sultan	PROPN
ejpam-6519	245	9	,	,	PUNCT
ejpam-6519	245	10	and	and	CCONJ
ejpam-6519	245	11	a.	a.	NOUN
ejpam-6519	245	12	hussain	hussain	PROPN
ejpam-6519	245	13	.	.	PUNCT
ejpam-6519	246	1	boundedness	boundedness	NOUN
ejpam-6519	246	2	of	of	ADP
ejpam-6519	246	3	the	the	DET
ejpam-6519	246	4	bochner	bochner	NOUN
ejpam-6519	246	5	–	–	PUNCT
ejpam-6519	246	6	riesz	riesz	NOUN
ejpam-6519	246	7	operators	operator	NOUN
ejpam-6519	246	8	on	on	ADP
ejpam-6519	246	9	the	the	DET
ejpam-6519	246	10	weighted	weight	VERB
ejpam-6519	246	11	herz	herz	PROPN
ejpam-6519	246	12	–	–	PUNCT
ejpam-6519	246	13	morrey	morrey	PROPN
ejpam-6519	246	14	type	type	NOUN
ejpam-6519	246	15	hardy	hardy	ADJ
ejpam-6519	246	16	spaces	space	NOUN
ejpam-6519	246	17	.	.	PUNCT
ejpam-6519	247	1	complex	complex	ADJ
ejpam-6519	247	2	analysis	analysis	NOUN
ejpam-6519	247	3	and	and	CCONJ
ejpam-6519	247	4	operator	operator	NOUN
ejpam-6519	247	5	theory	theory	NOUN
ejpam-6519	247	6	,	,	PUNCT
ejpam-6519	247	7	19:49	19:49	NUM
ejpam-6519	247	8	,	,	PUNCT
ejpam-6519	247	9	2025	2025	NUM
ejpam-6519	247	10	.	.	PUNCT
ejpam-6519	248	1	[	[	X
ejpam-6519	248	2	24	24	NUM
ejpam-6519	248	3	]	]	PUNCT
ejpam-6519	248	4	a.	a.	NOUN
ejpam-6519	248	5	hussain	hussain	PROPN
ejpam-6519	248	6	and	and	CCONJ
ejpam-6519	248	7	g.	g.	PROPN
ejpam-6519	248	8	gao	gao	PROPN
ejpam-6519	248	9	.	.	PUNCT
ejpam-6519	249	1	some	some	DET
ejpam-6519	249	2	new	new	ADJ
ejpam-6519	249	3	estimates	estimate	NOUN
ejpam-6519	249	4	for	for	ADP
ejpam-6519	249	5	the	the	DET
ejpam-6519	249	6	commutators	commutator	NOUN
ejpam-6519	249	7	of	of	ADP
ejpam-6519	249	8	n	n	CCONJ
ejpam-6519	249	9	-	-	PUNCT
ejpam-6519	249	10	dimensional	dimensional	ADJ
ejpam-6519	249	11	hausdorff	hausdorff	NOUN
ejpam-6519	249	12	operator	operator	NOUN
ejpam-6519	249	13	.	.	PUNCT
ejpam-6519	250	1	applied	apply	VERB
ejpam-6519	250	2	mathematics	mathematic	NOUN
ejpam-6519	250	3	.	.	PUNCT
ejpam-6519	251	1	a	a	DET
ejpam-6519	251	2	journal	journal	NOUN
ejpam-6519	251	3	of	of	ADP
ejpam-6519	251	4	chinese	chinese	ADJ
ejpam-6519	251	5	universities	university	NOUN
ejpam-6519	251	6	,	,	PUNCT
ejpam-6519	251	7	29(2):139–150	29(2):139–150	PROPN
ejpam-6519	251	8	,	,	PUNCT
ejpam-6519	251	9	2014	2014	NUM
ejpam-6519	251	10	.	.	PUNCT
ejpam-6519	252	1	[	[	X
ejpam-6519	252	2	25	25	NUM
ejpam-6519	252	3	]	]	PUNCT
ejpam-6519	252	4	a.	a.	NOUN
ejpam-6519	252	5	hussain	hussain	PROPN
ejpam-6519	252	6	and	and	CCONJ
ejpam-6519	252	7	g.	g.	PROPN
ejpam-6519	252	8	gao	gao	PROPN
ejpam-6519	252	9	.	.	PUNCT
ejpam-6519	253	1	multidimensional	multidimensional	ADJ
ejpam-6519	253	2	hausdorff	hausdorff	NOUN
ejpam-6519	253	3	operators	operator	NOUN
ejpam-6519	253	4	and	and	CCONJ
ejpam-6519	253	5	commutators	commutator	NOUN
ejpam-6519	253	6	on	on	ADP
ejpam-6519	253	7	herz	herz	ADJ
ejpam-6519	253	8	-	-	PUNCT
ejpam-6519	253	9	type	type	NOUN
ejpam-6519	253	10	spaces	space	NOUN
ejpam-6519	253	11	.	.	PUNCT
ejpam-6519	254	1	journal	journal	PROPN
ejpam-6519	254	2	of	of	ADP
ejpam-6519	254	3	inequalities	inequality	NOUN
ejpam-6519	254	4	and	and	CCONJ
ejpam-6519	254	5	applications	application	NOUN
ejpam-6519	254	6	,	,	PUNCT
ejpam-6519	254	7	page	page	NOUN
ejpam-6519	254	8	594	594	NUM
ejpam-6519	254	9	,	,	PUNCT
ejpam-6519	254	10	2013	2013	NUM
ejpam-6519	254	11	.	.	PUNCT
ejpam-6519	255	1	[	[	X
ejpam-6519	255	2	26	26	NUM
ejpam-6519	255	3	]	]	X
ejpam-6519	255	4	c.	c.	PROPN
ejpam-6519	255	5	heil	heil	PROPN
ejpam-6519	255	6	.	.	PUNCT
ejpam-6519	256	1	wiener	wiener	NOUN
ejpam-6519	256	2	amalgam	amalgam	NOUN
ejpam-6519	256	3	spaces	space	NOUN
ejpam-6519	256	4	in	in	ADP
ejpam-6519	256	5	generalized	generalized	ADJ
ejpam-6519	256	6	harmonic	harmonic	ADJ
ejpam-6519	256	7	analysis	analysis	NOUN
ejpam-6519	256	8	and	and	CCONJ
ejpam-6519	256	9	wavelet	wavelet	NOUN
ejpam-6519	256	10	theory	theory	NOUN
ejpam-6519	256	11	.	.	PUNCT
ejpam-6519	257	1	phd	phd	NOUN
ejpam-6519	257	2	thesis	thesis	PROPN
ejpam-6519	257	3	,	,	PUNCT
ejpam-6519	257	4	university	university	NOUN
ejpam-6519	257	5	of	of	ADP
ejpam-6519	257	6	maryland	maryland	PROPN
ejpam-6519	257	7	,	,	PUNCT
ejpam-6519	257	8	college	college	NOUN
ejpam-6519	257	9	park	park	NOUN
ejpam-6519	257	10	,	,	PUNCT
ejpam-6519	257	11	md	md	PROPN
ejpam-6519	257	12	,	,	PUNCT
ejpam-6519	257	13	1990	1990	NUM
ejpam-6519	257	14	.	.	PUNCT
ejpam-6519	258	1	[	[	X
ejpam-6519	258	2	27	27	NUM
ejpam-6519	258	3	]	]	X
ejpam-6519	258	4	y.	y.	PROPN
ejpam-6519	258	5	lu	lu	PROPN
ejpam-6519	258	6	,	,	PUNCT
ejpam-6519	258	7	j.	j.	PROPN
ejpam-6519	258	8	zhou	zhou	PROPN
ejpam-6519	258	9	,	,	PUNCT
ejpam-6519	258	10	and	and	CCONJ
ejpam-6519	258	11	s.	s.	PROPN
ejpam-6519	258	12	wang	wang	PROPN
ejpam-6519	258	13	.	.	PUNCT
ejpam-6519	258	14	herz	herz	ADJ
ejpam-6519	258	15	-	-	PUNCT
ejpam-6519	258	16	slice	slice	NOUN
ejpam-6519	258	17	spaces	space	NOUN
ejpam-6519	258	18	and	and	CCONJ
ejpam-6519	258	19	applications	application	NOUN
ejpam-6519	258	20	,	,	PUNCT
ejpam-6519	258	21	2022	2022	NUM
ejpam-6519	258	22	.	.	PUNCT
ejpam-6519	259	1	arxiv:2204.08635	arxiv:2204.08635	NOUN
ejpam-6519	259	2	.	.	PUNCT
ejpam-6519	260	1	introduction	introduction	NOUN
ejpam-6519	260	2	preliminaries	preliminary	NOUN
ejpam-6519	260	3	atomic	atomic	ADJ
ejpam-6519	260	4	decomposition	decomposition	NOUN
ejpam-6519	260	5	of	of	ADP
ejpam-6519	260	6	anisotropic	anisotropic	NOUN
ejpam-6519	260	7	herz	herz	ADJ
ejpam-6519	260	8	-	-	PUNCT
ejpam-6519	260	9	slice	slice	NOUN
ejpam-6519	260	10	spaces	space	NOUN
ejpam-6519	260	11	boundedness	boundedness	NOUN
ejpam-6519	260	12	of	of	ADP
ejpam-6519	260	13	sublinear	sublinear	NOUN
ejpam-6519	260	14	operators	operator	NOUN
ejpam-6519	260	15	on	on	ADP
ejpam-6519	260	16	anisotropic	anisotropic	NOUN
ejpam-6519	260	17	herz	herz	ADJ
ejpam-6519	260	18	-	-	PUNCT
ejpam-6519	260	19	slice	slice	NOUN
ejpam-6519	260	20	spaces	space	NOUN
ejpam-6519	260	21	ethics	ethic	NOUN
ejpam-6519	260	22	declarations	declaration	NOUN