id	sid	tid	token	lemma	pos
ejpam-6641	1	1	european	european	PROPN
ejpam-6641	1	2	journal	journal	PROPN
ejpam-6641	1	3	of	of	ADP
ejpam-6641	1	4	pure	pure	ADJ
ejpam-6641	1	5	and	and	CCONJ
ejpam-6641	1	6	applied	applied	ADJ
ejpam-6641	1	7	mathematics	mathematic	NOUN
ejpam-6641	1	8	2025	2025	NUM
ejpam-6641	1	9	,	,	PUNCT
ejpam-6641	1	10	vol	vol	NOUN
ejpam-6641	1	11	.	.	PROPN
ejpam-6641	1	12	18	18	NUM
ejpam-6641	1	13	,	,	PUNCT
ejpam-6641	1	14	issue	issue	NOUN
ejpam-6641	1	15	4	4	NUM
ejpam-6641	1	16	,	,	PUNCT
ejpam-6641	1	17	article	article	NOUN
ejpam-6641	1	18	number	number	NOUN
ejpam-6641	1	19	6641	6641	NUM
ejpam-6641	1	20	issn	issn	VERB
ejpam-6641	1	21	1307	1307	NUM
ejpam-6641	1	22	-	-	SYM
ejpam-6641	1	23	5543	5543	NUM
ejpam-6641	1	24	–	–	PUNCT
ejpam-6641	1	25	ejpam.com	ejpam.com	X
ejpam-6641	1	26	published	publish	VERB
ejpam-6641	1	27	by	by	ADP
ejpam-6641	1	28	new	new	PROPN
ejpam-6641	1	29	york	york	PROPN
ejpam-6641	1	30	business	business	PROPN
ejpam-6641	1	31	global	global	PROPN
ejpam-6641	1	32	on	on	ADP
ejpam-6641	1	33	the	the	DET
ejpam-6641	1	34	boundedness	boundedness	NOUN
ejpam-6641	1	35	of	of	ADP
ejpam-6641	1	36	the	the	DET
ejpam-6641	1	37	intrinsic	intrinsic	ADJ
ejpam-6641	1	38	square	square	ADJ
ejpam-6641	1	39	function	function	NOUN
ejpam-6641	1	40	on	on	ADP
ejpam-6641	1	41	continual	continual	ADJ
ejpam-6641	1	42	herz	herz	PROPN
ejpam-6641	1	43	spaces	space	NOUN
ejpam-6641	1	44	with	with	ADP
ejpam-6641	1	45	variable	variable	ADJ
ejpam-6641	1	46	exponents	exponent	NOUN
ejpam-6641	1	47	ghada	ghada	PROPN
ejpam-6641	1	48	ali	ali	PROPN
ejpam-6641	1	49	basendwah1	basendwah1	PROPN
ejpam-6641	1	50	,	,	PUNCT
ejpam-6641	1	51	mehvish	mehvish	PROPN
ejpam-6641	1	52	sultan2	sultan2	NOUN
ejpam-6641	1	53	,	,	PUNCT
ejpam-6641	1	54	babar	babar	PROPN
ejpam-6641	1	55	sultan3,∗	sultan3,∗	PROPN
ejpam-6641	1	56	,	,	PUNCT
ejpam-6641	1	57	ioan	ioan	NOUN
ejpam-6641	1	58	-	-	PUNCT
ejpam-6641	1	59	lucian	lucian	ADJ
ejpam-6641	1	60	popa4,5,∗	popa4,5,∗	NOUN
ejpam-6641	1	61	1	1	NUM
ejpam-6641	1	62	department	department	NOUN
ejpam-6641	1	63	of	of	ADP
ejpam-6641	1	64	mathematics	mathematic	NOUN
ejpam-6641	1	65	,	,	PUNCT
ejpam-6641	1	66	king	king	PROPN
ejpam-6641	1	67	abdulaziz	abdulaziz	PROPN
ejpam-6641	1	68	university	university	PROPN
ejpam-6641	1	69	,	,	PUNCT
ejpam-6641	1	70	jeddah	jeddah	PROPN
ejpam-6641	1	71	21589	21589	NUM
ejpam-6641	1	72	,	,	PUNCT
ejpam-6641	1	73	saudi	saudi	PROPN
ejpam-6641	1	74	arabia	arabia	PROPN
ejpam-6641	1	75	2	2	NUM
ejpam-6641	1	76	department	department	NOUN
ejpam-6641	1	77	of	of	ADP
ejpam-6641	1	78	mathematics	mathematic	NOUN
ejpam-6641	1	79	,	,	PUNCT
ejpam-6641	1	80	capital	capital	NOUN
ejpam-6641	1	81	university	university	PROPN
ejpam-6641	1	82	of	of	ADP
ejpam-6641	1	83	science	science	NOUN
ejpam-6641	1	84	and	and	CCONJ
ejpam-6641	1	85	technology	technology	NOUN
ejpam-6641	1	86	,	,	PUNCT
ejpam-6641	1	87	islamabad	islamabad	PROPN
ejpam-6641	1	88	,	,	PUNCT
ejpam-6641	1	89	pakistan	pakistan	PROPN
ejpam-6641	1	90	3	3	NUM
ejpam-6641	1	91	department	department	NOUN
ejpam-6641	1	92	of	of	ADP
ejpam-6641	1	93	mathematics	mathematic	NOUN
ejpam-6641	1	94	,	,	PUNCT
ejpam-6641	1	95	quaid	quaid	PROPN
ejpam-6641	1	96	-	-	PUNCT
ejpam-6641	1	97	i	i	PROPN
ejpam-6641	1	98	-	-	PUNCT
ejpam-6641	1	99	azam	azam	PROPN
ejpam-6641	1	100	university	university	PROPN
ejpam-6641	1	101	,	,	PUNCT
ejpam-6641	1	102	islamabad	islamabad	PROPN
ejpam-6641	1	103	45320	45320	NUM
ejpam-6641	1	104	,	,	PUNCT
ejpam-6641	1	105	pakistan	pakistan	PROPN
ejpam-6641	1	106	4	4	NUM
ejpam-6641	1	107	department	department	NOUN
ejpam-6641	1	108	of	of	ADP
ejpam-6641	1	109	computing	computing	NOUN
ejpam-6641	1	110	,	,	PUNCT
ejpam-6641	1	111	mathematics	mathematic	NOUN
ejpam-6641	1	112	and	and	CCONJ
ejpam-6641	1	113	electronics	electronic	NOUN
ejpam-6641	1	114	,	,	PUNCT
ejpam-6641	1	115	“	"	PUNCT
ejpam-6641	1	116	1	1	NUM
ejpam-6641	1	117	decembrie	decembrie	NOUN
ejpam-6641	1	118	1918	1918	NUM
ejpam-6641	1	119	”	"	PUNCT
ejpam-6641	1	120	university	university	PROPN
ejpam-6641	1	121	of	of	ADP
ejpam-6641	1	122	alba	alba	PROPN
ejpam-6641	1	123	iulia	iulia	PROPN
ejpam-6641	1	124	,	,	PUNCT
ejpam-6641	1	125	510009	510009	NUM
ejpam-6641	1	126	alba	alba	NOUN
ejpam-6641	1	127	iulia	iulia	PROPN
ejpam-6641	1	128	,	,	PUNCT
ejpam-6641	1	129	romania	romania	PROPN
ejpam-6641	1	130	5	5	NUM
ejpam-6641	1	131	faculty	faculty	NOUN
ejpam-6641	1	132	of	of	ADP
ejpam-6641	1	133	mathematics	mathematic	NOUN
ejpam-6641	1	134	and	and	CCONJ
ejpam-6641	1	135	computer	computer	NOUN
ejpam-6641	1	136	science	science	NOUN
ejpam-6641	1	137	,	,	PUNCT
ejpam-6641	1	138	transilvania	transilvania	PROPN
ejpam-6641	1	139	university	university	PROPN
ejpam-6641	1	140	of	of	ADP
ejpam-6641	1	141	brasov	brasov	NOUN
ejpam-6641	1	142	,	,	PUNCT
ejpam-6641	1	143	iuliu	iuliu	PROPN
ejpam-6641	1	144	maniu	maniu	PROPN
ejpam-6641	1	145	street	street	PROPN
ejpam-6641	1	146	50	50	NUM
ejpam-6641	1	147	,	,	PUNCT
ejpam-6641	1	148	500091	500091	NUM
ejpam-6641	1	149	brasov	brasov	NOUN
ejpam-6641	1	150	,	,	PUNCT
ejpam-6641	1	151	romania	romania	PROPN
ejpam-6641	1	152	abstract	abstract	NOUN
ejpam-6641	1	153	.	.	PUNCT
ejpam-6641	2	1	our	our	PRON
ejpam-6641	2	2	aim	aim	NOUN
ejpam-6641	2	3	in	in	ADP
ejpam-6641	2	4	this	this	DET
ejpam-6641	2	5	paper	paper	NOUN
ejpam-6641	2	6	is	be	AUX
ejpam-6641	2	7	to	to	PART
ejpam-6641	2	8	prove	prove	VERB
ejpam-6641	2	9	the	the	DET
ejpam-6641	2	10	boundedness	boundedness	NOUN
ejpam-6641	2	11	of	of	ADP
ejpam-6641	2	12	the	the	DET
ejpam-6641	2	13	intrinsic	intrinsic	ADJ
ejpam-6641	2	14	square	square	ADJ
ejpam-6641	2	15	function	function	NOUN
ejpam-6641	2	16	on	on	ADP
ejpam-6641	2	17	herz	herz	PROPN
ejpam-6641	2	18	spaces	space	NOUN
ejpam-6641	2	19	with	with	ADP
ejpam-6641	2	20	variable	variable	ADJ
ejpam-6641	2	21	exponents	exponent	NOUN
ejpam-6641	2	22	.	.	PUNCT
ejpam-6641	3	1	firstly	firstly	ADV
ejpam-6641	3	2	we	we	PRON
ejpam-6641	3	3	define	define	VERB
ejpam-6641	3	4	the	the	DET
ejpam-6641	3	5	lebesgue	lebesgue	NOUN
ejpam-6641	3	6	spaces	space	NOUN
ejpam-6641	3	7	with	with	ADP
ejpam-6641	3	8	variable	variable	ADJ
ejpam-6641	3	9	exponent	exponent	NOUN
ejpam-6641	3	10	,	,	PUNCT
ejpam-6641	3	11	herz	herz	PROPN
ejpam-6641	3	12	spaces	space	VERB
ejpam-6641	3	13	with	with	ADP
ejpam-6641	3	14	variable	variable	ADJ
ejpam-6641	3	15	exponents	exponent	NOUN
ejpam-6641	3	16	and	and	CCONJ
ejpam-6641	3	17	some	some	DET
ejpam-6641	3	18	basic	basic	ADJ
ejpam-6641	3	19	notations	notation	NOUN
ejpam-6641	3	20	.	.	PUNCT
ejpam-6641	4	1	then	then	ADV
ejpam-6641	4	2	we	we	PRON
ejpam-6641	4	3	give	give	VERB
ejpam-6641	4	4	some	some	DET
ejpam-6641	4	5	basic	basic	ADJ
ejpam-6641	4	6	lemmas	lemma	NOUN
ejpam-6641	4	7	and	and	CCONJ
ejpam-6641	4	8	definition	definition	NOUN
ejpam-6641	4	9	of	of	ADP
ejpam-6641	4	10	continual	continual	ADJ
ejpam-6641	4	11	herz	herz	PROPN
ejpam-6641	4	12	spaces	space	NOUN
ejpam-6641	4	13	.	.	PUNCT
ejpam-6641	5	1	finally	finally	ADV
ejpam-6641	5	2	we	we	PRON
ejpam-6641	5	3	obtain	obtain	VERB
ejpam-6641	5	4	the	the	DET
ejpam-6641	5	5	boundedness	boundedness	NOUN
ejpam-6641	5	6	of	of	ADP
ejpam-6641	5	7	the	the	DET
ejpam-6641	5	8	intrinsic	intrinsic	ADJ
ejpam-6641	5	9	square	square	ADJ
ejpam-6641	5	10	function	function	NOUN
ejpam-6641	5	11	on	on	ADP
ejpam-6641	5	12	continual	continual	ADJ
ejpam-6641	5	13	herz	herz	PROPN
ejpam-6641	5	14	spaces	space	NOUN
ejpam-6641	5	15	under	under	ADP
ejpam-6641	5	16	some	some	DET
ejpam-6641	5	17	proper	proper	ADJ
ejpam-6641	5	18	assumptions	assumption	NOUN
ejpam-6641	5	19	.	.	PUNCT
ejpam-6641	6	1	2020	2020	NUM
ejpam-6641	6	2	mathematics	mathematic	NOUN
ejpam-6641	6	3	subject	subject	NOUN
ejpam-6641	6	4	classifications	classification	NOUN
ejpam-6641	6	5	:	:	PUNCT
ejpam-6641	6	6	46e30	46e30	NUM
ejpam-6641	6	7	,	,	PUNCT
ejpam-6641	6	8	47b38	47b38	NUM
ejpam-6641	6	9	key	key	ADJ
ejpam-6641	6	10	words	word	NOUN
ejpam-6641	6	11	and	and	CCONJ
ejpam-6641	6	12	phrases	phrase	NOUN
ejpam-6641	6	13	:	:	PUNCT
ejpam-6641	6	14	intrinsic	intrinsic	ADJ
ejpam-6641	6	15	square	square	ADJ
ejpam-6641	6	16	function	function	NOUN
ejpam-6641	6	17	,	,	PUNCT
ejpam-6641	6	18	continual	continual	ADJ
ejpam-6641	6	19	herz	herz	PROPN
ejpam-6641	6	20	spaces	space	VERB
ejpam-6641	6	21	1	1	X
ejpam-6641	6	22	.	.	PUNCT
ejpam-6641	7	1	introduction	introduction	NOUN
ejpam-6641	7	2	consider	consider	VERB
ejpam-6641	7	3	an	an	DET
ejpam-6641	7	4	open	open	ADJ
ejpam-6641	7	5	set	set	ADJ
ejpam-6641	7	6	h	h	NOUN
ejpam-6641	7	7	of	of	ADP
ejpam-6641	7	8	rn	rn	PROPN
ejpam-6641	7	9	and	and	CCONJ
ejpam-6641	7	10	a	a	DET
ejpam-6641	7	11	measurable	measurable	ADJ
ejpam-6641	7	12	function	function	NOUN
ejpam-6641	7	13	q	q	X
ejpam-6641	7	14	(	(	PUNCT
ejpam-6641	7	15	·	·	PUNCT
ejpam-6641	7	16	)	)	PUNCT
ejpam-6641	7	17	:	:	PUNCT
ejpam-6641	7	18	h	h	X
ejpam-6641	7	19	→	→	PUNCT
ejpam-6641	7	20	[	[	X
ejpam-6641	7	21	1,∞	1,∞	NUM
ejpam-6641	7	22	)	)	PUNCT
ejpam-6641	7	23	.	.	PUNCT
ejpam-6641	8	1	assume	assume	VERB
ejpam-6641	8	2	that	that	SCONJ
ejpam-6641	8	3	the	the	DET
ejpam-6641	8	4	following	follow	VERB
ejpam-6641	8	5	condition	condition	NOUN
ejpam-6641	8	6	holds	hold	VERB
ejpam-6641	8	7	,	,	PUNCT
ejpam-6641	8	8	1	1	NUM
ejpam-6641	8	9	≤	≤	NUM
ejpam-6641	8	10	q−(h	q−(h	NOUN
ejpam-6641	8	11	)	)	PUNCT
ejpam-6641	8	12	≤	≤	NUM
ejpam-6641	8	13	q+(h	q+(h	NOUN
ejpam-6641	8	14	)	)	PUNCT
ejpam-6641	8	15	<	<	X
ejpam-6641	8	16	∞	∞	PROPN
ejpam-6641	8	17	,	,	PUNCT
ejpam-6641	8	18	(	(	PUNCT
ejpam-6641	8	19	1.1	1.1	NUM
ejpam-6641	8	20	)	)	PUNCT
ejpam-6641	8	21	where	where	SCONJ
ejpam-6641	8	22	i	i	PRON
ejpam-6641	8	23	)	)	PUNCT
ejpam-6641	8	24	q−	q−	PROPN
ejpam-6641	8	25	:	:	PUNCT
ejpam-6641	8	26	=	=	PUNCT
ejpam-6641	8	27	essinf	essinf	PROPN
ejpam-6641	8	28	h∈h	h∈h	NOUN
ejpam-6641	8	29	q(h	q(h	PROPN
ejpam-6641	8	30	)	)	PUNCT
ejpam-6641	8	31	∗corresponding	∗corresponde	VERB
ejpam-6641	8	32	author	author	NOUN
ejpam-6641	8	33	.	.	PUNCT
ejpam-6641	9	1	∗corresponding	∗corresponde	VERB
ejpam-6641	9	2	author	author	NOUN
ejpam-6641	9	3	.	.	PUNCT
ejpam-6641	10	1	doi	doi	NOUN
ejpam-6641	10	2	:	:	PUNCT
ejpam-6641	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6641	https://doi.org/10.29020/nybg.ejpam.v18i4.6641	X
ejpam-6641	10	4	email	email	NOUN
ejpam-6641	10	5	addresses	address	NOUN
ejpam-6641	10	6	:	:	PUNCT
ejpam-6641	10	7	gbasendwah@kau.edu.sa	gbasendwah@kau.edu.sa	PROPN
ejpam-6641	10	8	(	(	PUNCT
ejpam-6641	10	9	g.	g.	PROPN
ejpam-6641	10	10	a.	a.	PROPN
ejpam-6641	10	11	basendwah	basendwah	PROPN
ejpam-6641	10	12	)	)	PUNCT
ejpam-6641	10	13	,	,	PUNCT
ejpam-6641	10	14	mehvishsultanbaz@gmail.com	mehvishsultanbaz@gmail.com	X
ejpam-6641	10	15	(	(	PUNCT
ejpam-6641	10	16	m.	m.	NOUN
ejpam-6641	10	17	sultan	sultan	PROPN
ejpam-6641	10	18	)	)	PUNCT
ejpam-6641	10	19	,	,	PUNCT
ejpam-6641	10	20	babarsultan40@yahoo.com	babarsultan40@yahoo.com	X
ejpam-6641	10	21	(	(	PUNCT
ejpam-6641	10	22	b.	b.	PROPN
ejpam-6641	10	23	sultan	sultan	PROPN
ejpam-6641	10	24	)	)	PUNCT
ejpam-6641	10	25	,	,	PUNCT
ejpam-6641	10	26	lucian.popa@uab.ro	lucian.popa@uab.ro	NOUN
ejpam-6641	10	27	(	(	PUNCT
ejpam-6641	10	28	i.-l	i.-l	NOUN
ejpam-6641	10	29	.	.	PUNCT
ejpam-6641	11	1	popa	popa	ADJ
ejpam-6641	11	2	)	)	PUNCT
ejpam-6641	11	3	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6641	12	1	1	1	NUM
ejpam-6641	12	2	copyright	copyright	NOUN
ejpam-6641	12	3	:	:	PUNCT
ejpam-6641	12	4	©	©	PROPN
ejpam-6641	12	5	2025	2025	NUM
ejpam-6641	12	6	the	the	DET
ejpam-6641	12	7	author(s	author(s	NOUN
ejpam-6641	12	8	)	)	PUNCT
ejpam-6641	12	9	.	.	PUNCT
ejpam-6641	13	1	(	(	PUNCT
ejpam-6641	13	2	cc	cc	NOUN
ejpam-6641	13	3	by	by	ADP
ejpam-6641	13	4	-	-	PUNCT
ejpam-6641	13	5	nc	nc	PROPN
ejpam-6641	13	6	4.0	4.0	NUM
ejpam-6641	13	7	)	)	PUNCT
ejpam-6641	13	8	g.	g.	PROPN
ejpam-6641	13	9	a.	a.	PROPN
ejpam-6641	13	10	basendwah	basendwah	PROPN
ejpam-6641	13	11	et	et	PROPN
ejpam-6641	13	12	al	al	PROPN
ejpam-6641	13	13	.	.	PUNCT
ejpam-6641	13	14	/	/	SYM
ejpam-6641	13	15	eur	eur	PROPN
ejpam-6641	13	16	.	.	PUNCT
ejpam-6641	14	1	j.	j.	PROPN
ejpam-6641	14	2	pure	pure	PROPN
ejpam-6641	14	3	appl	appl	PROPN
ejpam-6641	14	4	.	.	PROPN
ejpam-6641	14	5	math	math	PROPN
ejpam-6641	14	6	,	,	PUNCT
ejpam-6641	14	7	18	18	NUM
ejpam-6641	14	8	(	(	PUNCT
ejpam-6641	14	9	4	4	NUM
ejpam-6641	14	10	)	)	PUNCT
ejpam-6641	14	11	(	(	PUNCT
ejpam-6641	14	12	2025	2025	NUM
ejpam-6641	14	13	)	)	PUNCT
ejpam-6641	14	14	,	,	PUNCT
ejpam-6641	14	15	6641	6641	NUM
ejpam-6641	14	16	2	2	NUM
ejpam-6641	14	17	of	of	ADP
ejpam-6641	14	18	16	16	NUM
ejpam-6641	14	19	ii	ii	NOUN
ejpam-6641	14	20	)	)	PUNCT
ejpam-6641	14	21	q+	q+	ADP
ejpam-6641	14	22	:	:	PUNCT
ejpam-6641	14	23	=	=	SYM
ejpam-6641	14	24	esssup	esssup	NOUN
ejpam-6641	14	25	h∈h	h∈h	NOUN
ejpam-6641	14	26	q(h	q(h	PROPN
ejpam-6641	14	27	)	)	PUNCT
ejpam-6641	14	28	.	.	PUNCT
ejpam-6641	15	1	let	let	VERB
ejpam-6641	15	2	q′(h	q′(h	PUNCT
ejpam-6641	15	3	)	)	PUNCT
ejpam-6641	15	4	=	=	SYM
ejpam-6641	15	5	q(h	q(h	PROPN
ejpam-6641	15	6	)	)	PUNCT
ejpam-6641	15	7	q(h)−1	q(h)−1	PROPN
ejpam-6641	15	8	denotes	denote	VERB
ejpam-6641	15	9	the	the	DET
ejpam-6641	15	10	conjugate	conjugate	ADJ
ejpam-6641	15	11	exponent	exponent	NOUN
ejpam-6641	15	12	of	of	ADP
ejpam-6641	15	13	q(h	q(h	PROPN
ejpam-6641	15	14	)	)	PUNCT
ejpam-6641	15	15	.	.	PUNCT
ejpam-6641	16	1	we	we	PRON
ejpam-6641	16	2	denote	denote	VERB
ejpam-6641	16	3	by	by	ADP
ejpam-6641	16	4	p(rn	p(rn	PROPN
ejpam-6641	16	5	)	)	PUNCT
ejpam-6641	16	6	the	the	DET
ejpam-6641	16	7	set	set	NOUN
ejpam-6641	16	8	of	of	ADP
ejpam-6641	16	9	all	all	DET
ejpam-6641	16	10	measurable	measurable	ADJ
ejpam-6641	16	11	function	function	NOUN
ejpam-6641	16	12	satisfying	satisfy	VERB
ejpam-6641	16	13	(	(	PUNCT
ejpam-6641	16	14	1.1	1.1	NUM
ejpam-6641	16	15	)	)	PUNCT
ejpam-6641	16	16	.	.	PUNCT
ejpam-6641	17	1	for	for	ADP
ejpam-6641	17	2	measurable	measurable	ADJ
ejpam-6641	17	3	function	function	NOUN
ejpam-6641	17	4	f	f	PROPN
ejpam-6641	17	5	,	,	PUNCT
ejpam-6641	17	6	lebesgue	lebesgue	PROPN
ejpam-6641	17	7	space	space	PROPN
ejpam-6641	17	8	lq(·)(h	lq(·)(h	PROPN
ejpam-6641	17	9	)	)	PUNCT
ejpam-6641	17	10	is	be	AUX
ejpam-6641	17	11	given	give	VERB
ejpam-6641	17	12	by	by	ADP
ejpam-6641	17	13	lq(·)(f	lq(·)(f	NOUN
ejpam-6641	17	14	)	)	PUNCT
ejpam-6641	18	1	=	=	SYM
ejpam-6641	19	1	∫	∫	PROPN
ejpam-6641	19	2	g	g	PROPN
ejpam-6641	19	3	|f(h|q(h)dh	|f(h|q(h)dh	PROPN
ejpam-6641	19	4	<	<	X
ejpam-6641	19	5	∞	∞	PROPN
ejpam-6641	19	6	,	,	PUNCT
ejpam-6641	19	7	with	with	ADP
ejpam-6641	19	8	the	the	DET
ejpam-6641	19	9	norm	norm	NOUN
ejpam-6641	19	10	defined	define	VERB
ejpam-6641	19	11	by	by	ADP
ejpam-6641	19	12	,	,	PUNCT
ejpam-6641	19	13	∥f∥lp(·)(h	∥f∥lp(·)(h	NOUN
ejpam-6641	19	14	)	)	PUNCT
ejpam-6641	19	15	=	=	SYM
ejpam-6641	19	16	inf	inf	PROPN
ejpam-6641	19	17	{	{	PUNCT
ejpam-6641	19	18	η	η	PROPN
ejpam-6641	19	19	>	>	X
ejpam-6641	19	20	0	0	NUM
ejpam-6641	19	21	:	:	PUNCT
ejpam-6641	19	22	lq	lq	X
ejpam-6641	19	23	(	(	PUNCT
ejpam-6641	19	24	·	·	PUNCT
ejpam-6641	19	25	)	)	PUNCT
ejpam-6641	19	26	(	(	PUNCT
ejpam-6641	19	27	f	f	PROPN
ejpam-6641	19	28	η	η	PROPN
ejpam-6641	19	29	)	)	PUNCT
ejpam-6641	19	30	≤	≤	NUM
ejpam-6641	19	31	1	1	NUM
ejpam-6641	19	32	}	}	PUNCT
ejpam-6641	19	33	.	.	PUNCT
ejpam-6641	20	1	note	note	VERB
ejpam-6641	20	2	that	that	SCONJ
ejpam-6641	20	3	lp(·)(h	lp(·)(h	NOUN
ejpam-6641	20	4	)	)	PUNCT
ejpam-6641	20	5	is	be	AUX
ejpam-6641	20	6	the	the	DET
ejpam-6641	20	7	banach	banach	NOUN
ejpam-6641	20	8	function	function	NOUN
ejpam-6641	20	9	space	space	NOUN
ejpam-6641	20	10	.	.	PUNCT
ejpam-6641	21	1	in	in	ADP
ejpam-6641	21	2	the	the	DET
ejpam-6641	21	3	last	last	ADJ
ejpam-6641	21	4	two	two	NUM
ejpam-6641	21	5	decades	decade	NOUN
ejpam-6641	21	6	it	it	PRON
ejpam-6641	21	7	was	be	AUX
ejpam-6641	21	8	evident	evident	ADJ
ejpam-6641	21	9	that	that	SCONJ
ejpam-6641	21	10	classical	classical	ADJ
ejpam-6641	21	11	function	function	NOUN
ejpam-6641	21	12	spaces	space	NOUN
ejpam-6641	21	13	are	be	AUX
ejpam-6641	21	14	no	no	ADV
ejpam-6641	21	15	longer	long	ADV
ejpam-6641	21	16	appropriate	appropriate	ADJ
ejpam-6641	21	17	for	for	ADP
ejpam-6641	21	18	studying	study	VERB
ejpam-6641	21	19	a	a	DET
ejpam-6641	21	20	number	number	NOUN
ejpam-6641	21	21	of	of	ADP
ejpam-6641	21	22	modern	modern	ADJ
ejpam-6641	21	23	problems	problem	NOUN
ejpam-6641	21	24	arising	arise	VERB
ejpam-6641	21	25	in	in	ADP
ejpam-6641	21	26	many	many	ADJ
ejpam-6641	21	27	mathematical	mathematical	ADJ
ejpam-6641	21	28	models	model	NOUN
ejpam-6641	21	29	of	of	ADP
ejpam-6641	21	30	applied	applied	ADJ
ejpam-6641	21	31	sciences	science	NOUN
ejpam-6641	21	32	.	.	PUNCT
ejpam-6641	22	1	it	it	PRON
ejpam-6641	22	2	thus	thus	ADV
ejpam-6641	22	3	became	become	VERB
ejpam-6641	22	4	necessary	necessary	ADJ
ejpam-6641	22	5	to	to	PART
ejpam-6641	22	6	introduce	introduce	VERB
ejpam-6641	22	7	and	and	CCONJ
ejpam-6641	22	8	study	study	VERB
ejpam-6641	22	9	new	new	ADJ
ejpam-6641	22	10	function	function	NOUN
ejpam-6641	22	11	spaces	space	NOUN
ejpam-6641	22	12	.	.	PUNCT
ejpam-6641	23	1	such	such	ADJ
ejpam-6641	23	2	spaces	space	NOUN
ejpam-6641	23	3	are	be	AUX
ejpam-6641	23	4	:	:	PUNCT
ejpam-6641	23	5	variable	variable	ADJ
ejpam-6641	23	6	exponent	exponent	NOUN
ejpam-6641	23	7	lebesgue	lebesgue	NOUN
ejpam-6641	23	8	and	and	CCONJ
ejpam-6641	23	9	sobolev	sobolev	NOUN
ejpam-6641	23	10	spaces	space	NOUN
ejpam-6641	23	11	,	,	PUNCT
ejpam-6641	23	12	grand	grand	ADJ
ejpam-6641	23	13	function	function	NOUN
ejpam-6641	23	14	spaces	space	NOUN
ejpam-6641	23	15	,	,	PUNCT
ejpam-6641	23	16	morrey	morrey	NOUN
ejpam-6641	23	17	-	-	PUNCT
ejpam-6641	23	18	type	type	NOUN
ejpam-6641	23	19	spaces	space	NOUN
ejpam-6641	23	20	,	,	PUNCT
ejpam-6641	23	21	amalgam	amalgam	NOUN
ejpam-6641	23	22	spaces	space	NOUN
ejpam-6641	23	23	,	,	PUNCT
ejpam-6641	23	24	herz	herz	PROPN
ejpam-6641	23	25	spaces	space	NOUN
ejpam-6641	23	26	,	,	PUNCT
ejpam-6641	23	27	their	their	PRON
ejpam-6641	23	28	hybrid	hybrid	ADJ
ejpam-6641	23	29	variants	variant	NOUN
ejpam-6641	23	30	,	,	PUNCT
ejpam-6641	23	31	etc	etc	X
ejpam-6641	23	32	(	(	PUNCT
ejpam-6641	23	33	see	see	VERB
ejpam-6641	23	34	e.g.	e.g.	ADV
ejpam-6641	23	35	,	,	PUNCT
ejpam-6641	23	36	the	the	DET
ejpam-6641	23	37	monographs	monograph	NOUN
ejpam-6641	24	1	[	[	X
ejpam-6641	24	2	1	1	NUM
ejpam-6641	24	3	]	]	PUNCT
ejpam-6641	24	4	,	,	PUNCT
ejpam-6641	25	1	[	[	X
ejpam-6641	25	2	2	2	NUM
ejpam-6641	25	3	]	]	PUNCT
ejpam-6641	25	4	,	,	PUNCT
ejpam-6641	25	5	[	[	X
ejpam-6641	25	6	3	3	NUM
ejpam-6641	25	7	]	]	PUNCT
ejpam-6641	25	8	,	,	PUNCT
ejpam-6641	25	9	[	[	X
ejpam-6641	25	10	28	28	NUM
ejpam-6641	25	11	]	]	PUNCT
ejpam-6641	25	12	and	and	CCONJ
ejpam-6641	25	13	references	reference	NOUN
ejpam-6641	25	14	therein	therein	ADV
ejpam-6641	25	15	dedicated	dedicate	VERB
ejpam-6641	25	16	to	to	ADP
ejpam-6641	25	17	new	new	ADJ
ejpam-6641	25	18	function	function	NOUN
ejpam-6641	25	19	spaces	space	NOUN
ejpam-6641	25	20	)	)	PUNCT
ejpam-6641	25	21	.	.	PUNCT
ejpam-6641	26	1	morrey	morrey	PROPN
ejpam-6641	26	2	spaces	space	NOUN
ejpam-6641	26	3	describe	describe	VERB
ejpam-6641	26	4	local	local	ADJ
ejpam-6641	26	5	regularity	regularity	NOUN
ejpam-6641	26	6	more	more	ADV
ejpam-6641	26	7	precisely	precisely	ADV
ejpam-6641	26	8	than	than	ADP
ejpam-6641	26	9	lebesgue	lebesgue	NOUN
ejpam-6641	26	10	spaces	space	NOUN
ejpam-6641	26	11	.	.	PUNCT
ejpam-6641	27	1	for	for	ADP
ejpam-6641	27	2	more	more	ADJ
ejpam-6641	27	3	results	result	NOUN
ejpam-6641	27	4	in	in	ADP
ejpam-6641	27	5	herz	herz	PROPN
ejpam-6641	27	6	spaces	space	NOUN
ejpam-6641	27	7	see	see	VERB
ejpam-6641	27	8	[	[	X
ejpam-6641	27	9	45–48	45–48	NUM
ejpam-6641	27	10	]	]	PUNCT
ejpam-6641	27	11	.	.	PUNCT
ejpam-6641	28	1	as	as	ADP
ejpam-6641	28	2	a	a	DET
ejpam-6641	28	3	result	result	NOUN
ejpam-6641	28	4	,	,	PUNCT
ejpam-6641	28	5	one	one	PRON
ejpam-6641	28	6	can	can	AUX
ejpam-6641	28	7	use	use	VERB
ejpam-6641	28	8	morrey	morrey	NOUN
ejpam-6641	28	9	spaces	space	NOUN
ejpam-6641	28	10	widely	widely	ADV
ejpam-6641	28	11	not	not	PART
ejpam-6641	28	12	only	only	ADV
ejpam-6641	28	13	in	in	ADP
ejpam-6641	28	14	harmonic	harmonic	ADJ
ejpam-6641	28	15	analysis	analysis	NOUN
ejpam-6641	28	16	but	but	CCONJ
ejpam-6641	28	17	also	also	ADV
ejpam-6641	28	18	in	in	ADP
ejpam-6641	28	19	the	the	DET
ejpam-6641	28	20	theory	theory	NOUN
ejpam-6641	28	21	of	of	ADP
ejpam-6641	28	22	pdes	pde	NOUN
ejpam-6641	28	23	.	.	PUNCT
ejpam-6641	29	1	we	we	PRON
ejpam-6641	29	2	refer	refer	VERB
ejpam-6641	29	3	to	to	ADP
ejpam-6641	29	4	the	the	DET
ejpam-6641	29	5	recent	recent	ADJ
ejpam-6641	29	6	monographs	monograph	NOUN
ejpam-6641	29	7	[	[	X
ejpam-6641	29	8	4	4	X
ejpam-6641	29	9	]	]	PUNCT
ejpam-6641	29	10	for	for	ADP
ejpam-6641	29	11	morrey	morrey	NOUN
ejpam-6641	29	12	-	-	PUNCT
ejpam-6641	29	13	type	type	NOUN
ejpam-6641	29	14	spaces	space	NOUN
ejpam-6641	29	15	and	and	CCONJ
ejpam-6641	29	16	applications	application	NOUN
ejpam-6641	29	17	.	.	PUNCT
ejpam-6641	30	1	for	for	ADP
ejpam-6641	30	2	more	more	ADJ
ejpam-6641	30	3	results	result	NOUN
ejpam-6641	30	4	on	on	ADP
ejpam-6641	30	5	variable	variable	ADJ
ejpam-6641	30	6	exponent	exponent	NOUN
ejpam-6641	30	7	function	function	NOUN
ejpam-6641	30	8	spaces	space	NOUN
ejpam-6641	30	9	see	see	VERB
ejpam-6641	30	10	[	[	X
ejpam-6641	30	11	5–9	5–9	NUM
ejpam-6641	30	12	,	,	PUNCT
ejpam-6641	30	13	39	39	NUM
ejpam-6641	30	14	,	,	PUNCT
ejpam-6641	30	15	40	40	NUM
ejpam-6641	30	16	]	]	PUNCT
ejpam-6641	30	17	.	.	PUNCT
ejpam-6641	31	1	herz	herz	PROPN
ejpam-6641	31	2	spaces	space	NOUN
ejpam-6641	31	3	are	be	AUX
ejpam-6641	31	4	indeed	indeed	ADV
ejpam-6641	31	5	important	important	ADJ
ejpam-6641	31	6	in	in	ADP
ejpam-6641	31	7	the	the	DET
ejpam-6641	31	8	field	field	NOUN
ejpam-6641	31	9	of	of	ADP
ejpam-6641	31	10	harmonic	harmonic	ADJ
ejpam-6641	31	11	analysis	analysis	NOUN
ejpam-6641	31	12	and	and	CCONJ
ejpam-6641	31	13	partial	partial	ADJ
ejpam-6641	31	14	differential	differential	NOUN
ejpam-6641	31	15	equations	equation	NOUN
ejpam-6641	31	16	,	,	PUNCT
ejpam-6641	31	17	particularly	particularly	ADV
ejpam-6641	31	18	as	as	ADP
ejpam-6641	31	19	substitutes	substitute	NOUN
ejpam-6641	31	20	for	for	ADP
ejpam-6641	31	21	hardy	hardy	ADJ
ejpam-6641	31	22	spaces	space	NOUN
ejpam-6641	31	23	in	in	ADP
ejpam-6641	31	24	certain	certain	ADJ
ejpam-6641	31	25	contexts	context	NOUN
ejpam-6641	31	26	.	.	PUNCT
ejpam-6641	32	1	this	this	DET
ejpam-6641	32	2	substitution	substitution	NOUN
ejpam-6641	32	3	is	be	AUX
ejpam-6641	32	4	particularly	particularly	ADV
ejpam-6641	32	5	useful	useful	ADJ
ejpam-6641	32	6	when	when	SCONJ
ejpam-6641	32	7	dealing	deal	VERB
ejpam-6641	32	8	with	with	ADP
ejpam-6641	32	9	non	non	ADJ
ejpam-6641	32	10	-	-	ADJ
ejpam-6641	32	11	translation	translation	ADJ
ejpam-6641	32	12	invariant	invariant	ADJ
ejpam-6641	32	13	singular	singular	ADJ
ejpam-6641	32	14	integral	integral	ADJ
ejpam-6641	32	15	operators	operator	NOUN
ejpam-6641	32	16	.	.	PUNCT
ejpam-6641	33	1	herz	herz	PROPN
ejpam-6641	33	2	spaces	space	NOUN
ejpam-6641	33	3	continue	continue	VERB
ejpam-6641	33	4	to	to	PART
ejpam-6641	33	5	play	play	VERB
ejpam-6641	33	6	a	a	DET
ejpam-6641	33	7	significant	significant	ADJ
ejpam-6641	33	8	role	role	NOUN
ejpam-6641	33	9	in	in	ADP
ejpam-6641	33	10	various	various	ADJ
ejpam-6641	33	11	mathematical	mathematical	ADJ
ejpam-6641	33	12	contexts	contexts	NOUN
ejpam-6641	33	13	,	,	PUNCT
ejpam-6641	33	14	including	include	VERB
ejpam-6641	33	15	the	the	DET
ejpam-6641	33	16	characterization	characterization	NOUN
ejpam-6641	33	17	of	of	ADP
ejpam-6641	33	18	multipliers	multiplier	NOUN
ejpam-6641	33	19	on	on	ADP
ejpam-6641	33	20	hardy	hardy	ADJ
ejpam-6641	33	21	spaces	space	NOUN
ejpam-6641	33	22	and	and	CCONJ
ejpam-6641	33	23	in	in	ADP
ejpam-6641	33	24	the	the	DET
ejpam-6641	33	25	regularity	regularity	NOUN
ejpam-6641	33	26	theory	theory	NOUN
ejpam-6641	33	27	for	for	ADP
ejpam-6641	33	28	elliptic	elliptic	ADJ
ejpam-6641	33	29	and	and	CCONJ
ejpam-6641	33	30	parabolic	parabolic	ADJ
ejpam-6641	33	31	equations	equation	NOUN
ejpam-6641	33	32	in	in	ADP
ejpam-6641	33	33	divergence	divergence	NOUN
ejpam-6641	33	34	form	form	NOUN
ejpam-6641	33	35	,	,	PUNCT
ejpam-6641	33	36	see	see	VERB
ejpam-6641	33	37	[	[	X
ejpam-6641	33	38	10	10	NUM
ejpam-6641	33	39	,	,	PUNCT
ejpam-6641	33	40	11	11	NUM
ejpam-6641	33	41	]	]	PUNCT
ejpam-6641	33	42	.	.	PUNCT
ejpam-6641	34	1	herz	herz	PROPN
ejpam-6641	34	2	space	space	NOUN
ejpam-6641	34	3	has	have	AUX
ejpam-6641	34	4	undergone	undergo	VERB
ejpam-6641	34	5	significant	significant	ADJ
ejpam-6641	34	6	advancements	advancement	NOUN
ejpam-6641	34	7	,	,	PUNCT
ejpam-6641	34	8	proving	prove	VERB
ejpam-6641	34	9	to	to	PART
ejpam-6641	34	10	be	be	AUX
ejpam-6641	34	11	highly	highly	ADV
ejpam-6641	34	12	valuable	valuable	ADJ
ejpam-6641	34	13	in	in	ADP
ejpam-6641	34	14	the	the	DET
ejpam-6641	34	15	field	field	NOUN
ejpam-6641	34	16	of	of	ADP
ejpam-6641	34	17	harmonic	harmonic	ADJ
ejpam-6641	34	18	analysis	analysis	NOUN
ejpam-6641	34	19	.	.	PUNCT
ejpam-6641	35	1	for	for	ADP
ejpam-6641	35	2	more	more	ADJ
ejpam-6641	35	3	results	result	NOUN
ejpam-6641	35	4	in	in	ADP
ejpam-6641	35	5	variable	variable	ADJ
ejpam-6641	35	6	exponent	exponent	NOUN
ejpam-6641	35	7	function	function	NOUN
ejpam-6641	35	8	spaces	space	NOUN
ejpam-6641	35	9	see	see	VERB
ejpam-6641	35	10	[	[	X
ejpam-6641	35	11	35–44	35–44	NUM
ejpam-6641	35	12	]	]	X
ejpam-6641	35	13	.	.	PUNCT
ejpam-6641	36	1	the	the	DET
ejpam-6641	36	2	classical	classical	ADJ
ejpam-6641	36	3	versions	version	NOUN
ejpam-6641	36	4	of	of	ADP
ejpam-6641	36	5	the	the	DET
ejpam-6641	36	6	homogeneous	homogeneous	ADJ
ejpam-6641	36	7	and	and	CCONJ
ejpam-6641	36	8	non	non	ADJ
ejpam-6641	36	9	-	-	ADJ
ejpam-6641	36	10	homogeneous	homogeneous	ADJ
ejpam-6641	36	11	herz	herz	ADJ
ejpam-6641	36	12	spaces	space	NOUN
ejpam-6641	36	13	are	be	AUX
ejpam-6641	36	14	defined	define	VERB
ejpam-6641	36	15	as	as	SCONJ
ejpam-6641	36	16	:	:	PUNCT
ejpam-6641	36	17	izuki	izuki	PROPN
ejpam-6641	36	18	introduced	introduce	VERB
ejpam-6641	36	19	the	the	DET
ejpam-6641	36	20	idea	idea	NOUN
ejpam-6641	36	21	of	of	ADP
ejpam-6641	36	22	herz	herz	PROPN
ejpam-6641	36	23	spaces	space	NOUN
ejpam-6641	36	24	k̇κ	k̇κ	PROPN
ejpam-6641	36	25	p(·),q(r	p(·),q(r	PROPN
ejpam-6641	36	26	n	n	CCONJ
ejpam-6641	36	27	)	)	PUNCT
ejpam-6641	36	28	and	and	CCONJ
ejpam-6641	36	29	kκ	kκ	X
ejpam-6641	36	30	p(·),q(r	p(·),q(r	PROPN
ejpam-6641	36	31	n	n	CCONJ
ejpam-6641	36	32	)	)	PUNCT
ejpam-6641	36	33	,	,	PUNCT
ejpam-6641	36	34	where	where	SCONJ
ejpam-6641	36	35	the	the	DET
ejpam-6641	36	36	exponent	exponent	NOUN
ejpam-6641	36	37	p	p	PROPN
ejpam-6641	36	38	was	be	AUX
ejpam-6641	36	39	a	a	DET
ejpam-6641	36	40	variable	variable	NOUN
ejpam-6641	36	41	and	and	CCONJ
ejpam-6641	36	42	norms	norm	NOUN
ejpam-6641	36	43	are	be	AUX
ejpam-6641	36	44	defined	define	VERB
ejpam-6641	36	45	as	as	ADP
ejpam-6641	36	46	,	,	PUNCT
ejpam-6641	36	47	for	for	ADP
ejpam-6641	36	48	p	p	PROPN
ejpam-6641	36	49	∈	∈	PROPN
ejpam-6641	37	1	[	[	X
ejpam-6641	37	2	1,∞	1,∞	NUM
ejpam-6641	37	3	)	)	PUNCT
ejpam-6641	37	4	,	,	PUNCT
ejpam-6641	37	5	q	q	X
ejpam-6641	37	6	(	(	PUNCT
ejpam-6641	37	7	·	·	PUNCT
ejpam-6641	37	8	)	)	PUNCT
ejpam-6641	37	9	∈	∈	PROPN
ejpam-6641	37	10	p(rn	p(rn	PROPN
ejpam-6641	37	11	)	)	PUNCT
ejpam-6641	37	12	and	and	CCONJ
ejpam-6641	37	13	κ	κ	PROPN
ejpam-6641	37	14	∈	∈	PROPN
ejpam-6641	37	15	r.	r.	PROPN
ejpam-6641	37	16	the	the	DET
ejpam-6641	37	17	herz	herz	PROPN
ejpam-6641	37	18	space	space	PROPN
ejpam-6641	37	19	k̇κ	k̇κ	PROPN
ejpam-6641	37	20	p	p	PROPN
ejpam-6641	37	21	,	,	PUNCT
ejpam-6641	37	22	q(·)(r	q(·)(r	NOUN
ejpam-6641	37	23	n	n	CCONJ
ejpam-6641	37	24	)	)	PUNCT
ejpam-6641	37	25	of	of	ADP
ejpam-6641	37	26	homogeneous	homogeneous	ADJ
ejpam-6641	37	27	type	type	NOUN
ejpam-6641	37	28	is	be	AUX
ejpam-6641	37	29	given	give	VERB
ejpam-6641	37	30	by	by	ADP
ejpam-6641	37	31	k̇κ	k̇κ	PROPN
ejpam-6641	37	32	p	p	PROPN
ejpam-6641	37	33	,	,	PUNCT
ejpam-6641	37	34	q(·)(r	q(·)(r	NOUN
ejpam-6641	37	35	n	n	CCONJ
ejpam-6641	37	36	)	)	PUNCT
ejpam-6641	37	37	=	=	PRON
ejpam-6641	37	38	{	{	PUNCT
ejpam-6641	37	39	g	g	PROPN
ejpam-6641	37	40	∈	∈	PROPN
ejpam-6641	37	41	l	l	NOUN
ejpam-6641	37	42	q	q	X
ejpam-6641	37	43	(	(	PUNCT
ejpam-6641	37	44	·	·	PUNCT
ejpam-6641	37	45	)	)	PUNCT
ejpam-6641	37	46	loc	loc	NOUN
ejpam-6641	37	47	(	(	PUNCT
ejpam-6641	37	48	r	r	NOUN
ejpam-6641	37	49	n	n	CCONJ
ejpam-6641	37	50	\	\	NOUN
ejpam-6641	37	51	{	{	PUNCT
ejpam-6641	37	52	0	0	NUM
ejpam-6641	37	53	}	}	PUNCT
ejpam-6641	37	54	)	)	PUNCT
ejpam-6641	37	55	:	:	PUNCT
ejpam-6641	38	1	∥g∥k̇κ	∥g∥k̇κ	ADP
ejpam-6641	38	2	p	p	X
ejpam-6641	38	3	,	,	PUNCT
ejpam-6641	38	4	q(·)(r	q(·)(r	NOUN
ejpam-6641	38	5	n	n	CCONJ
ejpam-6641	38	6	)	)	PUNCT
ejpam-6641	38	7	<	<	X
ejpam-6641	38	8	∞	∞	NUM
ejpam-6641	38	9	}	}	PUNCT
ejpam-6641	38	10	,	,	PUNCT
ejpam-6641	38	11	(	(	PUNCT
ejpam-6641	38	12	1.2	1.2	NUM
ejpam-6641	38	13	)	)	PUNCT
ejpam-6641	38	14	g.	g.	PROPN
ejpam-6641	38	15	a.	a.	PROPN
ejpam-6641	38	16	basendwah	basendwah	PROPN
ejpam-6641	38	17	et	et	PROPN
ejpam-6641	38	18	al	al	PROPN
ejpam-6641	38	19	.	.	PUNCT
ejpam-6641	38	20	/	/	SYM
ejpam-6641	38	21	eur	eur	PROPN
ejpam-6641	38	22	.	.	PUNCT
ejpam-6641	39	1	j.	j.	PROPN
ejpam-6641	39	2	pure	pure	PROPN
ejpam-6641	39	3	appl	appl	PROPN
ejpam-6641	39	4	.	.	PROPN
ejpam-6641	39	5	math	math	PROPN
ejpam-6641	39	6	,	,	PUNCT
ejpam-6641	39	7	18	18	NUM
ejpam-6641	39	8	(	(	PUNCT
ejpam-6641	39	9	4	4	NUM
ejpam-6641	39	10	)	)	PUNCT
ejpam-6641	39	11	(	(	PUNCT
ejpam-6641	39	12	2025	2025	NUM
ejpam-6641	39	13	)	)	PUNCT
ejpam-6641	39	14	,	,	PUNCT
ejpam-6641	39	15	6641	6641	NUM
ejpam-6641	39	16	3	3	NUM
ejpam-6641	39	17	of	of	ADP
ejpam-6641	39	18	16	16	NUM
ejpam-6641	39	19	where	where	SCONJ
ejpam-6641	39	20	∥g∥k̇κ	∥g∥k̇κ	PROPN
ejpam-6641	39	21	p	p	NOUN
ejpam-6641	39	22	,	,	PUNCT
ejpam-6641	39	23	q(·)(r	q(·)(r	NOUN
ejpam-6641	39	24	n	n	CCONJ
ejpam-6641	39	25	)	)	PUNCT
ejpam-6641	39	26	=	=	SYM
ejpam-6641	39	27	(	(	PUNCT
ejpam-6641	39	28	i=∞∑	i=∞∑	VERB
ejpam-6641	39	29	i=−∞	i=−∞	ADJ
ejpam-6641	39	30	∥2iκg1i∥plq	∥2iκg1i∥plq	PROPN
ejpam-6641	39	31	(	(	PUNCT
ejpam-6641	39	32	·	·	PUNCT
ejpam-6641	39	33	)	)	PUNCT
ejpam-6641	39	34	)	)	PUNCT
ejpam-6641	40	1	1	1	NUM
ejpam-6641	40	2	p	p	NOUN
ejpam-6641	40	3	.	.	PUNCT
ejpam-6641	41	1	the	the	DET
ejpam-6641	41	2	non	non	ADJ
ejpam-6641	41	3	-	-	ADJ
ejpam-6641	41	4	homogeneous	homogeneous	ADJ
ejpam-6641	41	5	version	version	NOUN
ejpam-6641	41	6	of	of	ADP
ejpam-6641	41	7	herz	herz	PROPN
ejpam-6641	41	8	spaces	space	NOUN
ejpam-6641	41	9	kκ	kκ	PROPN
ejpam-6641	41	10	p(·),q(r	p(·),q(r	PROPN
ejpam-6641	41	11	n	n	CCONJ
ejpam-6641	41	12	)	)	PUNCT
ejpam-6641	41	13	are	be	AUX
ejpam-6641	41	14	defined	define	VERB
ejpam-6641	41	15	below	below	ADV
ejpam-6641	41	16	.	.	PUNCT
ejpam-6641	42	1	let	let	VERB
ejpam-6641	42	2	κ	κ	PROPN
ejpam-6641	42	3	∈	∈	PROPN
ejpam-6641	42	4	r	r	NOUN
ejpam-6641	42	5	,	,	PUNCT
ejpam-6641	42	6	p	p	NOUN
ejpam-6641	42	7	∈	∈	PROPN
ejpam-6641	43	1	[	[	X
ejpam-6641	43	2	1,∞	1,∞	NUM
ejpam-6641	43	3	)	)	PUNCT
ejpam-6641	43	4	and	and	CCONJ
ejpam-6641	43	5	q	q	ADJ
ejpam-6641	43	6	(	(	PUNCT
ejpam-6641	43	7	·	·	PUNCT
ejpam-6641	43	8	)	)	PUNCT
ejpam-6641	43	9	∈	∈	PROPN
ejpam-6641	43	10	p(rn	p(rn	PROPN
ejpam-6641	43	11	)	)	PUNCT
ejpam-6641	43	12	.	.	PUNCT
ejpam-6641	44	1	the	the	DET
ejpam-6641	44	2	herz	herz	PROPN
ejpam-6641	44	3	space	space	NOUN
ejpam-6641	44	4	kκ	kκ	PROPN
ejpam-6641	44	5	p	p	NOUN
ejpam-6641	44	6	,	,	PUNCT
ejpam-6641	44	7	q(·)(r	q(·)(r	NOUN
ejpam-6641	44	8	n	n	CCONJ
ejpam-6641	44	9	)	)	PUNCT
ejpam-6641	44	10	of	of	ADP
ejpam-6641	44	11	nonhomogeneous	nonhomogeneous	ADJ
ejpam-6641	44	12	type	type	NOUN
ejpam-6641	44	13	is	be	AUX
ejpam-6641	44	14	given	give	VERB
ejpam-6641	44	15	by	by	ADP
ejpam-6641	44	16	kκ	kκ	PROPN
ejpam-6641	44	17	p	p	PROPN
ejpam-6641	44	18	,	,	PUNCT
ejpam-6641	44	19	q(·)(r	q(·)(r	NOUN
ejpam-6641	44	20	n	n	CCONJ
ejpam-6641	44	21	)	)	PUNCT
ejpam-6641	44	22	=	=	PRON
ejpam-6641	44	23	{	{	PUNCT
ejpam-6641	44	24	g	g	PROPN
ejpam-6641	44	25	∈	∈	PROPN
ejpam-6641	44	26	l	l	NOUN
ejpam-6641	44	27	q	q	X
ejpam-6641	44	28	(	(	PUNCT
ejpam-6641	44	29	·	·	PUNCT
ejpam-6641	44	30	)	)	PUNCT
ejpam-6641	44	31	loc	loc	NOUN
ejpam-6641	44	32	(	(	PUNCT
ejpam-6641	44	33	r	r	NOUN
ejpam-6641	44	34	n	n	CCONJ
ejpam-6641	44	35	\	\	NOUN
ejpam-6641	44	36	{	{	PUNCT
ejpam-6641	44	37	0	0	NUM
ejpam-6641	44	38	}	}	PUNCT
ejpam-6641	44	39	)	)	PUNCT
ejpam-6641	44	40	:	:	PUNCT
ejpam-6641	45	1	∥g∥kκ	∥g∥kκ	PROPN
ejpam-6641	45	2	p	p	PROPN
ejpam-6641	45	3	,	,	PUNCT
ejpam-6641	45	4	q(·)(r	q(·)(r	NOUN
ejpam-6641	45	5	n	n	CCONJ
ejpam-6641	45	6	)	)	PUNCT
ejpam-6641	45	7	<	<	X
ejpam-6641	45	8	∞	∞	NUM
ejpam-6641	45	9	}	}	PUNCT
ejpam-6641	45	10	,	,	PUNCT
ejpam-6641	45	11	(	(	PUNCT
ejpam-6641	45	12	1.3	1.3	NUM
ejpam-6641	45	13	)	)	PUNCT
ejpam-6641	45	14	where	where	SCONJ
ejpam-6641	45	15	∥g∥kκ	∥g∥kκ	PROPN
ejpam-6641	45	16	p	p	PROPN
ejpam-6641	45	17	,	,	PUNCT
ejpam-6641	45	18	q(·)(r	q(·)(r	NOUN
ejpam-6641	45	19	n	n	CCONJ
ejpam-6641	45	20	)	)	PUNCT
ejpam-6641	45	21	=	=	SYM
ejpam-6641	45	22	∥g∥lq(·)(o(0,1	∥g∥lq(·)(o(0,1	NOUN
ejpam-6641	45	23	)	)	PUNCT
ejpam-6641	45	24	)	)	PUNCT
ejpam-6641	46	1	+	+	CCONJ
ejpam-6641	46	2	(	(	PUNCT
ejpam-6641	46	3	∞∑	∞∑	NUM
ejpam-6641	46	4	τ=−∞	τ=−∞	X
ejpam-6641	46	5	∥2iκg1i∥plq	∥2iκg1i∥plq	PROPN
ejpam-6641	46	6	(	(	PUNCT
ejpam-6641	46	7	·	·	PUNCT
ejpam-6641	46	8	)	)	PUNCT
ejpam-6641	46	9	)	)	PUNCT
ejpam-6641	46	10	1	1	NUM
ejpam-6641	46	11	p	p	NOUN
ejpam-6641	46	12	.	.	PUNCT
ejpam-6641	47	1	an	an	DET
ejpam-6641	47	2	important	important	ADJ
ejpam-6641	47	3	focus	focus	NOUN
ejpam-6641	47	4	within	within	ADP
ejpam-6641	47	5	herz	herz	PROPN
ejpam-6641	47	6	spaces	space	NOUN
ejpam-6641	47	7	involves	involve	VERB
ejpam-6641	47	8	investigating	investigate	VERB
ejpam-6641	47	9	the	the	DET
ejpam-6641	47	10	boundedness	boundedness	NOUN
ejpam-6641	47	11	of	of	ADP
ejpam-6641	47	12	sublinear	sublinear	NOUN
ejpam-6641	47	13	operators	operator	NOUN
ejpam-6641	47	14	.	.	PUNCT
ejpam-6641	48	1	this	this	DET
ejpam-6641	48	2	exploration	exploration	NOUN
ejpam-6641	48	3	has	have	AUX
ejpam-6641	48	4	led	lead	VERB
ejpam-6641	48	5	to	to	ADP
ejpam-6641	48	6	studies	study	NOUN
ejpam-6641	48	7	motivated	motivate	VERB
ejpam-6641	48	8	by	by	ADP
ejpam-6641	48	9	this	this	DET
ejpam-6641	48	10	topic	topic	NOUN
ejpam-6641	48	11	,	,	PUNCT
ejpam-6641	48	12	culminating	culminate	VERB
ejpam-6641	48	13	in	in	ADP
ejpam-6641	48	14	the	the	DET
ejpam-6641	48	15	establishment	establishment	NOUN
ejpam-6641	48	16	of	of	ADP
ejpam-6641	48	17	sublinear	sublinear	NOUN
ejpam-6641	48	18	operator	operator	NOUN
ejpam-6641	48	19	boundedness	boundedness	NOUN
ejpam-6641	48	20	in	in	ADP
ejpam-6641	48	21	herz	herz	PROPN
ejpam-6641	48	22	spaces	space	NOUN
ejpam-6641	48	23	with	with	ADP
ejpam-6641	48	24	variable	variable	ADJ
ejpam-6641	48	25	exponents	exponent	NOUN
ejpam-6641	48	26	,	,	PUNCT
ejpam-6641	48	27	as	as	SCONJ
ejpam-6641	48	28	demonstrated	demonstrate	VERB
ejpam-6641	48	29	in	in	ADP
ejpam-6641	48	30	[	[	X
ejpam-6641	48	31	12	12	NUM
ejpam-6641	48	32	]	]	PUNCT
ejpam-6641	48	33	.	.	PUNCT
ejpam-6641	49	1	in	in	ADP
ejpam-6641	49	2	[	[	X
ejpam-6641	49	3	13	13	NUM
ejpam-6641	49	4	]	]	PUNCT
ejpam-6641	49	5	,	,	PUNCT
ejpam-6641	49	6	an	an	DET
ejpam-6641	49	7	alternative	alternative	ADJ
ejpam-6641	49	8	method	method	NOUN
ejpam-6641	49	9	was	be	AUX
ejpam-6641	49	10	employed	employ	VERB
ejpam-6641	49	11	to	to	PART
ejpam-6641	49	12	define	define	VERB
ejpam-6641	49	13	variable	variable	ADJ
ejpam-6641	49	14	exponent	exponent	NOUN
ejpam-6641	49	15	herz	herz	PROPN
ejpam-6641	49	16	spaces	space	VERB
ejpam-6641	49	17	.	.	PUNCT
ejpam-6641	50	1	a	a	DET
ejpam-6641	50	2	notable	notable	ADJ
ejpam-6641	50	3	aspect	aspect	NOUN
ejpam-6641	50	4	of	of	ADP
ejpam-6641	50	5	this	this	DET
ejpam-6641	50	6	method	method	NOUN
ejpam-6641	50	7	involves	involve	VERB
ejpam-6641	50	8	substituting	substitute	VERB
ejpam-6641	50	9	the	the	DET
ejpam-6641	50	10	discrete	discrete	ADJ
ejpam-6641	50	11	lp	lp	ADJ
ejpam-6641	50	12	-	-	PUNCT
ejpam-6641	50	13	norm	norm	NOUN
ejpam-6641	50	14	(	(	PUNCT
ejpam-6641	50	15	lebesguenorm	lebesguenorm	NOUN
ejpam-6641	50	16	)	)	PUNCT
ejpam-6641	50	17	with	with	ADP
ejpam-6641	50	18	the	the	DET
ejpam-6641	50	19	continuous	continuous	ADJ
ejpam-6641	50	20	lp	lp	ADJ
ejpam-6641	50	21	-	-	PUNCT
ejpam-6641	50	22	norm	norm	NOUN
ejpam-6641	50	23	relative	relative	ADJ
ejpam-6641	50	24	to	to	ADP
ejpam-6641	50	25	haar	haar	PROPN
ejpam-6641	50	26	measure	measure	NOUN
ejpam-6641	50	27	,	,	PUNCT
ejpam-6641	50	28	streamlining	streamline	VERB
ejpam-6641	50	29	and	and	CCONJ
ejpam-6641	50	30	clarifying	clarify	VERB
ejpam-6641	50	31	the	the	DET
ejpam-6641	50	32	proofs	proof	NOUN
ejpam-6641	50	33	.	.	PUNCT
ejpam-6641	51	1	these	these	DET
ejpam-6641	51	2	spaces	space	NOUN
ejpam-6641	51	3	are	be	AUX
ejpam-6641	51	4	called	call	VERB
ejpam-6641	51	5	variable	variable	ADJ
ejpam-6641	51	6	continual	continual	ADJ
ejpam-6641	51	7	herz	herz	PROPN
ejpam-6641	51	8	spaces	space	NOUN
ejpam-6641	51	9	.	.	PUNCT
ejpam-6641	52	1	for	for	ADP
ejpam-6641	52	2	the	the	DET
ejpam-6641	52	3	boundedness	boundedness	NOUN
ejpam-6641	52	4	results	result	NOUN
ejpam-6641	52	5	on	on	ADP
ejpam-6641	52	6	some	some	DET
ejpam-6641	52	7	operators	operator	NOUN
ejpam-6641	52	8	on	on	ADP
ejpam-6641	52	9	continual	continual	ADJ
ejpam-6641	52	10	herz	herz	PROPN
ejpam-6641	52	11	spaces	space	NOUN
ejpam-6641	52	12	see	see	VERB
ejpam-6641	52	13	[	[	X
ejpam-6641	52	14	15–17	15–17	NUM
ejpam-6641	52	15	]	]	PUNCT
ejpam-6641	52	16	.	.	PUNCT
ejpam-6641	53	1	in	in	ADP
ejpam-6641	53	2	[	[	X
ejpam-6641	53	3	18	18	NUM
ejpam-6641	53	4	]	]	PUNCT
ejpam-6641	53	5	,	,	PUNCT
ejpam-6641	53	6	authors	author	NOUN
ejpam-6641	53	7	defined	define	VERB
ejpam-6641	53	8	the	the	DET
ejpam-6641	53	9	variable	variable	ADJ
ejpam-6641	53	10	herz	herz	ADJ
ejpam-6641	53	11	-	-	PUNCT
ejpam-6641	53	12	morrey	morrey	PROPN
ejpam-6641	53	13	spaces	space	VERB
ejpam-6641	53	14	mk̇κ	mk̇κ	NOUN
ejpam-6641	53	15	,	,	PUNCT
ejpam-6641	53	16	λ	λ	PROPN
ejpam-6641	53	17	p	p	NOUN
ejpam-6641	53	18	,	,	PUNCT
ejpam-6641	53	19	q(·)(r	q(·)(r	NOUN
ejpam-6641	53	20	n	n	CCONJ
ejpam-6641	53	21	)	)	PUNCT
ejpam-6641	53	22	,	,	PUNCT
ejpam-6641	53	23	and	and	CCONJ
ejpam-6641	53	24	obtained	obtain	VERB
ejpam-6641	53	25	the	the	DET
ejpam-6641	53	26	estimates	estimate	NOUN
ejpam-6641	53	27	of	of	ADP
ejpam-6641	53	28	sublinear	sublinear	NOUN
ejpam-6641	53	29	operators	operator	NOUN
ejpam-6641	53	30	within	within	ADP
ejpam-6641	53	31	these	these	DET
ejpam-6641	53	32	spaces	space	NOUN
ejpam-6641	53	33	.	.	PUNCT
ejpam-6641	54	1	it	it	PRON
ejpam-6641	54	2	’s	’	VERB
ejpam-6641	54	3	worth	worth	ADJ
ejpam-6641	54	4	mentioning	mention	VERB
ejpam-6641	54	5	that	that	SCONJ
ejpam-6641	54	6	herz	herz	PROPN
ejpam-6641	54	7	-	-	PUNCT
ejpam-6641	54	8	morrey	morrey	PROPN
ejpam-6641	54	9	spaces	space	NOUN
ejpam-6641	54	10	with	with	ADP
ejpam-6641	54	11	variable	variable	ADJ
ejpam-6641	54	12	exponents	exponent	NOUN
ejpam-6641	54	13	serve	serve	VERB
ejpam-6641	54	14	as	as	ADP
ejpam-6641	54	15	extensions	extension	NOUN
ejpam-6641	54	16	of	of	ADP
ejpam-6641	54	17	herz	herz	PROPN
ejpam-6641	54	18	spaces	space	NOUN
ejpam-6641	54	19	with	with	ADP
ejpam-6641	54	20	variable	variable	ADJ
ejpam-6641	54	21	exponents	exponent	NOUN
ejpam-6641	54	22	.	.	PUNCT
ejpam-6641	55	1	additionally	additionally	ADV
ejpam-6641	55	2	,	,	PUNCT
ejpam-6641	55	3	in	in	ADP
ejpam-6641	55	4	[	[	X
ejpam-6641	55	5	19	19	NUM
ejpam-6641	55	6	]	]	PUNCT
ejpam-6641	55	7	,	,	PUNCT
ejpam-6641	55	8	the	the	DET
ejpam-6641	55	9	boundedness	boundedness	NOUN
ejpam-6641	55	10	of	of	ADP
ejpam-6641	55	11	higher	high	ADJ
ejpam-6641	55	12	-	-	PUNCT
ejpam-6641	55	13	order	order	NOUN
ejpam-6641	55	14	commutators	commutator	NOUN
ejpam-6641	55	15	of	of	ADP
ejpam-6641	55	16	fractional	fractional	ADJ
ejpam-6641	55	17	integrals	integral	NOUN
ejpam-6641	55	18	on	on	ADP
ejpam-6641	55	19	herz	herz	PROPN
ejpam-6641	55	20	-	-	PUNCT
ejpam-6641	55	21	morrey	morrey	PROPN
ejpam-6641	55	22	spaces	space	NOUN
ejpam-6641	55	23	can	can	AUX
ejpam-6641	55	24	be	be	AUX
ejpam-6641	55	25	verified	verify	VERB
ejpam-6641	55	26	.	.	PUNCT
ejpam-6641	56	1	our	our	PRON
ejpam-6641	56	2	findings	finding	NOUN
ejpam-6641	56	3	not	not	PART
ejpam-6641	56	4	only	only	ADV
ejpam-6641	56	5	consolidate	consolidate	VERB
ejpam-6641	56	6	and	and	CCONJ
ejpam-6641	56	7	build	build	VERB
ejpam-6641	56	8	on	on	ADP
ejpam-6641	56	9	prior	prior	ADJ
ejpam-6641	56	10	discoveries	discovery	NOUN
ejpam-6641	56	11	,	,	PUNCT
ejpam-6641	56	12	but	but	CCONJ
ejpam-6641	56	13	also	also	ADV
ejpam-6641	56	14	offer	offer	VERB
ejpam-6641	56	15	novel	novel	ADJ
ejpam-6641	56	16	applications	application	NOUN
ejpam-6641	56	17	to	to	ADP
ejpam-6641	56	18	the	the	DET
ejpam-6641	56	19	regularity	regularity	NOUN
ejpam-6641	56	20	solutions	solution	NOUN
ejpam-6641	56	21	of	of	ADP
ejpam-6641	56	22	some	some	DET
ejpam-6641	56	23	elliptic	elliptic	ADJ
ejpam-6641	56	24	pdes	pde	NOUN
ejpam-6641	56	25	with	with	ADP
ejpam-6641	56	26	smooth	smooth	ADJ
ejpam-6641	56	27	boundaries	boundary	NOUN
ejpam-6641	56	28	.	.	PUNCT
ejpam-6641	57	1	the	the	DET
ejpam-6641	57	2	investigation	investigation	NOUN
ejpam-6641	57	3	of	of	ADP
ejpam-6641	57	4	the	the	DET
ejpam-6641	57	5	fractional	fractional	ADJ
ejpam-6641	57	6	hardy	hardy	ADJ
ejpam-6641	57	7	operator	operator	NOUN
ejpam-6641	57	8	,	,	PUNCT
ejpam-6641	57	9	belongs	belong	VERB
ejpam-6641	57	10	to	to	ADP
ejpam-6641	57	11	one	one	NUM
ejpam-6641	57	12	of	of	ADP
ejpam-6641	57	13	the	the	DET
ejpam-6641	57	14	hot	hot	ADJ
ejpam-6641	57	15	topics	topic	NOUN
ejpam-6641	57	16	in	in	ADP
ejpam-6641	57	17	the	the	DET
ejpam-6641	57	18	area	area	NOUN
ejpam-6641	57	19	of	of	ADP
ejpam-6641	57	20	pdes	pde	NOUN
ejpam-6641	57	21	because	because	SCONJ
ejpam-6641	57	22	of	of	ADP
ejpam-6641	57	23	its	its	PRON
ejpam-6641	57	24	wide	wide	ADV
ejpam-6641	57	25	-	-	PUNCT
ejpam-6641	57	26	ranging	range	VERB
ejpam-6641	57	27	interest	interest	NOUN
ejpam-6641	57	28	to	to	ADP
ejpam-6641	57	29	various	various	ADJ
ejpam-6641	57	30	fields	field	NOUN
ejpam-6641	57	31	in	in	ADP
ejpam-6641	57	32	mathematics	mathematic	NOUN
ejpam-6641	57	33	and	and	CCONJ
ejpam-6641	57	34	physics	physics	NOUN
ejpam-6641	57	35	.	.	PUNCT
ejpam-6641	58	1	for	for	ADP
ejpam-6641	58	2	instance	instance	NOUN
ejpam-6641	58	3	,	,	PUNCT
ejpam-6641	58	4	it	it	PRON
ejpam-6641	58	5	is	be	AUX
ejpam-6641	58	6	motivated	motivate	VERB
ejpam-6641	58	7	by	by	ADP
ejpam-6641	58	8	physical	physical	ADJ
ejpam-6641	58	9	models	model	NOUN
ejpam-6641	58	10	related	relate	VERB
ejpam-6641	58	11	to	to	ADP
ejpam-6641	58	12	relativistic	relativistic	ADJ
ejpam-6641	58	13	schrödinger	schrödinger	NOUN
ejpam-6641	58	14	operator	operator	NOUN
ejpam-6641	58	15	with	with	ADP
ejpam-6641	58	16	coulomb	coulomb	NOUN
ejpam-6641	58	17	potential	potential	NOUN
ejpam-6641	58	18	(	(	PUNCT
ejpam-6641	58	19	see	see	VERB
ejpam-6641	58	20	[	[	X
ejpam-6641	58	21	22	22	NUM
ejpam-6641	58	22	,	,	PUNCT
ejpam-6641	58	23	23	23	NUM
ejpam-6641	58	24	]	]	PUNCT
ejpam-6641	58	25	)	)	PUNCT
ejpam-6641	58	26	and	and	CCONJ
ejpam-6641	58	27	by	by	ADP
ejpam-6641	58	28	the	the	DET
ejpam-6641	58	29	study	study	NOUN
ejpam-6641	58	30	of	of	ADP
ejpam-6641	58	31	hardy	hardy	ADJ
ejpam-6641	58	32	inequalities	inequality	NOUN
ejpam-6641	58	33	and	and	CCONJ
ejpam-6641	58	34	hardy	hardy	ADJ
ejpam-6641	58	35	-	-	PUNCT
ejpam-6641	58	36	lieb	lieb	NOUN
ejpam-6641	58	37	-	-	PUNCT
ejpam-6641	58	38	thirring	thirre	VERB
ejpam-6641	58	39	inequalities	inequality	NOUN
ejpam-6641	58	40	(	(	PUNCT
ejpam-6641	58	41	see	see	VERB
ejpam-6641	58	42	,	,	PUNCT
ejpam-6641	58	43	e.g.	e.g.	ADV
ejpam-6641	58	44	,	,	PUNCT
ejpam-6641	58	45	[	[	X
ejpam-6641	58	46	20–26	20–26	NUM
ejpam-6641	58	47	]	]	PUNCT
ejpam-6641	58	48	)	)	PUNCT
ejpam-6641	58	49	.	.	PUNCT
ejpam-6641	59	1	the	the	DET
ejpam-6641	59	2	intrinsic	intrinsic	ADJ
ejpam-6641	59	3	square	square	ADJ
ejpam-6641	59	4	function	function	NOUN
ejpam-6641	59	5	sζ	sζ	PROPN
ejpam-6641	59	6	holds	hold	VERB
ejpam-6641	59	7	significant	significant	ADJ
ejpam-6641	59	8	importance	importance	NOUN
ejpam-6641	59	9	in	in	ADP
ejpam-6641	59	10	function	function	NOUN
ejpam-6641	59	11	spaces	space	NOUN
ejpam-6641	59	12	.	.	PUNCT
ejpam-6641	60	1	izuki	izuki	PROPN
ejpam-6641	60	2	obtained	obtain	VERB
ejpam-6641	60	3	the	the	DET
ejpam-6641	60	4	boundedness	boundedness	NOUN
ejpam-6641	60	5	of	of	ADP
ejpam-6641	60	6	sζ	sζ	PROPN
ejpam-6641	60	7	on	on	ADP
ejpam-6641	60	8	weighted	weight	VERB
ejpam-6641	60	9	variable	variable	ADJ
ejpam-6641	60	10	herz	herz	PROPN
ejpam-6641	60	11	spaces	space	NOUN
ejpam-6641	60	12	under	under	ADP
ejpam-6641	60	13	certain	certain	ADJ
ejpam-6641	60	14	appropriate	appropriate	ADJ
ejpam-6641	60	15	conditions	condition	NOUN
ejpam-6641	60	16	,	,	PUNCT
ejpam-6641	60	17	as	as	SCONJ
ejpam-6641	60	18	detailed	detailed	ADJ
ejpam-6641	60	19	in	in	ADP
ejpam-6641	60	20	[	[	X
ejpam-6641	60	21	27	27	NUM
ejpam-6641	60	22	]	]	PUNCT
ejpam-6641	60	23	.	.	PUNCT
ejpam-6641	61	1	this	this	DET
ejpam-6641	61	2	study	study	NOUN
ejpam-6641	61	3	investigates	investigate	VERB
ejpam-6641	61	4	the	the	DET
ejpam-6641	61	5	boundedness	boundedness	NOUN
ejpam-6641	61	6	of	of	ADP
ejpam-6641	61	7	the	the	DET
ejpam-6641	61	8	intrinsic	intrinsic	ADJ
ejpam-6641	61	9	square	square	ADJ
ejpam-6641	61	10	function	function	NOUN
ejpam-6641	61	11	on	on	ADP
ejpam-6641	61	12	continuous	continuous	ADJ
ejpam-6641	61	13	herz	herz	PROPN
ejpam-6641	61	14	spaces	space	NOUN
ejpam-6641	61	15	with	with	ADP
ejpam-6641	61	16	variable	variable	ADJ
ejpam-6641	61	17	exponents	exponent	NOUN
ejpam-6641	61	18	.	.	PUNCT
ejpam-6641	62	1	the	the	DET
ejpam-6641	62	2	article	article	NOUN
ejpam-6641	62	3	is	be	AUX
ejpam-6641	62	4	structured	structure	VERB
ejpam-6641	62	5	into	into	ADP
ejpam-6641	62	6	four	four	NUM
ejpam-6641	62	7	sections	section	NOUN
ejpam-6641	62	8	:	:	PUNCT
ejpam-6641	62	9	the	the	DET
ejpam-6641	62	10	first	first	ADJ
ejpam-6641	62	11	section	section	NOUN
ejpam-6641	62	12	serves	serve	VERB
ejpam-6641	62	13	as	as	ADP
ejpam-6641	62	14	an	an	DET
ejpam-6641	62	15	introduction	introduction	NOUN
ejpam-6641	62	16	,	,	PUNCT
ejpam-6641	62	17	the	the	DET
ejpam-6641	62	18	second	second	ADJ
ejpam-6641	62	19	section	section	NOUN
ejpam-6641	62	20	presents	present	VERB
ejpam-6641	62	21	fundamental	fundamental	ADJ
ejpam-6641	62	22	definitions	definition	NOUN
ejpam-6641	62	23	and	and	CCONJ
ejpam-6641	62	24	lemmas	lemma	NOUN
ejpam-6641	62	25	,	,	PUNCT
ejpam-6641	62	26	the	the	DET
ejpam-6641	62	27	concept	concept	NOUN
ejpam-6641	62	28	of	of	ADP
ejpam-6641	62	29	continuous	continuous	ADJ
ejpam-6641	62	30	herz	herz	PROPN
ejpam-6641	62	31	spaces	space	NOUN
ejpam-6641	62	32	is	be	AUX
ejpam-6641	62	33	defined	define	VERB
ejpam-6641	62	34	in	in	ADP
ejpam-6641	62	35	part	part	NOUN
ejpam-6641	62	36	three	three	NUM
ejpam-6641	62	37	,	,	PUNCT
ejpam-6641	62	38	and	and	CCONJ
ejpam-6641	62	39	the	the	DET
ejpam-6641	62	40	final	final	ADJ
ejpam-6641	62	41	section	section	NOUN
ejpam-6641	62	42	delves	delve	VERB
ejpam-6641	62	43	into	into	ADP
ejpam-6641	62	44	examining	examine	VERB
ejpam-6641	62	45	the	the	DET
ejpam-6641	62	46	boundedness	boundedness	NOUN
ejpam-6641	62	47	of	of	ADP
ejpam-6641	62	48	the	the	DET
ejpam-6641	62	49	intrinsic	intrinsic	ADJ
ejpam-6641	62	50	square	square	ADJ
ejpam-6641	62	51	function	function	NOUN
ejpam-6641	62	52	on	on	ADP
ejpam-6641	62	53	variable	variable	ADJ
ejpam-6641	62	54	continuous	continuous	ADJ
ejpam-6641	62	55	herz	herz	PROPN
ejpam-6641	62	56	spaces	space	NOUN
ejpam-6641	62	57	with	with	ADP
ejpam-6641	62	58	variable	variable	ADJ
ejpam-6641	62	59	exponents	exponent	NOUN
ejpam-6641	62	60	.	.	PUNCT
ejpam-6641	63	1	for	for	ADP
ejpam-6641	63	2	more	more	ADJ
ejpam-6641	63	3	results	result	NOUN
ejpam-6641	63	4	see	see	VERB
ejpam-6641	63	5	[	[	X
ejpam-6641	63	6	29–34	29–34	NUM
ejpam-6641	63	7	]	]	PUNCT
ejpam-6641	63	8	.	.	PUNCT
ejpam-6641	64	1	we	we	PRON
ejpam-6641	64	2	will	will	AUX
ejpam-6641	64	3	use	use	VERB
ejpam-6641	64	4	following	follow	VERB
ejpam-6641	64	5	notations	notation	NOUN
ejpam-6641	64	6	in	in	ADP
ejpam-6641	64	7	the	the	DET
ejpam-6641	64	8	paper	paper	NOUN
ejpam-6641	64	9	:	:	PUNCT
ejpam-6641	64	10	g.	g.	PROPN
ejpam-6641	64	11	a.	a.	PROPN
ejpam-6641	64	12	basendwah	basendwah	PROPN
ejpam-6641	64	13	et	et	PROPN
ejpam-6641	64	14	al	al	PROPN
ejpam-6641	64	15	.	.	PUNCT
ejpam-6641	64	16	/	/	SYM
ejpam-6641	64	17	eur	eur	PROPN
ejpam-6641	64	18	.	.	PUNCT
ejpam-6641	65	1	j.	j.	PROPN
ejpam-6641	65	2	pure	pure	PROPN
ejpam-6641	65	3	appl	appl	PROPN
ejpam-6641	65	4	.	.	PROPN
ejpam-6641	65	5	math	math	PROPN
ejpam-6641	65	6	,	,	PUNCT
ejpam-6641	65	7	18	18	NUM
ejpam-6641	65	8	(	(	PUNCT
ejpam-6641	65	9	4	4	NUM
ejpam-6641	65	10	)	)	PUNCT
ejpam-6641	65	11	(	(	PUNCT
ejpam-6641	65	12	2025	2025	NUM
ejpam-6641	65	13	)	)	PUNCT
ejpam-6641	65	14	,	,	PUNCT
ejpam-6641	65	15	6641	6641	NUM
ejpam-6641	65	16	4	4	NUM
ejpam-6641	65	17	of	of	ADP
ejpam-6641	65	18	16	16	NUM
ejpam-6641	65	19	notations	notation	NOUN
ejpam-6641	65	20	(	(	PUNCT
ejpam-6641	65	21	i	i	NOUN
ejpam-6641	65	22	)	)	PUNCT
ejpam-6641	66	1	o(y	o(y	PROPN
ejpam-6641	66	2	,	,	PUNCT
ejpam-6641	66	3	s	s	X
ejpam-6641	66	4	)	)	PUNCT
ejpam-6641	66	5	denotes	denote	VERB
ejpam-6641	66	6	a	a	DET
ejpam-6641	66	7	ball	ball	NOUN
ejpam-6641	66	8	with	with	ADP
ejpam-6641	66	9	center	center	NOUN
ejpam-6641	66	10	at	at	ADP
ejpam-6641	66	11	y	y	PROPN
ejpam-6641	66	12	and	and	CCONJ
ejpam-6641	66	13	radius	radius	PROPN
ejpam-6641	66	14	s	s	PART
ejpam-6641	66	15	;	;	PUNCT
ejpam-6641	66	16	(	(	PUNCT
ejpam-6641	66	17	ii	ii	NOUN
ejpam-6641	66	18	)	)	PUNCT
ejpam-6641	66	19	t	t	PROPN
ejpam-6641	66	20	(	(	PUNCT
ejpam-6641	66	21	τ	τ	PROPN
ejpam-6641	66	22	,	,	PUNCT
ejpam-6641	66	23	t	t	PROPN
ejpam-6641	66	24	)	)	PUNCT
ejpam-6641	66	25	denotes	denote	VERB
ejpam-6641	66	26	the	the	DET
ejpam-6641	66	27	spherical	spherical	ADJ
ejpam-6641	66	28	layer	layer	NOUN
ejpam-6641	66	29	such	such	ADJ
ejpam-6641	66	30	that	that	SCONJ
ejpam-6641	66	31	(	(	PUNCT
ejpam-6641	66	32	iii	iii	X
ejpam-6641	66	33	)	)	PUNCT
ejpam-6641	66	34	t	t	PROPN
ejpam-6641	66	35	τ	τ	PROPN
ejpam-6641	66	36	,	,	PUNCT
ejpam-6641	66	37	t	t	PROPN
ejpam-6641	66	38	)	)	PUNCT
ejpam-6641	66	39	:	:	PUNCT
ejpam-6641	67	1	=	=	SYM
ejpam-6641	67	2	o(0	o(0	PROPN
ejpam-6641	67	3	,	,	PUNCT
ejpam-6641	67	4	t	t	PROPN
ejpam-6641	67	5	)	)	PUNCT
ejpam-6641	67	6	\	\	PROPN
ejpam-6641	68	1	o(0	o(0	PROPN
ejpam-6641	68	2	,	,	PUNCT
ejpam-6641	68	3	τ	τ	NOUN
ejpam-6641	68	4	)	)	PUNCT
ejpam-6641	68	5	=	=	PRON
ejpam-6641	68	6	{	{	PUNCT
ejpam-6641	68	7	y	y	PROPN
ejpam-6641	68	8	∈	∈	PROPN
ejpam-6641	68	9	rn	rn	PROPN
ejpam-6641	68	10	:	:	PUNCT
ejpam-6641	68	11	τ	τ	PROPN
ejpam-6641	68	12	<	<	X
ejpam-6641	68	13	|y|	|y|	PROPN
ejpam-6641	68	14	<	<	X
ejpam-6641	68	15	t	t	PROPN
ejpam-6641	68	16	}	}	PUNCT
ejpam-6641	68	17	;	;	PUNCT
ejpam-6641	68	18	(	(	PUNCT
ejpam-6641	68	19	iv	iv	X
ejpam-6641	68	20	)	)	PUNCT
ejpam-6641	68	21	tm	tm	NOUN
ejpam-6641	68	22	:	:	PUNCT
ejpam-6641	68	23	=	=	SYM
ejpam-6641	68	24	t	t	PROPN
ejpam-6641	68	25	(	(	PUNCT
ejpam-6641	68	26	2m−1	2m−1	PROPN
ejpam-6641	68	27	,	,	PUNCT
ejpam-6641	68	28	2	2	NUM
ejpam-6641	68	29	m	m	NOUN
ejpam-6641	68	30	)	)	PUNCT
ejpam-6641	68	31	;	;	PUNCT
ejpam-6641	68	32	(	(	PUNCT
ejpam-6641	68	33	v	v	NOUN
ejpam-6641	68	34	)	)	PUNCT
ejpam-6641	68	35	1e(y	1e(y	NUM
ejpam-6641	68	36	)	)	PUNCT
ejpam-6641	68	37	is	be	AUX
ejpam-6641	68	38	the	the	DET
ejpam-6641	68	39	characteristic	characteristic	ADJ
ejpam-6641	68	40	function	function	NOUN
ejpam-6641	68	41	of	of	ADP
ejpam-6641	68	42	a	a	DET
ejpam-6641	68	43	set	set	NOUN
ejpam-6641	68	44	e	e	NOUN
ejpam-6641	68	45	;	;	PUNCT
ejpam-6641	68	46	(	(	PUNCT
ejpam-6641	68	47	vi	vi	NOUN
ejpam-6641	68	48	)	)	PUNCT
ejpam-6641	68	49	rµ+	rµ+	NOUN
ejpam-6641	68	50	:	:	PUNCT
ejpam-6641	69	1	=	=	SYM
ejpam-6641	69	2	(	(	PUNCT
ejpam-6641	69	3	µ,∞	µ,∞	PROPN
ejpam-6641	69	4	)	)	PUNCT
ejpam-6641	69	5	,	,	PUNCT
ejpam-6641	69	6	where	where	SCONJ
ejpam-6641	69	7	µ	µ	PRON
ejpam-6641	69	8	≥	≥	NOUN
ejpam-6641	69	9	0	0	NUM
ejpam-6641	69	10	;	;	PUNCT
ejpam-6641	69	11	(	(	PUNCT
ejpam-6641	69	12	vii	vii	PROPN
ejpam-6641	69	13	)	)	PUNCT
ejpam-6641	69	14	1τ	1τ	NUM
ejpam-6641	69	15	,	,	PUNCT
ejpam-6641	69	16	t(y	t(y	NUM
ejpam-6641	69	17	)	)	PUNCT
ejpam-6641	69	18	=	=	SYM
ejpam-6641	69	19	1tτ	1tτ	NOUN
ejpam-6641	69	20	,	,	PUNCT
ejpam-6641	69	21	t(y	t(y	PROPN
ejpam-6641	69	22	)	)	PUNCT
ejpam-6641	69	23	;	;	PUNCT
ejpam-6641	69	24	(	(	PUNCT
ejpam-6641	69	25	viii	viii	NOUN
ejpam-6641	69	26	)	)	PUNCT
ejpam-6641	69	27	dτ	dτ	PROPN
ejpam-6641	69	28	/	/	SYM
ejpam-6641	69	29	τ	τ	PROPN
ejpam-6641	69	30	represents	represent	VERB
ejpam-6641	69	31	the	the	DET
ejpam-6641	69	32	haar	haar	NOUN
ejpam-6641	69	33	measure	measure	NOUN
ejpam-6641	69	34	on	on	ADP
ejpam-6641	69	35	r+	r+	X
ejpam-6641	69	36	;	;	PUNCT
ejpam-6641	69	37	(	(	PUNCT
ejpam-6641	69	38	ix	ix	X
ejpam-6641	69	39	)	)	PUNCT
ejpam-6641	69	40	n	n	NOUN
ejpam-6641	69	41	denotes	denote	VERB
ejpam-6641	69	42	the	the	DET
ejpam-6641	69	43	set	set	NOUN
ejpam-6641	69	44	of	of	ADP
ejpam-6641	69	45	natural	natural	ADJ
ejpam-6641	69	46	numbers	number	NOUN
ejpam-6641	69	47	;	;	PUNCT
ejpam-6641	69	48	(	(	PUNCT
ejpam-6641	69	49	x	x	X
ejpam-6641	69	50	)	)	PUNCT
ejpam-6641	69	51	n0	n0	NOUN
ejpam-6641	69	52	=	=	SYM
ejpam-6641	69	53	n	n	PRON
ejpam-6641	69	54	∪	∪	X
ejpam-6641	69	55	{	{	PUNCT
ejpam-6641	69	56	0	0	NUM
ejpam-6641	69	57	}	}	PUNCT
ejpam-6641	69	58	;	;	PUNCT
ejpam-6641	69	59	(	(	PUNCT
ejpam-6641	69	60	xi	xi	X
ejpam-6641	69	61	)	)	PUNCT
ejpam-6641	69	62	z	z	NOUN
ejpam-6641	69	63	denotes	denote	VERB
ejpam-6641	69	64	the	the	DET
ejpam-6641	69	65	set	set	NOUN
ejpam-6641	69	66	of	of	ADP
ejpam-6641	69	67	all	all	DET
ejpam-6641	69	68	integers	integer	NOUN
ejpam-6641	69	69	;	;	PUNCT
ejpam-6641	69	70	(	(	PUNCT
ejpam-6641	69	71	xii	xii	NOUN
ejpam-6641	69	72	)	)	PUNCT
ejpam-6641	69	73	for	for	ADP
ejpam-6641	69	74	two	two	NUM
ejpam-6641	69	75	non	non	ADJ
ejpam-6641	69	76	-	-	ADJ
ejpam-6641	69	77	nagative	nagative	ADJ
ejpam-6641	69	78	functions	function	NOUN
ejpam-6641	69	79	f	f	PROPN
ejpam-6641	69	80	and	and	CCONJ
ejpam-6641	69	81	g	g	PROPN
ejpam-6641	69	82	,	,	PUNCT
ejpam-6641	69	83	f	f	PROPN
ejpam-6641	69	84	≤	≤	PROPN
ejpam-6641	70	1	g	g	NOUN
ejpam-6641	71	1	we	we	PRON
ejpam-6641	71	2	mean	mean	VERB
ejpam-6641	71	3	f	f	PROPN
ejpam-6641	71	4	≤	≤	PROPN
ejpam-6641	71	5	cg	cg	NOUN
ejpam-6641	71	6	,	,	PUNCT
ejpam-6641	71	7	(	(	PUNCT
ejpam-6641	71	8	xiii	xiii	PROPN
ejpam-6641	71	9	)	)	PUNCT
ejpam-6641	71	10	c	c	NOUN
ejpam-6641	71	11	denote	denote	VERB
ejpam-6641	71	12	the	the	DET
ejpam-6641	71	13	positive	positive	ADJ
ejpam-6641	71	14	constant	constant	NOUN
ejpam-6641	71	15	.	.	PUNCT
ejpam-6641	72	1	2	2	X
ejpam-6641	72	2	.	.	X
ejpam-6641	72	3	preliminaries	preliminary	NOUN
ejpam-6641	72	4	next	next	ADV
ejpam-6641	72	5	for	for	ADP
ejpam-6641	72	6	compact	compact	ADJ
ejpam-6641	72	7	subsets	subset	NOUN
ejpam-6641	73	1	k	k	PROPN
ejpam-6641	73	2	⊂	⊂	PROPN
ejpam-6641	73	3	h	h	PROPN
ejpam-6641	73	4	,	,	PUNCT
ejpam-6641	73	5	the	the	DET
ejpam-6641	73	6	space	space	NOUN
ejpam-6641	73	7	l	l	NOUN
ejpam-6641	73	8	q	q	X
ejpam-6641	73	9	(	(	PUNCT
ejpam-6641	73	10	·	·	PUNCT
ejpam-6641	73	11	)	)	PUNCT
ejpam-6641	73	12	loc	loc	NOUN
ejpam-6641	73	13	(	(	PUNCT
ejpam-6641	73	14	h	h	NOUN
ejpam-6641	73	15	)	)	PUNCT
ejpam-6641	73	16	is	be	AUX
ejpam-6641	73	17	given	give	VERB
ejpam-6641	73	18	as	as	ADP
ejpam-6641	73	19	l	l	NOUN
ejpam-6641	73	20	p	p	X
ejpam-6641	73	21	(	(	PUNCT
ejpam-6641	73	22	·	·	PUNCT
ejpam-6641	73	23	)	)	PUNCT
ejpam-6641	73	24	loc	loc	NOUN
ejpam-6641	73	25	(	(	PUNCT
ejpam-6641	73	26	h	h	NOUN
ejpam-6641	73	27	)	)	PUNCT
ejpam-6641	73	28	:	:	PUNCT
ejpam-6641	74	1	=	=	PRON
ejpam-6641	74	2	{	{	PUNCT
ejpam-6641	75	1	k	k	NOUN
ejpam-6641	75	2	:	:	PUNCT
ejpam-6641	75	3	k	k	PROPN
ejpam-6641	75	4	∈	∈	PROPN
ejpam-6641	75	5	lq(·)(k	lq(·)(k	PROPN
ejpam-6641	75	6	)	)	PUNCT
ejpam-6641	75	7	}	}	PUNCT
ejpam-6641	75	8	.	.	PUNCT
ejpam-6641	76	1	let	let	VERB
ejpam-6641	76	2	x	x	PRON
ejpam-6641	76	3	,	,	PUNCT
ejpam-6641	76	4	y	y	PROPN
ejpam-6641	76	5	∈	∈	PROPN
ejpam-6641	76	6	h	h	NOUN
ejpam-6641	76	7	with	with	ADP
ejpam-6641	76	8	|x−y|	|x−y|	ADV
ejpam-6641	76	9	≤	≤	NUM
ejpam-6641	76	10	1	1	NUM
ejpam-6641	76	11	2	2	NUM
ejpam-6641	76	12	and	and	CCONJ
ejpam-6641	76	13	c(q	c(q	PROPN
ejpam-6641	76	14	)	)	PUNCT
ejpam-6641	76	15	is	be	AUX
ejpam-6641	76	16	not	not	PART
ejpam-6641	76	17	depending	depend	VERB
ejpam-6641	76	18	on	on	ADP
ejpam-6641	76	19	x	x	PRON
ejpam-6641	76	20	,	,	PUNCT
ejpam-6641	76	21	y.	y.	NOUN
ejpam-6641	76	22	we	we	PRON
ejpam-6641	76	23	have	have	VERB
ejpam-6641	76	24	the	the	DET
ejpam-6641	76	25	log	log	NOUN
ejpam-6641	76	26	-	-	PUNCT
ejpam-6641	76	27	condition	condition	NOUN
ejpam-6641	76	28	,	,	PUNCT
ejpam-6641	76	29	|q(x)−	|q(x)−	X
ejpam-6641	76	30	q(y)|	q(y)|	NOUN
ejpam-6641	76	31	≤	≤	PUNCT
ejpam-6641	76	32	c(q	c(q	PROPN
ejpam-6641	76	33	)	)	PUNCT
ejpam-6641	77	1	−	−	PROPN
ejpam-6641	77	2	ln	ln	PROPN
ejpam-6641	77	3	|x−	|x−	PROPN
ejpam-6641	77	4	y|	y|	NOUN
ejpam-6641	77	5	.	.	PUNCT
ejpam-6641	78	1	(	(	PUNCT
ejpam-6641	78	2	2.1	2.1	NUM
ejpam-6641	78	3	)	)	PUNCT
ejpam-6641	78	4	we	we	PRON
ejpam-6641	78	5	say	say	VERB
ejpam-6641	78	6	that	that	SCONJ
ejpam-6641	78	7	q	q	X
ejpam-6641	78	8	(	(	PUNCT
ejpam-6641	78	9	·	·	PUNCT
ejpam-6641	78	10	)	)	PUNCT
ejpam-6641	78	11	satisfies	satisfie	NOUN
ejpam-6641	78	12	log	log	VERB
ejpam-6641	78	13	decay	decay	NOUN
ejpam-6641	78	14	condition	condition	NOUN
ejpam-6641	78	15	at	at	ADP
ejpam-6641	78	16	infinity	infinity	NOUN
ejpam-6641	78	17	if	if	SCONJ
ejpam-6641	78	18	there	there	PRON
ejpam-6641	78	19	exists	exist	VERB
ejpam-6641	78	20	q∞	q∞	PROPN
ejpam-6641	78	21	∈	∈	PROPN
ejpam-6641	78	22	(	(	PUNCT
ejpam-6641	78	23	1,∞	1,∞	NUM
ejpam-6641	78	24	)	)	PUNCT
ejpam-6641	78	25	,	,	PUNCT
ejpam-6641	78	26	such	such	ADJ
ejpam-6641	78	27	that	that	SCONJ
ejpam-6641	78	28	|q(x)−	|q(x)−	ADJ
ejpam-6641	78	29	q∞|	q∞|	NOUN
ejpam-6641	78	30	≤	≤	NUM
ejpam-6641	78	31	c	c	PROPN
ejpam-6641	78	32	ln(e+	ln(e+	PROPN
ejpam-6641	78	33	|x|	|x|	PROPN
ejpam-6641	78	34	)	)	PUNCT
ejpam-6641	78	35	.	.	PUNCT
ejpam-6641	79	1	(	(	PUNCT
ejpam-6641	79	2	2.2	2.2	NUM
ejpam-6641	79	3	)	)	PUNCT
ejpam-6641	79	4	similarly	similarly	ADV
ejpam-6641	79	5	,	,	PUNCT
ejpam-6641	79	6	we	we	PRON
ejpam-6641	79	7	say	say	VERB
ejpam-6641	79	8	that	that	SCONJ
ejpam-6641	79	9	q	q	X
ejpam-6641	79	10	(	(	PUNCT
ejpam-6641	79	11	·	·	PUNCT
ejpam-6641	79	12	)	)	PUNCT
ejpam-6641	79	13	satisfies	satisfie	NOUN
ejpam-6641	79	14	log	log	VERB
ejpam-6641	79	15	decay	decay	NOUN
ejpam-6641	79	16	condition	condition	NOUN
ejpam-6641	79	17	at	at	ADP
ejpam-6641	79	18	origin	origin	NOUN
ejpam-6641	79	19	if	if	SCONJ
ejpam-6641	79	20	there	there	PRON
ejpam-6641	79	21	exists	exist	VERB
ejpam-6641	79	22	q0	q0	PROPN
ejpam-6641	79	23	∈	∈	PROPN
ejpam-6641	79	24	(	(	PUNCT
ejpam-6641	79	25	1,∞	1,∞	NUM
ejpam-6641	79	26	)	)	PUNCT
ejpam-6641	79	27	,	,	PUNCT
ejpam-6641	79	28	such	such	ADJ
ejpam-6641	79	29	that	that	SCONJ
ejpam-6641	79	30	|q(x)−	|q(x)−	ADJ
ejpam-6641	79	31	q0|	q0|	NOUN
ejpam-6641	79	32	≤	≤	NUM
ejpam-6641	79	33	c	c	AUX
ejpam-6641	79	34	ln	ln	ADJ
ejpam-6641	80	1	|x|	|x|	PROPN
ejpam-6641	80	2	,	,	PUNCT
ejpam-6641	80	3	|x|	|x|	PROPN
ejpam-6641	80	4	≤	≤	ADV
ejpam-6641	80	5	1	1	NUM
ejpam-6641	80	6	2	2	NUM
ejpam-6641	80	7	.	.	PUNCT
ejpam-6641	81	1	(	(	PUNCT
ejpam-6641	81	2	2.3	2.3	NUM
ejpam-6641	81	3	)	)	PUNCT
ejpam-6641	81	4	with	with	ADP
ejpam-6641	81	5	respect	respect	NOUN
ejpam-6641	81	6	to	to	ADP
ejpam-6641	81	7	classes	class	NOUN
ejpam-6641	81	8	of	of	ADP
ejpam-6641	81	9	variable	variable	ADJ
ejpam-6641	81	10	exponents	exponent	NOUN
ejpam-6641	81	11	used	use	VERB
ejpam-6641	81	12	in	in	ADP
ejpam-6641	81	13	this	this	DET
ejpam-6641	81	14	paper	paper	NOUN
ejpam-6641	81	15	,	,	PUNCT
ejpam-6641	81	16	we	we	PRON
ejpam-6641	81	17	adopt	adopt	VERB
ejpam-6641	81	18	the	the	DET
ejpam-6641	81	19	following	follow	VERB
ejpam-6641	81	20	notation	notation	NOUN
ejpam-6641	81	21	:	:	PUNCT
ejpam-6641	81	22	g.	g.	PROPN
ejpam-6641	81	23	a.	a.	PROPN
ejpam-6641	81	24	basendwah	basendwah	PROPN
ejpam-6641	81	25	et	et	PROPN
ejpam-6641	81	26	al	al	PROPN
ejpam-6641	81	27	.	.	PUNCT
ejpam-6641	81	28	/	/	SYM
ejpam-6641	81	29	eur	eur	PROPN
ejpam-6641	81	30	.	.	PUNCT
ejpam-6641	82	1	j.	j.	PROPN
ejpam-6641	82	2	pure	pure	PROPN
ejpam-6641	82	3	appl	appl	PROPN
ejpam-6641	82	4	.	.	PROPN
ejpam-6641	82	5	math	math	PROPN
ejpam-6641	82	6	,	,	PUNCT
ejpam-6641	82	7	18	18	NUM
ejpam-6641	82	8	(	(	PUNCT
ejpam-6641	82	9	4	4	NUM
ejpam-6641	82	10	)	)	PUNCT
ejpam-6641	82	11	(	(	PUNCT
ejpam-6641	82	12	2025	2025	NUM
ejpam-6641	82	13	)	)	PUNCT
ejpam-6641	82	14	,	,	PUNCT
ejpam-6641	82	15	6641	6641	NUM
ejpam-6641	82	16	5	5	NUM
ejpam-6641	82	17	of	of	ADP
ejpam-6641	82	18	16	16	NUM
ejpam-6641	82	19	(	(	PUNCT
ejpam-6641	82	20	i	i	NOUN
ejpam-6641	82	21	)	)	PUNCT
ejpam-6641	82	22	the	the	DET
ejpam-6641	82	23	set	set	NOUN
ejpam-6641	82	24	plog	plog	NOUN
ejpam-6641	82	25	=	=	SYM
ejpam-6641	82	26	plog(h	plog(h	NOUN
ejpam-6641	82	27	)	)	PUNCT
ejpam-6641	82	28	comprises	comprise	VERB
ejpam-6641	82	29	all	all	DET
ejpam-6641	82	30	functions	function	NOUN
ejpam-6641	82	31	q	q	PROPN
ejpam-6641	82	32	∈	∈	PROPN
ejpam-6641	82	33	l∞(h	l∞(h	NOUN
ejpam-6641	82	34	)	)	PUNCT
ejpam-6641	82	35	that	that	PRON
ejpam-6641	82	36	fulfill	fulfill	VERB
ejpam-6641	82	37	both	both	PRON
ejpam-6641	82	38	(	(	PUNCT
ejpam-6641	82	39	1.1	1.1	NUM
ejpam-6641	82	40	)	)	PUNCT
ejpam-6641	82	41	and	and	CCONJ
ejpam-6641	82	42	(	(	PUNCT
ejpam-6641	82	43	2.1	2.1	NUM
ejpam-6641	82	44	)	)	PUNCT
ejpam-6641	82	45	.	.	PUNCT
ejpam-6641	83	1	(	(	PUNCT
ejpam-6641	83	2	ii	ii	NOUN
ejpam-6641	83	3	)	)	PUNCT
ejpam-6641	83	4	whenh	whenh	NOUN
ejpam-6641	83	5	is	be	AUX
ejpam-6641	83	6	unbounded	unbounde	VERB
ejpam-6641	83	7	,	,	PUNCT
ejpam-6641	83	8	p∞(h	p∞(h	NOUN
ejpam-6641	83	9	)	)	PUNCT
ejpam-6641	83	10	and	and	CCONJ
ejpam-6641	83	11	p0,∞(h	p0,∞(h	PROPN
ejpam-6641	83	12	)	)	PUNCT
ejpam-6641	83	13	are	be	AUX
ejpam-6641	83	14	subsets	subset	NOUN
ejpam-6641	83	15	of	of	ADP
ejpam-6641	83	16	l∞(h	l∞(h	NOUN
ejpam-6641	83	17	)	)	PUNCT
ejpam-6641	83	18	.	.	PUNCT
ejpam-6641	84	1	the	the	DET
ejpam-6641	84	2	functions	function	NOUN
ejpam-6641	84	3	in	in	ADP
ejpam-6641	84	4	these	these	DET
ejpam-6641	84	5	sets	set	NOUN
ejpam-6641	84	6	take	take	VERB
ejpam-6641	84	7	values	value	NOUN
ejpam-6641	84	8	in	in	ADP
ejpam-6641	84	9	the	the	DET
ejpam-6641	84	10	interval	interval	NOUN
ejpam-6641	84	11	[	[	X
ejpam-6641	84	12	1,∞	1,∞	NUM
ejpam-6641	84	13	)	)	PUNCT
ejpam-6641	84	14	and	and	CCONJ
ejpam-6641	84	15	satisfy	satisfy	VERB
ejpam-6641	84	16	condition	condition	NOUN
ejpam-6641	84	17	(	(	PUNCT
ejpam-6641	84	18	2.2	2.2	NUM
ejpam-6641	84	19	)	)	PUNCT
ejpam-6641	84	20	,	,	PUNCT
ejpam-6641	84	21	and	and	CCONJ
ejpam-6641	84	22	(	(	PUNCT
ejpam-6641	84	23	2.2	2.2	NUM
ejpam-6641	84	24	)	)	PUNCT
ejpam-6641	84	25	and	and	CCONJ
ejpam-6641	84	26	(	(	PUNCT
ejpam-6641	84	27	2.3	2.3	NUM
ejpam-6641	84	28	)	)	PUNCT
ejpam-6641	84	29	,	,	PUNCT
ejpam-6641	84	30	respectively	respectively	ADV
ejpam-6641	84	31	.	.	PUNCT
ejpam-6641	85	1	(	(	PUNCT
ejpam-6641	85	2	iii	iii	NOUN
ejpam-6641	85	3	)	)	PUNCT
ejpam-6641	85	4	plog	plog	NOUN
ejpam-6641	85	5	∞	∞	PROPN
ejpam-6641	85	6	(	(	PUNCT
ejpam-6641	85	7	h	h	NOUN
ejpam-6641	85	8	)	)	PUNCT
ejpam-6641	85	9	is	be	AUX
ejpam-6641	85	10	the	the	DET
ejpam-6641	85	11	set	set	NOUN
ejpam-6641	85	12	consists	consist	VERB
ejpam-6641	85	13	of	of	ADP
ejpam-6641	85	14	exponents	exponent	NOUN
ejpam-6641	85	15	that	that	PRON
ejpam-6641	85	16	satisfy	satisfy	VERB
ejpam-6641	85	17	the	the	DET
ejpam-6641	85	18	condition	condition	NOUN
ejpam-6641	85	19	(	(	PUNCT
ejpam-6641	85	20	2.1	2.1	NUM
ejpam-6641	85	21	)	)	PUNCT
ejpam-6641	85	22	;	;	PUNCT
ejpam-6641	85	23	(	(	PUNCT
ejpam-6641	85	24	iv	iv	X
ejpam-6641	85	25	)	)	PUNCT
ejpam-6641	85	26	the	the	DET
ejpam-6641	85	27	notation	notation	NOUN
ejpam-6641	85	28	rµ+	rµ+	NOUN
ejpam-6641	85	29	represents	represent	VERB
ejpam-6641	85	30	the	the	DET
ejpam-6641	85	31	set	set	NOUN
ejpam-6641	85	32	of	of	ADP
ejpam-6641	85	33	all	all	DET
ejpam-6641	85	34	non	non	ADJ
ejpam-6641	85	35	-	-	ADJ
ejpam-6641	85	36	negative	negative	ADJ
ejpam-6641	85	37	real	real	ADJ
ejpam-6641	85	38	numbers	number	NOUN
ejpam-6641	85	39	.	.	PUNCT
ejpam-6641	86	1	m∞(rµ+	m∞(rµ+	X
ejpam-6641	86	2	)	)	PUNCT
ejpam-6641	86	3	is	be	AUX
ejpam-6641	86	4	the	the	DET
ejpam-6641	86	5	class	class	NOUN
ejpam-6641	86	6	consists	consist	VERB
ejpam-6641	86	7	of	of	ADP
ejpam-6641	86	8	functions	function	NOUN
ejpam-6641	86	9	defined	define	VERB
ejpam-6641	86	10	on	on	ADP
ejpam-6641	86	11	the	the	DET
ejpam-6641	86	12	domain	domain	NOUN
ejpam-6641	86	13	rµ+	rµ+	NOUN
ejpam-6641	86	14	that	that	PRON
ejpam-6641	86	15	have	have	VERB
ejpam-6641	86	16	certain	certain	ADJ
ejpam-6641	86	17	properties	property	NOUN
ejpam-6641	86	18	.	.	PUNCT
ejpam-6641	87	1	specifically	specifically	ADV
ejpam-6641	87	2	,	,	PUNCT
ejpam-6641	87	3	these	these	DET
ejpam-6641	87	4	functions	function	NOUN
ejpam-6641	87	5	are	be	AUX
ejpam-6641	87	6	of	of	ADP
ejpam-6641	87	7	the	the	DET
ejpam-6641	87	8	form	form	NOUN
ejpam-6641	87	9	g(t	g(t	PROPN
ejpam-6641	87	10	)	)	PUNCT
ejpam-6641	88	1	=	=	SYM
ejpam-6641	88	2	constant+	constant+	NOUN
ejpam-6641	88	3	g0(t	g0(t	NOUN
ejpam-6641	88	4	)	)	PUNCT
ejpam-6641	88	5	,	,	PUNCT
ejpam-6641	88	6	where	where	SCONJ
ejpam-6641	88	7	g0(t	g0(t	X
ejpam-6641	88	8	)	)	PUNCT
ejpam-6641	88	9	is	be	AUX
ejpam-6641	88	10	a	a	DET
ejpam-6641	88	11	function	function	NOUN
ejpam-6641	88	12	belonging	belong	VERB
ejpam-6641	88	13	to	to	ADP
ejpam-6641	88	14	the	the	DET
ejpam-6641	88	15	class	class	NOUN
ejpam-6641	88	16	p∞(rµ+	p∞(rµ+	NOUN
ejpam-6641	88	17	)	)	PUNCT
ejpam-6641	88	18	,	,	PUNCT
ejpam-6641	88	19	where	where	SCONJ
ejpam-6641	88	20	h	h	NOUN
ejpam-6641	88	21	=	=	SYM
ejpam-6641	88	22	rµ+	rµ+	PROPN
ejpam-6641	88	23	,	,	PUNCT
ejpam-6641	88	24	µ	µ	X
ejpam-6641	88	25	≥	≥	NOUN
ejpam-6641	88	26	0	0	NUM
ejpam-6641	88	27	.	.	PUNCT
ejpam-6641	89	1	(	(	PUNCT
ejpam-6641	89	2	v	v	NOUN
ejpam-6641	89	3	)	)	PUNCT
ejpam-6641	89	4	when	when	SCONJ
ejpam-6641	89	5	h	h	NOUN
ejpam-6641	89	6	=	=	PRON
ejpam-6641	89	7	r+	r+	X
ejpam-6641	89	8	(	(	PUNCT
ejpam-6641	89	9	or	or	CCONJ
ejpam-6641	89	10	when	when	SCONJ
ejpam-6641	89	11	µ	µ	X
ejpam-6641	89	12	=	=	SYM
ejpam-6641	89	13	0	0	NUM
ejpam-6641	89	14	)	)	PUNCT
ejpam-6641	89	15	,	,	PUNCT
ejpam-6641	89	16	m0,∞(r+	m0,∞(r+	PROPN
ejpam-6641	89	17	)	)	PUNCT
ejpam-6641	89	18	represents	represent	VERB
ejpam-6641	89	19	the	the	DET
ejpam-6641	89	20	class	class	NOUN
ejpam-6641	89	21	of	of	ADP
ejpam-6641	89	22	functions	function	NOUN
ejpam-6641	89	23	defined	define	VERB
ejpam-6641	89	24	on	on	ADP
ejpam-6641	89	25	the	the	DET
ejpam-6641	89	26	positive	positive	ADJ
ejpam-6641	89	27	real	real	ADJ
ejpam-6641	89	28	line	line	NOUN
ejpam-6641	89	29	r+	r+	NOUN
ejpam-6641	89	30	that	that	PRON
ejpam-6641	89	31	belong	belong	VERB
ejpam-6641	89	32	to	to	ADP
ejpam-6641	89	33	the	the	DET
ejpam-6641	89	34	class	class	NOUN
ejpam-6641	89	35	m∞(r+	m∞(r+	PROPN
ejpam-6641	89	36	)	)	PUNCT
ejpam-6641	89	37	and	and	CCONJ
ejpam-6641	89	38	meet	meet	VERB
ejpam-6641	89	39	a	a	DET
ejpam-6641	89	40	decay	decay	NOUN
ejpam-6641	89	41	criterion	criterion	NOUN
ejpam-6641	89	42	at	at	ADP
ejpam-6641	89	43	the	the	DET
ejpam-6641	89	44	origin	origin	NOUN
ejpam-6641	89	45	(	(	PUNCT
ejpam-6641	89	46	y	y	NOUN
ejpam-6641	89	47	=	=	PROPN
ejpam-6641	89	48	0	0	NUM
ejpam-6641	89	49	)	)	PUNCT
ejpam-6641	89	50	.	.	PUNCT
ejpam-6641	90	1	the	the	DET
ejpam-6641	90	2	decay	decay	NOUN
ejpam-6641	90	3	condition	condition	NOUN
ejpam-6641	90	4	implies	imply	VERB
ejpam-6641	90	5	that	that	SCONJ
ejpam-6641	90	6	these	these	DET
ejpam-6641	90	7	functions	function	NOUN
ejpam-6641	90	8	are	be	AUX
ejpam-6641	90	9	bounded	bound	VERB
ejpam-6641	90	10	by	by	ADP
ejpam-6641	90	11	a	a	DET
ejpam-6641	90	12	logarithmic	logarithmic	ADJ
ejpam-6641	90	13	term	term	NOUN
ejpam-6641	90	14	as	as	SCONJ
ejpam-6641	90	15	y	y	PROPN
ejpam-6641	90	16	approaches	approach	VERB
ejpam-6641	90	17	zero	zero	NUM
ejpam-6641	90	18	.	.	PUNCT
ejpam-6641	91	1	specifically	specifically	ADV
ejpam-6641	91	2	,	,	PUNCT
ejpam-6641	91	3	for	for	ADP
ejpam-6641	91	4	|y|	|y|	PROPN
ejpam-6641	91	5	≤	≤	NUM
ejpam-6641	91	6	1	1	NUM
ejpam-6641	91	7	2	2	NUM
ejpam-6641	91	8	,	,	PUNCT
ejpam-6641	91	9	the	the	DET
ejpam-6641	91	10	function	function	NOUN
ejpam-6641	91	11	satisfies	satisfy	VERB
ejpam-6641	91	12	the	the	DET
ejpam-6641	91	13	inequality	inequality	NOUN
ejpam-6641	91	14	|f(y)−f0|	|f(y)−f0|	PROPN
ejpam-6641	91	15	≤	≤	NUM
ejpam-6641	91	16	c	c	PROPN
ejpam-6641	91	17	ln	ln	PROPN
ejpam-6641	91	18	|y|	|y|	PROPN
ejpam-6641	91	19	for	for	ADP
ejpam-6641	91	20	some	some	DET
ejpam-6641	91	21	real	real	ADJ
ejpam-6641	91	22	numbers	number	NOUN
ejpam-6641	91	23	f0	f0	PROPN
ejpam-6641	91	24	and	and	CCONJ
ejpam-6641	91	25	c.	c.	NOUN
ejpam-6641	91	26	we	we	PRON
ejpam-6641	91	27	also	also	ADV
ejpam-6641	91	28	write	write	VERB
ejpam-6641	91	29	f0	f0	PROPN
ejpam-6641	91	30	=	=	SYM
ejpam-6641	91	31	f(0	f(0	NOUN
ejpam-6641	91	32	)	)	PUNCT
ejpam-6641	91	33	,	,	PUNCT
ejpam-6641	91	34	f∞	f∞	X
ejpam-6641	91	35	=	=	SYM
ejpam-6641	91	36	f(∞	f(∞	NOUN
ejpam-6641	91	37	)	)	PUNCT
ejpam-6641	91	38	in	in	ADP
ejpam-6641	91	39	this	this	DET
ejpam-6641	91	40	case	case	NOUN
ejpam-6641	91	41	;	;	PUNCT
ejpam-6641	91	42	(	(	PUNCT
ejpam-6641	91	43	vi	vi	NOUN
ejpam-6641	91	44	)	)	PUNCT
ejpam-6641	91	45	p0,∞(r+	p0,∞(r+	NOUN
ejpam-6641	91	46	)	)	PUNCT
ejpam-6641	91	47	is	be	AUX
ejpam-6641	91	48	a	a	DET
ejpam-6641	91	49	subclass	subclass	NOUN
ejpam-6641	91	50	of	of	ADP
ejpam-6641	91	51	functions	function	NOUN
ejpam-6641	91	52	within	within	ADP
ejpam-6641	91	53	the	the	DET
ejpam-6641	91	54	class	class	NOUN
ejpam-6641	91	55	m0,∞(r+	m0,∞(r+	PROPN
ejpam-6641	91	56	)	)	PUNCT
ejpam-6641	91	57	that	that	PRON
ejpam-6641	91	58	have	have	VERB
ejpam-6641	91	59	values	value	NOUN
ejpam-6641	91	60	in	in	ADP
ejpam-6641	91	61	the	the	DET
ejpam-6641	91	62	interval	interval	NOUN
ejpam-6641	91	63	[	[	X
ejpam-6641	91	64	1,∞	1,∞	NUM
ejpam-6641	91	65	)	)	PUNCT
ejpam-6641	91	66	.	.	PUNCT
ejpam-6641	92	1	in	in	ADP
ejpam-6641	92	2	other	other	ADJ
ejpam-6641	92	3	words	word	NOUN
ejpam-6641	92	4	,	,	PUNCT
ejpam-6641	92	5	these	these	PRON
ejpam-6641	92	6	are	be	AUX
ejpam-6641	92	7	the	the	DET
ejpam-6641	92	8	functions	function	NOUN
ejpam-6641	92	9	from	from	ADP
ejpam-6641	92	10	m0,∞(r+	m0,∞(r+	PROPN
ejpam-6641	92	11	)	)	PUNCT
ejpam-6641	92	12	that	that	PRON
ejpam-6641	92	13	satisfy	satisfy	VERB
ejpam-6641	92	14	the	the	DET
ejpam-6641	92	15	given	give	VERB
ejpam-6641	92	16	conditions	condition	NOUN
ejpam-6641	92	17	and	and	CCONJ
ejpam-6641	92	18	have	have	VERB
ejpam-6641	92	19	their	their	PRON
ejpam-6641	92	20	values	value	NOUN
ejpam-6641	92	21	constrained	constrain	VERB
ejpam-6641	92	22	within	within	ADP
ejpam-6641	92	23	the	the	DET
ejpam-6641	92	24	specified	specified	ADJ
ejpam-6641	92	25	range	range	NOUN
ejpam-6641	92	26	,	,	PUNCT
ejpam-6641	92	27	with	with	ADP
ejpam-6641	92	28	values	value	NOUN
ejpam-6641	92	29	in	in	ADP
ejpam-6641	92	30	[	[	X
ejpam-6641	92	31	1,∞	1,∞	NUM
ejpam-6641	92	32	)	)	PUNCT
ejpam-6641	92	33	.	.	PUNCT
ejpam-6641	93	1	hölder	hölder	PROPN
ejpam-6641	93	2	’s	’s	PART
ejpam-6641	93	3	inequality	inequality	NOUN
ejpam-6641	93	4	in	in	ADP
ejpam-6641	93	5	variable	variable	ADJ
ejpam-6641	93	6	lebesgue	lebesgue	NOUN
ejpam-6641	93	7	spaces	space	NOUN
ejpam-6641	93	8	are	be	AUX
ejpam-6641	93	9	stated	state	VERB
ejpam-6641	93	10	as	as	ADP
ejpam-6641	93	11	∥fg∥r	∥fg∥r	NOUN
ejpam-6641	93	12	(	(	PUNCT
ejpam-6641	93	13	·	·	PUNCT
ejpam-6641	93	14	)	)	PUNCT
ejpam-6641	93	15	≤	≤	PUNCT
ejpam-6641	93	16	∥f∥p(·)∥g∥q	∥f∥p(·)∥g∥q	PROPN
ejpam-6641	93	17	(	(	PUNCT
ejpam-6641	93	18	·	·	PUNCT
ejpam-6641	93	19	)	)	PUNCT
ejpam-6641	93	20	,	,	PUNCT
ejpam-6641	93	21	where	where	SCONJ
ejpam-6641	93	22	we	we	PRON
ejpam-6641	93	23	define	define	VERB
ejpam-6641	93	24	r	r	NOUN
ejpam-6641	93	25	as	as	ADP
ejpam-6641	93	26	1	1	NUM
ejpam-6641	93	27	r(i	r(i	NOUN
ejpam-6641	93	28	)	)	PUNCT
ejpam-6641	93	29	=	=	PUNCT
ejpam-6641	93	30	1	1	NUM
ejpam-6641	93	31	p(i	p(i	PROPN
ejpam-6641	93	32	)	)	PUNCT
ejpam-6641	94	1	+	+	CCONJ
ejpam-6641	94	2	1	1	NUM
ejpam-6641	94	3	q(i	q(i	NOUN
ejpam-6641	94	4	)	)	PUNCT
ejpam-6641	94	5	for	for	ADP
ejpam-6641	94	6	every	every	DET
ejpam-6641	94	7	i	i	PROPN
ejpam-6641	94	8	∈	∈	PROPN
ejpam-6641	94	9	h	h	NOUN
ejpam-6641	94	10	,	,	PUNCT
ejpam-6641	94	11	and	and	CCONJ
ejpam-6641	94	12	p	p	X
ejpam-6641	94	13	,	,	PUNCT
ejpam-6641	94	14	q	q	INTJ
ejpam-6641	94	15	,	,	PUNCT
ejpam-6641	94	16	r	r	NOUN
ejpam-6641	94	17	∈	∈	PROPN
ejpam-6641	94	18	p(rn	p(rn	PROPN
ejpam-6641	94	19	)	)	PUNCT
ejpam-6641	94	20	the	the	DET
ejpam-6641	94	21	set	set	NOUN
ejpam-6641	94	22	b(rn	b(rn	NOUN
ejpam-6641	94	23	)	)	PUNCT
ejpam-6641	94	24	is	be	AUX
ejpam-6641	94	25	comprised	comprise	VERB
ejpam-6641	94	26	of	of	ADP
ejpam-6641	94	27	p	p	X
ejpam-6641	94	28	(	(	PUNCT
ejpam-6641	94	29	·	·	PUNCT
ejpam-6641	94	30	)	)	PUNCT
ejpam-6641	94	31	∈	∈	PROPN
ejpam-6641	94	32	p(rn	p(rn	PROPN
ejpam-6641	94	33	)	)	PUNCT
ejpam-6641	94	34	that	that	PRON
ejpam-6641	94	35	fulfill	fulfill	VERB
ejpam-6641	94	36	the	the	DET
ejpam-6641	94	37	requirement	requirement	NOUN
ejpam-6641	94	38	that	that	SCONJ
ejpam-6641	94	39	m	m	PROPN
ejpam-6641	94	40	is	be	AUX
ejpam-6641	94	41	bounded	bound	VERB
ejpam-6641	94	42	on	on	ADP
ejpam-6641	94	43	lp(·)(rn	lp(·)(rn	PROPN
ejpam-6641	94	44	)	)	PUNCT
ejpam-6641	94	45	.	.	PUNCT
ejpam-6641	95	1	lemma	lemma	PROPN
ejpam-6641	95	2	1	1	NUM
ejpam-6641	95	3	.	.	PUNCT
ejpam-6641	96	1	[	[	X
ejpam-6641	96	2	13	13	NUM
ejpam-6641	96	3	]	]	PUNCT
ejpam-6641	96	4	suppose	suppose	VERB
ejpam-6641	96	5	0	0	PUNCT
ejpam-6641	96	6	<	<	X
ejpam-6641	96	7	s	s	X
ejpam-6641	96	8	≤	≤	NUM
ejpam-6641	96	9	1	1	NUM
ejpam-6641	96	10	,	,	PUNCT
ejpam-6641	96	11	t0	t0	PROPN
ejpam-6641	96	12	≥	≥	NUM
ejpam-6641	96	13	1	1	NUM
ejpam-6641	96	14	,	,	PUNCT
ejpam-6641	96	15	t∞	t∞	NUM
ejpam-6641	96	16	≥	≥	NUM
ejpam-6641	96	17	1	1	NUM
ejpam-6641	96	18	,	,	PUNCT
ejpam-6641	96	19	p	p	PROPN
ejpam-6641	96	20	∈	∈	PROPN
ejpam-6641	96	21	p0,∞(rn	p0,∞(rn	NUM
ejpam-6641	96	22	)	)	PUNCT
ejpam-6641	96	23	and	and	CCONJ
ejpam-6641	96	24	d	d	X
ejpam-6641	96	25	>	>	X
ejpam-6641	96	26	1	1	NUM
ejpam-6641	97	1	such	such	ADJ
ejpam-6641	97	2	that	that	DET
ejpam-6641	97	3	d	d	NOUN
ejpam-6641	97	4	but	but	CCONJ
ejpam-6641	97	5	not	not	PART
ejpam-6641	97	6	on	on	ADP
ejpam-6641	97	7	s.	s.	PROPN
ejpam-6641	97	8	then	then	ADV
ejpam-6641	97	9	,	,	PUNCT
ejpam-6641	97	10	for	for	SCONJ
ejpam-6641	97	11	we	we	PRON
ejpam-6641	97	12	have	have	VERB
ejpam-6641	97	13	:	:	PUNCT
ejpam-6641	97	14	1	1	NUM
ejpam-6641	97	15	t0	t0	NOUN
ejpam-6641	97	16	s	s	VERB
ejpam-6641	97	17	n	n	PRON
ejpam-6641	97	18	p(0	p(0	NOUN
ejpam-6641	97	19	)	)	PUNCT
ejpam-6641	97	20	≤	≤	NOUN
ejpam-6641	98	1	∥1ts	∥1t	VERB
ejpam-6641	98	2	,	,	PUNCT
ejpam-6641	98	3	ds	ds	ADJ
ejpam-6641	98	4	∥p	∥p	ADJ
ejpam-6641	98	5	(	(	PUNCT
ejpam-6641	98	6	·	·	PUNCT
ejpam-6641	98	7	)	)	PUNCT
ejpam-6641	98	8	≤	≤	NOUN
ejpam-6641	99	1	t0s	t0s	ADJ
ejpam-6641	99	2	n	n	PRON
ejpam-6641	99	3	p(0	p(0	NOUN
ejpam-6641	99	4	)	)	PUNCT
ejpam-6641	99	5	.	.	PUNCT
ejpam-6641	100	1	(	(	PUNCT
ejpam-6641	100	2	2.4	2.4	NUM
ejpam-6641	100	3	)	)	PUNCT
ejpam-6641	100	4	similarly	similarly	ADV
ejpam-6641	100	5	,	,	PUNCT
ejpam-6641	100	6	for	for	ADP
ejpam-6641	100	7	s	s	PRON
ejpam-6641	100	8	≥	≥	NOUN
ejpam-6641	100	9	1	1	NUM
ejpam-6641	100	10	,	,	PUNCT
ejpam-6641	100	11	we	we	PRON
ejpam-6641	100	12	get	get	VERB
ejpam-6641	100	13	:	:	PUNCT
ejpam-6641	100	14	1	1	NUM
ejpam-6641	100	15	t∞	t∞	NOUN
ejpam-6641	100	16	s	s	NOUN
ejpam-6641	100	17	n	n	PRON
ejpam-6641	100	18	p∞	p∞	PROPN
ejpam-6641	100	19	≤	≤	NOUN
ejpam-6641	101	1	∥1ts	∥1t	VERB
ejpam-6641	101	2	,	,	PUNCT
ejpam-6641	101	3	ds	ds	ADJ
ejpam-6641	101	4	∥p	∥p	ADJ
ejpam-6641	101	5	(	(	PUNCT
ejpam-6641	101	6	·	·	PUNCT
ejpam-6641	101	7	)	)	PUNCT
ejpam-6641	101	8	≤	≤	NUM
ejpam-6641	101	9	t∞s	t∞s	NOUN
ejpam-6641	101	10	n	n	X
ejpam-6641	101	11	p∞	p∞	PROPN
ejpam-6641	101	12	.	.	PUNCT
ejpam-6641	102	1	(	(	PUNCT
ejpam-6641	102	2	2.5	2.5	NUM
ejpam-6641	102	3	)	)	PUNCT
ejpam-6641	102	4	g.	g.	PROPN
ejpam-6641	102	5	a.	a.	PROPN
ejpam-6641	102	6	basendwah	basendwah	PROPN
ejpam-6641	102	7	et	et	PROPN
ejpam-6641	102	8	al	al	PROPN
ejpam-6641	102	9	.	.	PUNCT
ejpam-6641	102	10	/	/	SYM
ejpam-6641	102	11	eur	eur	PROPN
ejpam-6641	102	12	.	.	PUNCT
ejpam-6641	103	1	j.	j.	PROPN
ejpam-6641	103	2	pure	pure	PROPN
ejpam-6641	103	3	appl	appl	PROPN
ejpam-6641	103	4	.	.	PROPN
ejpam-6641	103	5	math	math	PROPN
ejpam-6641	103	6	,	,	PUNCT
ejpam-6641	103	7	18	18	NUM
ejpam-6641	103	8	(	(	PUNCT
ejpam-6641	103	9	4	4	NUM
ejpam-6641	103	10	)	)	PUNCT
ejpam-6641	103	11	(	(	PUNCT
ejpam-6641	103	12	2025	2025	NUM
ejpam-6641	103	13	)	)	PUNCT
ejpam-6641	103	14	,	,	PUNCT
ejpam-6641	103	15	6641	6641	NUM
ejpam-6641	103	16	6	6	NUM
ejpam-6641	103	17	of	of	ADP
ejpam-6641	103	18	16	16	NUM
ejpam-6641	103	19	definition	definition	NOUN
ejpam-6641	103	20	1	1	NUM
ejpam-6641	103	21	.	.	PUNCT
ejpam-6641	104	1	if	if	SCONJ
ejpam-6641	104	2	rµ+	rµ+	PROPN
ejpam-6641	104	3	,	,	PUNCT
ejpam-6641	104	4	µ	µ	PRON
ejpam-6641	104	5	≥	≥	NOUN
ejpam-6641	104	6	0	0	NUM
ejpam-6641	104	7	and	and	CCONJ
ejpam-6641	104	8	dt	dt	PROPN
ejpam-6641	104	9	t	t	PROPN
ejpam-6641	104	10	denotes	denote	VERB
ejpam-6641	104	11	the	the	DET
ejpam-6641	104	12	haar	haar	NOUN
ejpam-6641	104	13	measure	measure	NOUN
ejpam-6641	104	14	,	,	PUNCT
ejpam-6641	104	15	norm	norm	NOUN
ejpam-6641	104	16	of	of	ADP
ejpam-6641	104	17	lebesgue	lebesgue	NOUN
ejpam-6641	104	18	spaces	space	NOUN
ejpam-6641	104	19	with	with	ADP
ejpam-6641	104	20	haar	haar	NOUN
ejpam-6641	104	21	measure	measure	NOUN
ejpam-6641	104	22	is	be	AUX
ejpam-6641	104	23	defined	define	VERB
ejpam-6641	104	24	as	as	ADP
ejpam-6641	104	25	,	,	PUNCT
ejpam-6641	104	26	∥g∥lq(·)(rµ+	∥g∥lq(·)(rµ+	PROPN
ejpam-6641	104	27	;	;	PUNCT
ejpam-6641	104	28	dt	dt	PROPN
ejpam-6641	104	29	t	t	NOUN
ejpam-6641	104	30	)	)	PUNCT
ejpam-6641	105	1	=	=	SYM
ejpam-6641	105	2	inf	inf	PROPN
ejpam-6641	105	3	γ	γ	NOUN
ejpam-6641	105	4	>	>	X
ejpam-6641	105	5	0	0	PUNCT
ejpam-6641	106	1	:	:	PUNCT
ejpam-6641	106	2	∞∫	∞∫	PROPN
ejpam-6641	106	3	µ	µ	PROPN
ejpam-6641	106	4	∣∣∣∣g(t)γ	∣∣∣∣g(t)γ	PROPN
ejpam-6641	106	5	∣∣∣∣q(t	∣∣∣∣q(t	PROPN
ejpam-6641	106	6	)	)	PUNCT
ejpam-6641	106	7	dtt	dtt	NOUN
ejpam-6641	106	8	≤	≤	NUM
ejpam-6641	106	9	1	1	NUM
ejpam-6641	106	10			NOUN
ejpam-6641	106	11	.	.	PUNCT
ejpam-6641	107	1	let	let	VERB
ejpam-6641	107	2	hω(j	hω(j	PUNCT
ejpam-6641	107	3	)	)	PUNCT
ejpam-6641	108	1	=	=	SYM
ejpam-6641	108	2	∞∫	∞∫	NOUN
ejpam-6641	108	3	0	0	PUNCT
ejpam-6641	109	1	k	k	PROPN
ejpam-6641	109	2	(	(	PUNCT
ejpam-6641	109	3	j	j	PROPN
ejpam-6641	109	4	θ	θ	PROPN
ejpam-6641	109	5	)	)	PUNCT
ejpam-6641	109	6	ω(θ	ω(θ	NUM
ejpam-6641	109	7	)	)	PUNCT
ejpam-6641	109	8	dθ	dθ	PROPN
ejpam-6641	109	9	θ	θ	PROPN
ejpam-6641	109	10	.	.	PUNCT
ejpam-6641	110	1	(	(	PUNCT
ejpam-6641	110	2	2.6	2.6	NUM
ejpam-6641	110	3	)	)	PUNCT
ejpam-6641	110	4	this	this	PRON
ejpam-6641	110	5	is	be	AUX
ejpam-6641	110	6	an	an	DET
ejpam-6641	110	7	integral	integral	ADJ
ejpam-6641	110	8	operator	operator	NOUN
ejpam-6641	110	9	referred	refer	VERB
ejpam-6641	110	10	to	to	ADP
ejpam-6641	110	11	as	as	ADP
ejpam-6641	110	12	the	the	DET
ejpam-6641	110	13	mellin	mellin	PROPN
ejpam-6641	110	14	convolution	convolution	NOUN
ejpam-6641	110	15	operator	operator	NOUN
ejpam-6641	110	16	,	,	PUNCT
ejpam-6641	110	17	employing	employ	VERB
ejpam-6641	110	18	haar	haar	NOUN
ejpam-6641	110	19	measure	measure	NOUN
ejpam-6641	110	20	dθ	dθ	PROPN
ejpam-6641	110	21	θ	θ	PROPN
ejpam-6641	110	22	and	and	CCONJ
ejpam-6641	110	23	featuring	feature	VERB
ejpam-6641	110	24	a	a	DET
ejpam-6641	110	25	kernel	kernel	NOUN
ejpam-6641	110	26	homogeneous	homogeneous	ADJ
ejpam-6641	110	27	of	of	ADP
ejpam-6641	110	28	order	order	NOUN
ejpam-6641	110	29	0	0	X
ejpam-6641	110	30	.	.	PUNCT
ejpam-6641	111	1	lemma	lemma	PROPN
ejpam-6641	111	2	2	2	NUM
ejpam-6641	111	3	.	.	PUNCT
ejpam-6641	112	1	(	(	PUNCT
ejpam-6641	112	2	see	see	VERB
ejpam-6641	112	3	[	[	X
ejpam-6641	112	4	13	13	NUM
ejpam-6641	112	5	]	]	PUNCT
ejpam-6641	112	6	)	)	PUNCT
ejpam-6641	112	7	let	let	VERB
ejpam-6641	112	8	p	p	X
ejpam-6641	112	9	∈	∈	NOUN
ejpam-6641	112	10	p0,∞(r+	p0,∞(r+	NOUN
ejpam-6641	112	11	)	)	PUNCT
ejpam-6641	112	12	and	and	CCONJ
ejpam-6641	112	13	p(0	p(0	NOUN
ejpam-6641	112	14	)	)	PUNCT
ejpam-6641	112	15	=	=	SYM
ejpam-6641	112	16	p(∞	p(∞	PROPN
ejpam-6641	112	17	)	)	PUNCT
ejpam-6641	112	18	.	.	PUNCT
ejpam-6641	113	1	the	the	DET
ejpam-6641	113	2	operator	operator	NOUN
ejpam-6641	113	3	h	h	NOUN
ejpam-6641	113	4	is	be	AUX
ejpam-6641	113	5	bounded	bound	VERB
ejpam-6641	113	6	on	on	ADP
ejpam-6641	113	7	lp(·)(r+	lp(·)(r+	PROPN
ejpam-6641	113	8	;	;	PUNCT
ejpam-6641	113	9	dt	dt	PROPN
ejpam-6641	113	10	t	t	PROPN
ejpam-6641	113	11	)	)	PUNCT
ejpam-6641	113	12	if	if	SCONJ
ejpam-6641	113	13	∞∫	∞∫	PROPN
ejpam-6641	113	14	0	0	NUM
ejpam-6641	113	15	|h(t)|sdt	|h(t)|sdt	NOUN
ejpam-6641	113	16	t	t	NOUN
ejpam-6641	113	17	<	<	X
ejpam-6641	113	18	∞	∞	NUM
ejpam-6641	113	19	when	when	SCONJ
ejpam-6641	113	20	s	s	VERB
ejpam-6641	113	21	=	=	SYM
ejpam-6641	113	22	1	1	NUM
ejpam-6641	113	23	&	&	CCONJ
ejpam-6641	113	24	s	s	PART
ejpam-6641	113	25	=	=	SYM
ejpam-6641	113	26	s0	s0	PROPN
ejpam-6641	113	27	,	,	PUNCT
ejpam-6641	113	28	(	(	PUNCT
ejpam-6641	113	29	2.7	2.7	NUM
ejpam-6641	113	30	)	)	PUNCT
ejpam-6641	113	31	for	for	ADP
ejpam-6641	113	32	1	1	NUM
ejpam-6641	113	33	s0	s0	NOUN
ejpam-6641	113	34	=	=	SYM
ejpam-6641	113	35	1−	1−	NUM
ejpam-6641	113	36	1	1	NUM
ejpam-6641	113	37	p−	p−	NOUN
ejpam-6641	113	38	+	+	SYM
ejpam-6641	113	39	1	1	NUM
ejpam-6641	113	40	p+	p+	NOUN
ejpam-6641	113	41	.	.	PUNCT
ejpam-6641	114	1	lemma	lemma	PROPN
ejpam-6641	114	2	3	3	X
ejpam-6641	114	3	.	.	PUNCT
ejpam-6641	115	1	(	(	PUNCT
ejpam-6641	115	2	see	see	VERB
ejpam-6641	115	3	[	[	X
ejpam-6641	115	4	13	13	NUM
ejpam-6641	115	5	]	]	PUNCT
ejpam-6641	115	6	)	)	PUNCT
ejpam-6641	115	7	for	for	ADP
ejpam-6641	115	8	every	every	DET
ejpam-6641	115	9	measurable	measurable	ADJ
ejpam-6641	115	10	function	function	NOUN
ejpam-6641	115	11	ω	ω	PROPN
ejpam-6641	115	12	,	,	PUNCT
ejpam-6641	115	13	the	the	DET
ejpam-6641	115	14	following	follow	VERB
ejpam-6641	115	15	relations∫	relations∫	X
ejpam-6641	115	16	2b<|x|<j	2b<|x|<j	NUM
ejpam-6641	115	17	|ω(x)|dx	|ω(x)|dx	PUNCT
ejpam-6641	116	1	=	=	SYM
ejpam-6641	116	2	1	1	NUM
ejpam-6641	116	3	ln	ln	NOUN
ejpam-6641	116	4	2	2	NUM
ejpam-6641	116	5	∫	∫	NOUN
ejpam-6641	116	6	t	t	PROPN
ejpam-6641	116	7	b	b	PROPN
ejpam-6641	116	8	dθ	dθ	PROPN
ejpam-6641	116	9	θ	θ	PROPN
ejpam-6641	116	10	∫	∫	PROPN
ejpam-6641	116	11	max(2b	max(2b	NOUN
ejpam-6641	116	12	,	,	PUNCT
ejpam-6641	116	13	θ)<|x|<min(j,2θ	θ)<|x|<min(j,2θ	NOUN
ejpam-6641	116	14	)	)	PUNCT
ejpam-6641	116	15	|ω(x)|dx	|ω(x)|dx	PROPN
ejpam-6641	116	16	,	,	PUNCT
ejpam-6641	116	17	j	j	PROPN
ejpam-6641	116	18	>	>	X
ejpam-6641	116	19	2κ	2κ	NOUN
ejpam-6641	116	20	>	>	X
ejpam-6641	116	21	0	0	NUM
ejpam-6641	116	22	,	,	PUNCT
ejpam-6641	116	23	(	(	PUNCT
ejpam-6641	116	24	2.8	2.8	NUM
ejpam-6641	116	25	)	)	PUNCT
ejpam-6641	116	26	and	and	CCONJ
ejpam-6641	116	27	∫	∫	PROPN
ejpam-6641	116	28	|x|≥2j	|x|≥2j	ADJ
ejpam-6641	116	29	|ω(x)|dx	|ω(x)|dx	PUNCT
ejpam-6641	117	1	=	=	SYM
ejpam-6641	117	2	1	1	NUM
ejpam-6641	117	3	ln	ln	NOUN
ejpam-6641	117	4	2	2	NUM
ejpam-6641	117	5	∫	∫	NOUN
ejpam-6641	117	6	∞	∞	PROPN
ejpam-6641	117	7	t	t	PROPN
ejpam-6641	117	8	dθ	dθ	PROPN
ejpam-6641	117	9	θ	θ	PROPN
ejpam-6641	117	10	∫	∫	PROPN
ejpam-6641	118	1	max(θ,2j)<|x|<2θ	max(θ,2j)<|x|<2θ	NOUN
ejpam-6641	118	2	|ω(x)|dx	|ω(x)|dx	PROPN
ejpam-6641	118	3	,	,	PUNCT
ejpam-6641	118	4	j	j	PROPN
ejpam-6641	118	5	>	>	X
ejpam-6641	118	6	0	0	NUM
ejpam-6641	118	7	.	.	PUNCT
ejpam-6641	119	1	(	(	PUNCT
ejpam-6641	119	2	2.9	2.9	NUM
ejpam-6641	119	3	)	)	PUNCT
ejpam-6641	119	4	these	these	DET
ejpam-6641	119	5	conditions	condition	NOUN
ejpam-6641	119	6	are	be	AUX
ejpam-6641	119	7	valid	valid	ADJ
ejpam-6641	119	8	provided	provide	VERB
ejpam-6641	119	9	that	that	SCONJ
ejpam-6641	119	10	the	the	DET
ejpam-6641	119	11	integrals	integral	NOUN
ejpam-6641	119	12	on	on	ADP
ejpam-6641	119	13	the	the	DET
ejpam-6641	119	14	left	left	ADJ
ejpam-6641	119	15	-	-	PUNCT
ejpam-6641	119	16	hand	hand	NOUN
ejpam-6641	119	17	side	side	NOUN
ejpam-6641	119	18	of	of	ADP
ejpam-6641	119	19	the	the	DET
ejpam-6641	119	20	above	above	ADJ
ejpam-6641	119	21	expressions	expression	NOUN
ejpam-6641	119	22	exist	exist	VERB
ejpam-6641	119	23	.	.	PUNCT
ejpam-6641	120	1	3	3	X
ejpam-6641	120	2	.	.	X
ejpam-6641	120	3	continual	continual	ADJ
ejpam-6641	120	4	herz	herz	PROPN
ejpam-6641	120	5	spaces	space	NOUN
ejpam-6641	120	6	with	with	ADP
ejpam-6641	120	7	variable	variable	ADJ
ejpam-6641	120	8	exponent	exponent	NOUN
ejpam-6641	120	9	definition	definition	NOUN
ejpam-6641	120	10	2	2	X
ejpam-6641	120	11	.	.	PUNCT
ejpam-6641	121	1	we	we	PRON
ejpam-6641	121	2	can	can	AUX
ejpam-6641	121	3	define	define	VERB
ejpam-6641	121	4	continual	continual	ADJ
ejpam-6641	121	5	herz	herz	PROPN
ejpam-6641	121	6	spaces	space	NOUN
ejpam-6641	121	7	with	with	ADP
ejpam-6641	121	8	variable	variable	ADJ
ejpam-6641	121	9	exponents	exponent	NOUN
ejpam-6641	121	10	h	h	PROPN
ejpam-6641	121	11	p(·),q(·),κ	p(·),q(·),κ	ADV
ejpam-6641	121	12	(	(	PUNCT
ejpam-6641	121	13	·	·	PUNCT
ejpam-6641	121	14	)	)	PUNCT
ejpam-6641	122	1	µ,δ	µ,δ	PROPN
ejpam-6641	122	2	(	(	PUNCT
ejpam-6641	122	3	rn	rn	NOUN
ejpam-6641	122	4	)	)	PUNCT
ejpam-6641	122	5	by	by	ADP
ejpam-6641	122	6	its	its	PRON
ejpam-6641	122	7	norm	norm	NOUN
ejpam-6641	122	8	,	,	PUNCT
ejpam-6641	122	9	∥g∥	∥g∥	PROPN
ejpam-6641	122	10	h	h	NOUN
ejpam-6641	122	11	p(·),q(·),κ	p(·),q(·),κ	ADP
ejpam-6641	122	12	(	(	PUNCT
ejpam-6641	122	13	·	·	PUNCT
ejpam-6641	122	14	)	)	PUNCT
ejpam-6641	122	15	µ,δ	µ,δ	PROPN
ejpam-6641	122	16	(	(	PUNCT
ejpam-6641	122	17	rn	rn	NOUN
ejpam-6641	122	18	)	)	PUNCT
ejpam-6641	122	19	:	:	PUNCT
ejpam-6641	122	20	=	=	PUNCT
ejpam-6641	122	21	∥g∥lp(·)(o(0,γµ+θ	∥g∥lp(·)(o(0,γµ+θ	ADV
ejpam-6641	122	22	)	)	PUNCT
ejpam-6641	122	23	)	)	PUNCT
ejpam-6641	123	1	+	+	CCONJ
ejpam-6641	124	1	∥tκ(t)∥g1rγt	∥tκ(t)∥g1rγt	NUM
ejpam-6641	124	2	,	,	PUNCT
ejpam-6641	124	3	δt	δt	X
ejpam-6641	124	4	∥lp(·)∥lq(·)((γµ,∞	∥lp(·)∥lq(·)((γµ,∞	PROPN
ejpam-6641	124	5	)	)	PUNCT
ejpam-6641	124	6	;	;	PUNCT
ejpam-6641	124	7	dt	dt	PROPN
ejpam-6641	124	8	t	t	PROPN
ejpam-6641	124	9	<	<	X
ejpam-6641	124	10	∞.	∞.	PROPN
ejpam-6641	124	11	(	(	PUNCT
ejpam-6641	124	12	3.1	3.1	NUM
ejpam-6641	124	13	)	)	PUNCT
ejpam-6641	124	14	these	these	DET
ejpam-6641	124	15	lemmas	lemma	NOUN
ejpam-6641	124	16	are	be	AUX
ejpam-6641	124	17	already	already	ADV
ejpam-6641	124	18	proved	prove	VERB
ejpam-6641	124	19	in	in	ADP
ejpam-6641	124	20	[	[	X
ejpam-6641	124	21	13	13	NUM
ejpam-6641	124	22	]	]	PUNCT
ejpam-6641	124	23	.	.	PUNCT
ejpam-6641	125	1	lemma	lemma	PROPN
ejpam-6641	125	2	4	4	X
ejpam-6641	125	3	.	.	PUNCT
ejpam-6641	126	1	let	let	VERB
ejpam-6641	126	2	4	4	NUM
ejpam-6641	126	3	≤	≤	NOUN
ejpam-6641	126	4	r	r	NOUN
ejpam-6641	126	5	<	<	X
ejpam-6641	126	6	∞	∞	NUM
ejpam-6641	126	7	and	and	CCONJ
ejpam-6641	126	8	0	0	NUM
ejpam-6641	126	9	<	<	X
ejpam-6641	126	10	ρ	ρ	X
ejpam-6641	126	11	<	<	X
ejpam-6641	126	12	2	2	NUM
ejpam-6641	126	13	∥g∥lp(·)(o(0,r)\o(0,2+θ	∥g∥lp(·)(o(0,r)\o(0,2+θ	NUM
ejpam-6641	126	14	)	)	PUNCT
ejpam-6641	126	15	)	)	PUNCT
ejpam-6641	127	1	≤	≤	PROPN
ejpam-6641	127	2	c(ρ	c(ρ	PROPN
ejpam-6641	127	3	,	,	PUNCT
ejpam-6641	127	4	r)∥jκ(j)∥g1j,2j∥lp(·)∥lq((2,∞	r)∥jκ(j)∥g1j,2j∥lp(·)∥lq((2,∞	NOUN
ejpam-6641	127	5	)	)	PUNCT
ejpam-6641	127	6	;	;	PUNCT
ejpam-6641	127	7	dj	dj	PROPN
ejpam-6641	127	8	j	j	PROPN
ejpam-6641	127	9	)	)	PUNCT
ejpam-6641	127	10	.	.	PUNCT
ejpam-6641	128	1	g.	g.	PROPN
ejpam-6641	128	2	a.	a.	PROPN
ejpam-6641	128	3	basendwah	basendwah	PROPN
ejpam-6641	128	4	et	et	PROPN
ejpam-6641	128	5	al	al	PROPN
ejpam-6641	128	6	.	.	PUNCT
ejpam-6641	128	7	/	/	SYM
ejpam-6641	128	8	eur	eur	PROPN
ejpam-6641	128	9	.	.	PUNCT
ejpam-6641	129	1	j.	j.	PROPN
ejpam-6641	129	2	pure	pure	PROPN
ejpam-6641	129	3	appl	appl	PROPN
ejpam-6641	129	4	.	.	PROPN
ejpam-6641	129	5	math	math	PROPN
ejpam-6641	129	6	,	,	PUNCT
ejpam-6641	129	7	18	18	NUM
ejpam-6641	129	8	(	(	PUNCT
ejpam-6641	129	9	4	4	NUM
ejpam-6641	129	10	)	)	PUNCT
ejpam-6641	129	11	(	(	PUNCT
ejpam-6641	129	12	2025	2025	NUM
ejpam-6641	129	13	)	)	PUNCT
ejpam-6641	129	14	,	,	PUNCT
ejpam-6641	129	15	6641	6641	NUM
ejpam-6641	129	16	7	7	NUM
ejpam-6641	129	17	of	of	ADP
ejpam-6641	129	18	16	16	NUM
ejpam-6641	129	19	lemma	lemma	PROPN
ejpam-6641	129	20	5	5	NUM
ejpam-6641	129	21	.	.	PUNCT
ejpam-6641	130	1	let	let	VERB
ejpam-6641	130	2	1	1	NUM
ejpam-6641	130	3	≤	≤	NOUN
ejpam-6641	130	4	p−	p−	NOUN
ejpam-6641	130	5	≤	≤	NUM
ejpam-6641	130	6	p(x	p(x	PROPN
ejpam-6641	130	7	)	)	PUNCT
ejpam-6641	130	8	≤	≤	NOUN
ejpam-6641	130	9	p+	p+	VERB
ejpam-6641	130	10	<	<	X
ejpam-6641	130	11	∞	∞	NUM
ejpam-6641	130	12	holds	hold	NOUN
ejpam-6641	130	13	,	,	PUNCT
ejpam-6641	130	14	∥g∥	∥g∥	PROPN
ejpam-6641	130	15	h	h	PROPN
ejpam-6641	130	16	p(·),q	p(·),q	PROPN
ejpam-6641	130	17	,	,	PUNCT
ejpam-6641	130	18	κ	κ	X
ejpam-6641	130	19	(	(	PUNCT
ejpam-6641	130	20	·	·	PUNCT
ejpam-6641	130	21	)	)	PUNCT
ejpam-6641	131	1	µ,δ	µ,δ	INTJ
ejpam-6641	131	2	≈	≈	PROPN
ejpam-6641	131	3	∥g∥lp(·)(o(0,γµ+θ	∥g∥lp(·)(o(0,γµ+θ	ADV
ejpam-6641	131	4	)	)	PUNCT
ejpam-6641	131	5	)	)	PUNCT
ejpam-6641	132	1	+	+	CCONJ
ejpam-6641	132	2	∥tκ∞∥g1tγt	∥tκ∞∥g1tγt	PROPN
ejpam-6641	132	3	,	,	PUNCT
ejpam-6641	132	4	δt∥lp(·)∥lq(r+.µ	δt∥lp(·)∥lq(r+.µ	X
ejpam-6641	132	5	;	;	PUNCT
ejpam-6641	132	6	dt	dt	PROPN
ejpam-6641	132	7	t	t	PROPN
ejpam-6641	132	8	)	)	PUNCT
ejpam-6641	132	9	,	,	PUNCT
ejpam-6641	132	10	µ	µ	X
ejpam-6641	132	11	>	>	X
ejpam-6641	132	12	0	0	NUM
ejpam-6641	132	13	,	,	PUNCT
ejpam-6641	132	14	(	(	PUNCT
ejpam-6641	132	15	3.2	3.2	NUM
ejpam-6641	132	16	)	)	PUNCT
ejpam-6641	132	17	and	and	CCONJ
ejpam-6641	132	18	∥g∥	∥g∥	PROPN
ejpam-6641	132	19	h	h	PROPN
ejpam-6641	132	20	p(·),q	p(·),q	PROPN
ejpam-6641	132	21	,	,	PUNCT
ejpam-6641	132	22	κ	κ	X
ejpam-6641	132	23	(	(	PUNCT
ejpam-6641	132	24	·	·	PUNCT
ejpam-6641	132	25	)	)	PUNCT
ejpam-6641	132	26	0,δ	0,δ	NOUN
ejpam-6641	133	1	≈	≈	INTJ
ejpam-6641	133	2	∥tκ(0)(1	∥tκ(0)(1	PROPN
ejpam-6641	133	3	+	+	CCONJ
ejpam-6641	133	4	t)κ∞−κ(0)∥g1rγt	t)κ∞−κ(0)∥g1rγt	PROPN
ejpam-6641	133	5	,	,	PUNCT
ejpam-6641	133	6	δt	δt	X
ejpam-6641	133	7	∥lp(·)∥lq(·)(r+	∥lp(·)∥lq(·)(r+	NUM
ejpam-6641	133	8	;	;	PUNCT
ejpam-6641	133	9	dt	dt	PROPN
ejpam-6641	133	10	t	t	PROPN
ejpam-6641	133	11	)	)	PUNCT
ejpam-6641	133	12	,	,	PUNCT
ejpam-6641	133	13	(	(	PUNCT
ejpam-6641	133	14	3.3	3.3	NUM
ejpam-6641	133	15	)	)	PUNCT
ejpam-6641	133	16	then	then	ADV
ejpam-6641	133	17	equivalences	equivalence	VERB
ejpam-6641	133	18	of	of	ADP
ejpam-6641	133	19	norms	norm	NOUN
ejpam-6641	133	20	given	give	VERB
ejpam-6641	133	21	above	above	ADP
ejpam-6641	133	22	are	be	AUX
ejpam-6641	133	23	valids	valid	NOUN
ejpam-6641	133	24	,	,	PUNCT
ejpam-6641	133	25	if	if	SCONJ
ejpam-6641	133	26	κ	κ	PROPN
ejpam-6641	133	27	∈	∈	PROPN
ejpam-6641	133	28	m	m	VERB
ejpam-6641	133	29	log	log	NOUN
ejpam-6641	133	30	∞	∞	PROPN
ejpam-6641	133	31	(	(	PUNCT
ejpam-6641	133	32	r+,µ	r+,µ	NOUN
ejpam-6641	133	33	)	)	PUNCT
ejpam-6641	133	34	for	for	ADP
ejpam-6641	133	35	(	(	PUNCT
ejpam-6641	133	36	3.2	3.2	NUM
ejpam-6641	133	37	)	)	PUNCT
ejpam-6641	133	38	and	and	CCONJ
ejpam-6641	133	39	κ	κ	PROPN
ejpam-6641	133	40	∈	∈	PROPN
ejpam-6641	133	41	m	m	VERB
ejpam-6641	133	42	log	log	NOUN
ejpam-6641	133	43	0,∞(r+	0,∞(r+	NOUN
ejpam-6641	133	44	)	)	PUNCT
ejpam-6641	133	45	in	in	ADP
ejpam-6641	133	46	the	the	DET
ejpam-6641	133	47	case	case	NOUN
ejpam-6641	133	48	of	of	ADP
ejpam-6641	133	49	(	(	PUNCT
ejpam-6641	133	50	3.3	3.3	NUM
ejpam-6641	133	51	)	)	PUNCT
ejpam-6641	133	52	.	.	PUNCT
ejpam-6641	134	1	4	4	X
ejpam-6641	134	2	.	.	X
ejpam-6641	134	3	boundedness	boundedness	PROPN
ejpam-6641	134	4	result	result	NOUN
ejpam-6641	134	5	on	on	ADP
ejpam-6641	134	6	continual	continual	ADJ
ejpam-6641	134	7	herz	herz	PROPN
ejpam-6641	134	8	spaces	space	NOUN
ejpam-6641	134	9	with	with	ADP
ejpam-6641	134	10	variable	variable	ADJ
ejpam-6641	134	11	exponent	exponent	NOUN
ejpam-6641	134	12	in	in	ADP
ejpam-6641	134	13	this	this	DET
ejpam-6641	134	14	section	section	NOUN
ejpam-6641	134	15	,	,	PUNCT
ejpam-6641	134	16	we	we	PRON
ejpam-6641	134	17	demonstrate	demonstrate	VERB
ejpam-6641	134	18	the	the	DET
ejpam-6641	134	19	boundedness	boundedness	NOUN
ejpam-6641	134	20	of	of	ADP
ejpam-6641	134	21	an	an	DET
ejpam-6641	134	22	intrinsic	intrinsic	ADJ
ejpam-6641	134	23	square	square	ADJ
ejpam-6641	134	24	function	function	NOUN
ejpam-6641	134	25	on	on	ADP
ejpam-6641	134	26	continuous	continuous	ADJ
ejpam-6641	134	27	herz	herz	PROPN
ejpam-6641	134	28	spaces	space	NOUN
ejpam-6641	134	29	with	with	ADP
ejpam-6641	134	30	variable	variable	ADJ
ejpam-6641	134	31	exponent	exponent	NOUN
ejpam-6641	134	32	.	.	PUNCT
ejpam-6641	135	1	initially	initially	ADV
ejpam-6641	135	2	,	,	PUNCT
ejpam-6641	135	3	we	we	PRON
ejpam-6641	135	4	will	will	AUX
ejpam-6641	135	5	introduce	introduce	VERB
ejpam-6641	135	6	the	the	DET
ejpam-6641	135	7	intrinsic	intrinsic	ADJ
ejpam-6641	135	8	square	square	ADJ
ejpam-6641	135	9	function	function	NOUN
ejpam-6641	135	10	sζf(x	sζf(x	PROPN
ejpam-6641	135	11	)	)	PUNCT
ejpam-6641	135	12	.	.	PUNCT
ejpam-6641	136	1	definition	definition	NOUN
ejpam-6641	136	2	3	3	X
ejpam-6641	136	3	.	.	PUNCT
ejpam-6641	137	1	let	let	VERB
ejpam-6641	137	2	x	x	X
ejpam-6641	137	3	∈	∈	PROPN
ejpam-6641	137	4	rn	rn	PROPN
ejpam-6641	137	5	and	and	CCONJ
ejpam-6641	137	6	rn+1	rn+1	VERB
ejpam-6641	137	7	+	+	CCONJ
ejpam-6641	137	8	=	=	PROPN
ejpam-6641	137	9	rn	rn	PROPN
ejpam-6641	137	10	×	×	PROPN
ejpam-6641	137	11	(	(	PUNCT
ejpam-6641	137	12	0,∞	0,∞	NUM
ejpam-6641	137	13	)	)	PUNCT
ejpam-6641	137	14	we	we	PRON
ejpam-6641	137	15	define	define	VERB
ejpam-6641	137	16	a	a	DET
ejpam-6641	137	17	set	set	NOUN
ejpam-6641	137	18	,	,	PUNCT
ejpam-6641	137	19	γ(x	γ(x	PROPN
ejpam-6641	137	20	)	)	PUNCT
ejpam-6641	137	21	:	:	PUNCT
ejpam-6641	137	22	≡	≡	PROPN
ejpam-6641	137	23	{	{	PUNCT
ejpam-6641	137	24	(	(	PUNCT
ejpam-6641	137	25	y	y	PROPN
ejpam-6641	137	26	,	,	PUNCT
ejpam-6641	137	27	t	t	PROPN
ejpam-6641	137	28	)	)	PUNCT
ejpam-6641	137	29	∈	∈	PROPN
ejpam-6641	137	30	rn+1	rn+1	PROPN
ejpam-6641	137	31	+	+	CCONJ
ejpam-6641	137	32	:	:	PUNCT
ejpam-6641	137	33	|x−	|x−	X
ejpam-6641	138	1	y|	y|	NOUN
ejpam-6641	138	2	<	<	X
ejpam-6641	138	3	t	t	PROPN
ejpam-6641	138	4	}	}	PUNCT
ejpam-6641	138	5	.	.	PUNCT
ejpam-6641	139	1	let	let	VERB
ejpam-6641	139	2	0	0	NUM
ejpam-6641	139	3	<	<	X
ejpam-6641	139	4	ζ	ζ	X
ejpam-6641	139	5	≤	≤	NUM
ejpam-6641	139	6	1	1	NUM
ejpam-6641	139	7	,	,	PUNCT
ejpam-6641	139	8	then	then	ADV
ejpam-6641	139	9	by	by	ADP
ejpam-6641	139	10	cζ	cζ	ADP
ejpam-6641	139	11	we	we	PRON
ejpam-6641	139	12	denote	denote	VERB
ejpam-6641	139	13	the	the	DET
ejpam-6641	139	14	functions	function	NOUN
ejpam-6641	139	15	ϕ	ϕ	NOUN
ejpam-6641	139	16	defined	define	VERB
ejpam-6641	139	17	on	on	ADP
ejpam-6641	139	18	rn	rn	PROPN
ejpam-6641	139	19	satisfying	satisfy	VERB
ejpam-6641	139	20	the	the	DET
ejpam-6641	139	21	following	follow	VERB
ejpam-6641	139	22	conditions	condition	NOUN
ejpam-6641	139	23	:	:	PUNCT
ejpam-6641	139	24	(	(	PUNCT
ejpam-6641	139	25	i	i	NOUN
ejpam-6641	139	26	)	)	PUNCT
ejpam-6641	139	27	supp	supp	PROPN
ejpam-6641	140	1	ϕ	ϕ	PROPN
ejpam-6641	140	2	⊂	⊂	PROPN
ejpam-6641	140	3	{	{	PUNCT
ejpam-6641	140	4	|x|	|x|	PROPN
ejpam-6641	140	5	≤	≤	PROPN
ejpam-6641	140	6	1	1	NUM
ejpam-6641	140	7	}	}	PUNCT
ejpam-6641	140	8	,	,	PUNCT
ejpam-6641	140	9	(	(	PUNCT
ejpam-6641	140	10	ii	ii	NOUN
ejpam-6641	140	11	)	)	PUNCT
ejpam-6641	140	12	∫	∫	PROPN
ejpam-6641	141	1	rn	rn	PROPN
ejpam-6641	141	2	ϕ(x)dx	ϕ(x)dx	PROPN
ejpam-6641	141	3	=	=	SYM
ejpam-6641	141	4	0	0	PROPN
ejpam-6641	141	5	,	,	PUNCT
ejpam-6641	141	6	(	(	PUNCT
ejpam-6641	141	7	iii	iii	X
ejpam-6641	141	8	)	)	PUNCT
ejpam-6641	141	9	|ϕ(x)−	|ϕ(x)−	NOUN
ejpam-6641	141	10	ϕ(x′)|	ϕ(x′)|	ADJ
ejpam-6641	141	11	≤	≤	PROPN
ejpam-6641	141	12	|x−	|x−	PROPN
ejpam-6641	141	13	x′|ζ	x′|ζ	NOUN
ejpam-6641	141	14	for	for	ADP
ejpam-6641	141	15	x	x	X
ejpam-6641	141	16	,	,	PUNCT
ejpam-6641	141	17	x′	x′	PROPN
ejpam-6641	141	18	∈	∈	PROPN
ejpam-6641	141	19	rn	rn	PROPN
ejpam-6641	141	20	.	.	PROPN
ejpam-6641	142	1	for	for	ADP
ejpam-6641	142	2	each	each	DET
ejpam-6641	142	3	(	(	PUNCT
ejpam-6641	142	4	y	y	PROPN
ejpam-6641	142	5	,	,	PUNCT
ejpam-6641	142	6	t	t	PROPN
ejpam-6641	142	7	)	)	PUNCT
ejpam-6641	142	8	∈	∈	PROPN
ejpam-6641	142	9	rn+1	rn+1	PROPN
ejpam-6641	142	10	+	+	PROPN
ejpam-6641	142	11	,	,	PUNCT
ejpam-6641	142	12	we	we	PRON
ejpam-6641	142	13	denote	denote	VERB
ejpam-6641	142	14	ϕt(y	ϕt(y	PUNCT
ejpam-6641	142	15	)	)	PUNCT
ejpam-6641	143	1	=	=	SYM
ejpam-6641	143	2	t−nϕ(y	t−nϕ(y	PROPN
ejpam-6641	143	3	/	/	SYM
ejpam-6641	143	4	t	t	PROPN
ejpam-6641	143	5	)	)	PUNCT
ejpam-6641	143	6	.	.	PUNCT
ejpam-6641	144	1	let	let	VERB
ejpam-6641	144	2	g	g	PROPN
ejpam-6641	144	3	∈	∈	PROPN
ejpam-6641	144	4	l1	l1	PROPN
ejpam-6641	144	5	loc(rn	loc(rn	PROPN
ejpam-6641	144	6	)	)	PUNCT
ejpam-6641	144	7	,	,	PUNCT
ejpam-6641	144	8	then	then	ADV
ejpam-6641	144	9	aζg(y	aζg(y	PROPN
ejpam-6641	144	10	,	,	PUNCT
ejpam-6641	144	11	t	t	PROPN
ejpam-6641	144	12	)	)	PUNCT
ejpam-6641	144	13	:	:	PUNCT
ejpam-6641	144	14	=	=	SYM
ejpam-6641	144	15	sup	sup	PROPN
ejpam-6641	144	16	ϕ∈cζ	ϕ∈cζ	NOUN
ejpam-6641	144	17	|g	|g	VERB
ejpam-6641	144	18	∗	∗	NOUN
ejpam-6641	144	19	ϕt(y)|	ϕt(y)|	PROPN
ejpam-6641	144	20	,	,	PUNCT
ejpam-6641	144	21	where	where	SCONJ
ejpam-6641	144	22	(	(	PUNCT
ejpam-6641	144	23	y	y	PROPN
ejpam-6641	144	24	,	,	PUNCT
ejpam-6641	144	25	t	t	PROPN
ejpam-6641	144	26	)	)	PUNCT
ejpam-6641	144	27	∈	∈	NOUN
ejpam-6641	144	28	rn+1	rn+1	PROPN
ejpam-6641	144	29	+	+	CCONJ
ejpam-6641	144	30	.	.	PUNCT
ejpam-6641	145	1	then	then	ADV
ejpam-6641	145	2	the	the	DET
ejpam-6641	145	3	intrinsic	intrinsic	ADJ
ejpam-6641	145	4	square	square	ADJ
ejpam-6641	145	5	function	function	NOUN
ejpam-6641	145	6	with	with	ADP
ejpam-6641	145	7	order	order	NOUN
ejpam-6641	145	8	ζ	ζ	NOUN
ejpam-6641	145	9	is	be	AUX
ejpam-6641	145	10	given	give	VERB
ejpam-6641	145	11	as	as	ADP
ejpam-6641	145	12	sζg(x	sζg(x	PROPN
ejpam-6641	145	13	)	)	PUNCT
ejpam-6641	145	14	:	:	PUNCT
ejpam-6641	145	15	=	=	PUNCT
ejpam-6641	145	16	∫	∫	PROPN
ejpam-6641	145	17	∫	∫	NOUN
ejpam-6641	145	18	γ(x	γ(x	NOUN
ejpam-6641	145	19	)	)	PUNCT
ejpam-6641	145	20	aζg(y	aζg(y	PROPN
ejpam-6641	145	21	,	,	PUNCT
ejpam-6641	145	22	t	t	PROPN
ejpam-6641	145	23	)	)	PUNCT
ejpam-6641	145	24	2dydt	2dydt	PROPN
ejpam-6641	145	25	tn+1	tn+1	NUM
ejpam-6641	145	26			PROPN
ejpam-6641	145	27	1/2	1/2	NUM
ejpam-6641	145	28	.	.	PUNCT
ejpam-6641	146	1	the	the	DET
ejpam-6641	146	2	boundedness	boundedness	NOUN
ejpam-6641	146	3	of	of	ADP
ejpam-6641	146	4	sζ	sζ	PROPN
ejpam-6641	146	5	in	in	ADP
ejpam-6641	146	6	variable	variable	ADJ
ejpam-6641	146	7	exponent	exponent	NOUN
ejpam-6641	146	8	lebesgue	lebesgue	NOUN
ejpam-6641	146	9	spaces	space	VERB
ejpam-6641	146	10	lp	lp	PROPN
ejpam-6641	146	11	(	(	PUNCT
ejpam-6641	146	12	·	·	PUNCT
ejpam-6641	146	13	)	)	PUNCT
ejpam-6641	146	14	is	be	AUX
ejpam-6641	146	15	discussed	discuss	VERB
ejpam-6641	146	16	in	in	ADP
ejpam-6641	146	17	detail	detail	NOUN
ejpam-6641	146	18	in	in	ADP
ejpam-6641	146	19	[	[	X
ejpam-6641	146	20	14	14	NUM
ejpam-6641	146	21	]	]	PUNCT
ejpam-6641	146	22	.	.	PUNCT
ejpam-6641	147	1	in	in	ADP
ejpam-6641	147	2	the	the	DET
ejpam-6641	147	3	subsequent	subsequent	ADJ
ejpam-6641	147	4	theorem	theorem	NOUN
ejpam-6641	147	5	,	,	PUNCT
ejpam-6641	147	6	we	we	PRON
ejpam-6641	147	7	establish	establish	VERB
ejpam-6641	147	8	the	the	DET
ejpam-6641	147	9	boundedness	boundedness	NOUN
ejpam-6641	147	10	of	of	ADP
ejpam-6641	147	11	the	the	DET
ejpam-6641	147	12	intrinsic	intrinsic	ADJ
ejpam-6641	147	13	square	square	ADJ
ejpam-6641	147	14	function	function	NOUN
ejpam-6641	147	15	in	in	ADP
ejpam-6641	147	16	variable	variable	ADJ
ejpam-6641	147	17	exponent	exponent	NOUN
ejpam-6641	147	18	continuous	continuous	ADJ
ejpam-6641	147	19	herz	herz	PROPN
ejpam-6641	147	20	spaces	space	NOUN
ejpam-6641	147	21	h	h	PROPN
ejpam-6641	147	22	p(·),q(·),κ	p(·),q(·),κ	ADP
ejpam-6641	147	23	(	(	PUNCT
ejpam-6641	147	24	·	·	PUNCT
ejpam-6641	147	25	)	)	PUNCT
ejpam-6641	147	26	µ;(γ	µ;(γ	ADV
ejpam-6641	147	27	,	,	PUNCT
ejpam-6641	147	28	δ	δ	PROPN
ejpam-6641	147	29	)	)	PUNCT
ejpam-6641	147	30	(	(	PUNCT
ejpam-6641	147	31	rn	rn	NOUN
ejpam-6641	147	32	)	)	PUNCT
ejpam-6641	147	33	.	.	PUNCT
ejpam-6641	148	1	here	here	ADV
ejpam-6641	148	2	,	,	PUNCT
ejpam-6641	148	3	the	the	DET
ejpam-6641	148	4	parameters	parameter	NOUN
ejpam-6641	148	5	p	p	X
ejpam-6641	148	6	(	(	PUNCT
ejpam-6641	148	7	·	·	PUNCT
ejpam-6641	148	8	)	)	PUNCT
ejpam-6641	148	9	,	,	PUNCT
ejpam-6641	148	10	q	q	X
ejpam-6641	148	11	(	(	PUNCT
ejpam-6641	148	12	·	·	PUNCT
ejpam-6641	148	13	)	)	PUNCT
ejpam-6641	148	14	,	,	PUNCT
ejpam-6641	148	15	and	and	CCONJ
ejpam-6641	148	16	κ	κ	X
ejpam-6641	148	17	(	(	PUNCT
ejpam-6641	148	18	·	·	PUNCT
ejpam-6641	148	19	)	)	PUNCT
ejpam-6641	148	20	are	be	AUX
ejpam-6641	148	21	variable	variable	ADJ
ejpam-6641	148	22	,	,	PUNCT
ejpam-6641	148	23	subject	subject	ADJ
ejpam-6641	148	24	to	to	ADP
ejpam-6641	148	25	the	the	DET
ejpam-6641	148	26	condition	condition	NOUN
ejpam-6641	148	27	that	that	PRON
ejpam-6641	148	28	sζ	sζ	PROPN
ejpam-6641	148	29	is	be	AUX
ejpam-6641	148	30	bounded	bound	VERB
ejpam-6641	148	31	on	on	ADP
ejpam-6641	148	32	lp(·)(rn	lp(·)(rn	PROPN
ejpam-6641	148	33	)	)	PUNCT
ejpam-6641	148	34	.	.	PUNCT
ejpam-6641	149	1	it	it	PRON
ejpam-6641	149	2	’s	’	VERB
ejpam-6641	149	3	important	important	ADJ
ejpam-6641	149	4	to	to	PART
ejpam-6641	149	5	mention	mention	VERB
ejpam-6641	149	6	that	that	SCONJ
ejpam-6641	149	7	when	when	SCONJ
ejpam-6641	149	8	the	the	DET
ejpam-6641	149	9	constants	constant	NOUN
ejpam-6641	149	10	q	q	NOUN
ejpam-6641	149	11	are	be	AUX
ejpam-6641	149	12	considered	consider	VERB
ejpam-6641	149	13	,	,	PUNCT
ejpam-6641	149	14	the	the	DET
ejpam-6641	149	15	norms	norm	NOUN
ejpam-6641	149	16	within	within	ADP
ejpam-6641	149	17	the	the	DET
ejpam-6641	149	18	continuous	continuous	ADJ
ejpam-6641	149	19	herz	herz	PROPN
ejpam-6641	149	20	space	space	NOUN
ejpam-6641	149	21	become	become	VERB
ejpam-6641	149	22	equivalent	equivalent	ADJ
ejpam-6641	149	23	for	for	ADP
ejpam-6641	149	24	various	various	ADJ
ejpam-6641	149	25	values	value	NOUN
ejpam-6641	149	26	of	of	ADP
ejpam-6641	149	27	γ	γ	PROPN
ejpam-6641	149	28	and	and	CCONJ
ejpam-6641	149	29	δ	δ	PROPN
ejpam-6641	149	30	,	,	PUNCT
ejpam-6641	149	31	particularly	particularly	ADV
ejpam-6641	149	32	when	when	SCONJ
ejpam-6641	149	33	0	0	NUM
ejpam-6641	149	34	<	<	X
ejpam-6641	149	35	γ	γ	X
ejpam-6641	149	36	<	<	X
ejpam-6641	149	37	δ	δ	PROPN
ejpam-6641	149	38	.	.	PUNCT
ejpam-6641	150	1	nonetheless	nonetheless	ADV
ejpam-6641	150	2	,	,	PUNCT
ejpam-6641	150	3	this	this	DET
ejpam-6641	150	4	equality	equality	NOUN
ejpam-6641	150	5	does	do	AUX
ejpam-6641	150	6	n’t	not	PART
ejpam-6641	150	7	persist	persist	VERB
ejpam-6641	150	8	when	when	SCONJ
ejpam-6641	150	9	q	q	NOUN
ejpam-6641	150	10	varies	vary	VERB
ejpam-6641	150	11	and	and	CCONJ
ejpam-6641	150	12	is	be	AUX
ejpam-6641	150	13	not	not	PART
ejpam-6641	150	14	constant	constant	ADJ
ejpam-6641	150	15	.	.	PUNCT
ejpam-6641	151	1	g.	g.	PROPN
ejpam-6641	151	2	a.	a.	PROPN
ejpam-6641	151	3	basendwah	basendwah	PROPN
ejpam-6641	151	4	et	et	PROPN
ejpam-6641	151	5	al	al	PROPN
ejpam-6641	151	6	.	.	PUNCT
ejpam-6641	151	7	/	/	SYM
ejpam-6641	151	8	eur	eur	PROPN
ejpam-6641	151	9	.	.	PUNCT
ejpam-6641	152	1	j.	j.	PROPN
ejpam-6641	152	2	pure	pure	PROPN
ejpam-6641	152	3	appl	appl	PROPN
ejpam-6641	152	4	.	.	PROPN
ejpam-6641	152	5	math	math	PROPN
ejpam-6641	152	6	,	,	PUNCT
ejpam-6641	152	7	18	18	NUM
ejpam-6641	152	8	(	(	PUNCT
ejpam-6641	152	9	4	4	NUM
ejpam-6641	152	10	)	)	PUNCT
ejpam-6641	152	11	(	(	PUNCT
ejpam-6641	152	12	2025	2025	NUM
ejpam-6641	152	13	)	)	PUNCT
ejpam-6641	152	14	,	,	PUNCT
ejpam-6641	152	15	6641	6641	NUM
ejpam-6641	152	16	8	8	NUM
ejpam-6641	152	17	of	of	ADP
ejpam-6641	152	18	16	16	NUM
ejpam-6641	152	19	4.1	4.1	NUM
ejpam-6641	152	20	.	.	PUNCT
ejpam-6641	153	1	non	non	ADJ
ejpam-6641	153	2	-	-	ADJ
ejpam-6641	153	3	homogeneous	homogeneous	ADJ
ejpam-6641	153	4	herz	herz	NOUN
ejpam-6641	153	5	space(when	space(when	PROPN
ejpam-6641	153	6	µ	µ	X
ejpam-6641	153	7	=	=	SYM
ejpam-6641	153	8	0	0	NUM
ejpam-6641	153	9	)	)	PUNCT
ejpam-6641	153	10	theorem	theorem	VERB
ejpam-6641	153	11	4.1	4.1	NUM
ejpam-6641	153	12	.	.	PUNCT
ejpam-6641	154	1	suppose	suppose	VERB
ejpam-6641	154	2	that	that	SCONJ
ejpam-6641	154	3	p	p	PROPN
ejpam-6641	154	4	∈	∈	PROPN
ejpam-6641	154	5	plog	plog	NOUN
ejpam-6641	154	6	∞	∞	PROPN
ejpam-6641	154	7	(	(	PUNCT
ejpam-6641	154	8	rn	rn	NOUN
ejpam-6641	154	9	)	)	PUNCT
ejpam-6641	154	10	,	,	PUNCT
ejpam-6641	154	11	q	q	PROPN
ejpam-6641	154	12	∈	∈	PROPN
ejpam-6641	154	13	plog	plog	NOUN
ejpam-6641	154	14	∞	∞	PROPN
ejpam-6641	154	15	(	(	PUNCT
ejpam-6641	154	16	µ,∞	µ,∞	PROPN
ejpam-6641	154	17	)	)	PUNCT
ejpam-6641	154	18	with	with	ADP
ejpam-6641	154	19	1	1	NUM
ejpam-6641	154	20	<	<	X
ejpam-6641	154	21	p−	p−	X
ejpam-6641	154	22	<	<	X
ejpam-6641	154	23	p+	p+	X
ejpam-6641	154	24	<	<	X
ejpam-6641	154	25	∞	∞	PROPN
ejpam-6641	154	26	,	,	PUNCT
ejpam-6641	154	27	1	1	NUM
ejpam-6641	154	28	<	<	X
ejpam-6641	154	29	q−	q−	PROPN
ejpam-6641	154	30	≤	≤	NUM
ejpam-6641	154	31	q+	q+	ADP
ejpam-6641	154	32	<	<	X
ejpam-6641	154	33	∞	∞	PROPN
ejpam-6641	154	34	,	,	PUNCT
ejpam-6641	154	35	then	then	ADV
ejpam-6641	154	36	every	every	DET
ejpam-6641	154	37	intrinsic	intrinsic	ADJ
ejpam-6641	154	38	square	square	ADJ
ejpam-6641	154	39	function	function	NOUN
ejpam-6641	154	40	is	be	AUX
ejpam-6641	154	41	bounded	bound	VERB
ejpam-6641	154	42	on	on	ADP
ejpam-6641	154	43	lp(·)(rn	lp(·)(rn	PROPN
ejpam-6641	154	44	)	)	PUNCT
ejpam-6641	154	45	,	,	PUNCT
ejpam-6641	154	46	is	be	AUX
ejpam-6641	154	47	also	also	ADV
ejpam-6641	154	48	bounded	bound	VERB
ejpam-6641	154	49	on	on	ADP
ejpam-6641	154	50	the	the	DET
ejpam-6641	154	51	continualherz	continualherz	NOUN
ejpam-6641	154	52	spaces	space	VERB
ejpam-6641	154	53	with	with	ADP
ejpam-6641	154	54	variable	variable	ADJ
ejpam-6641	154	55	exponent	exponent	NOUN
ejpam-6641	154	56	h	h	PROPN
ejpam-6641	154	57	p(·),q(·),κ	p(·),q(·),κ	ADP
ejpam-6641	154	58	(	(	PUNCT
ejpam-6641	154	59	·	·	PUNCT
ejpam-6641	154	60	)	)	PUNCT
ejpam-6641	154	61	µ;(γ	µ;(γ	ADV
ejpam-6641	154	62	,	,	PUNCT
ejpam-6641	154	63	δ	δ	PROPN
ejpam-6641	154	64	)	)	PUNCT
ejpam-6641	154	65	(	(	PUNCT
ejpam-6641	154	66	rn	rn	NOUN
ejpam-6641	154	67	)	)	PUNCT
ejpam-6641	154	68	,	,	PUNCT
ejpam-6641	154	69	if	if	SCONJ
ejpam-6641	154	70	−	−	PROPN
ejpam-6641	154	71	n	n	PRON
ejpam-6641	154	72	p∞	p∞	PROPN
ejpam-6641	154	73	<	<	X
ejpam-6641	154	74	κ∞	κ∞	PROPN
ejpam-6641	154	75	<	<	X
ejpam-6641	154	76	n	n	X
ejpam-6641	154	77	p′∞	p′∞	ADJ
ejpam-6641	154	78	.	.	PUNCT
ejpam-6641	155	1	(	(	PUNCT
ejpam-6641	155	2	4.1	4.1	NUM
ejpam-6641	155	3	)	)	PUNCT
ejpam-6641	155	4	proof	proof	NOUN
ejpam-6641	155	5	.	.	PUNCT
ejpam-6641	156	1	norms	norm	NOUN
ejpam-6641	156	2	of	of	ADP
ejpam-6641	156	3	h	h	PROPN
ejpam-6641	156	4	p(·),q(·),κ	p(·),q(·),κ	ADP
ejpam-6641	156	5	(	(	PUNCT
ejpam-6641	156	6	·	·	PUNCT
ejpam-6641	156	7	)	)	PUNCT
ejpam-6641	156	8	µ;(γ	µ;(γ	ADV
ejpam-6641	156	9	,	,	PUNCT
ejpam-6641	156	10	δ	δ	PROPN
ejpam-6641	156	11	)	)	PUNCT
ejpam-6641	156	12	(	(	PUNCT
ejpam-6641	156	13	rn	rn	NOUN
ejpam-6641	156	14	)	)	PUNCT
ejpam-6641	156	15	are	be	AUX
ejpam-6641	156	16	equal	equal	ADJ
ejpam-6641	156	17	for	for	ADP
ejpam-6641	156	18	different	different	ADJ
ejpam-6641	156	19	values	value	NOUN
ejpam-6641	156	20	of	of	ADP
ejpam-6641	156	21	µ	µ	X
ejpam-6641	156	22	>	>	X
ejpam-6641	156	23	0	0	NUM
ejpam-6641	156	24	,	,	PUNCT
ejpam-6641	156	25	and	and	CCONJ
ejpam-6641	156	26	δ	δ	X
ejpam-6641	156	27	>	>	X
ejpam-6641	156	28	0	0	PUNCT
ejpam-6641	156	29	when	when	SCONJ
ejpam-6641	156	30	q	q	PROPN
ejpam-6641	156	31	constant	constant	ADJ
ejpam-6641	156	32	,	,	PUNCT
ejpam-6641	156	33	so	so	ADV
ejpam-6641	156	34	for	for	ADP
ejpam-6641	156	35	simplicity	simplicity	NOUN
ejpam-6641	156	36	we	we	PRON
ejpam-6641	156	37	choose	choose	VERB
ejpam-6641	156	38	δ	δ	X
ejpam-6641	156	39	=	=	SYM
ejpam-6641	156	40	2	2	NUM
ejpam-6641	156	41	and	and	CCONJ
ejpam-6641	156	42	µ	µ	X
ejpam-6641	156	43	=	=	SYM
ejpam-6641	156	44	2	2	NUM
ejpam-6641	156	45	,	,	PUNCT
ejpam-6641	156	46	∥g∥	∥g∥	PROPN
ejpam-6641	156	47	h	h	PROPN
ejpam-6641	156	48	p(·),q	p(·),q	PROPN
ejpam-6641	156	49	,	,	PUNCT
ejpam-6641	156	50	κ	κ	X
ejpam-6641	156	51	(	(	PUNCT
ejpam-6641	156	52	·	·	PUNCT
ejpam-6641	156	53	)	)	PUNCT
ejpam-6641	156	54	2,2	2,2	PROPN
ejpam-6641	156	55	=	=	SYM
ejpam-6641	156	56	n(g)κp	n(g)κp	PROPN
ejpam-6641	156	57	,	,	PUNCT
ejpam-6641	156	58	q	q	X
ejpam-6641	156	59	+	+	NUM
ejpam-6641	156	60	∥g∥lp(·)(o(0,2+θ	∥g∥lp(·)(o(0,2+θ	NUM
ejpam-6641	156	61	)	)	PUNCT
ejpam-6641	156	62	)	)	PUNCT
ejpam-6641	156	63	(	(	PUNCT
ejpam-6641	156	64	4.2	4.2	NUM
ejpam-6641	156	65	)	)	PUNCT
ejpam-6641	156	66	where	where	SCONJ
ejpam-6641	156	67	we	we	PRON
ejpam-6641	156	68	can	can	AUX
ejpam-6641	156	69	define	define	VERB
ejpam-6641	156	70	,	,	PUNCT
ejpam-6641	156	71	n(g)κp	n(g)κp	ADP
ejpam-6641	156	72	,	,	PUNCT
ejpam-6641	156	73	q+	q+	ADV
ejpam-6641	156	74	=	=	PUNCT
ejpam-6641	156	75	∥tκ∞∥g1tt,2t∥lp(·)∥lq((2,∞	∥tκ∞∥g1tt,2t∥lp(·)∥lq((2,∞	NOUN
ejpam-6641	156	76	)	)	PUNCT
ejpam-6641	156	77	,	,	PUNCT
ejpam-6641	156	78	dt	dt	PROPN
ejpam-6641	156	79	t	t	PROPN
ejpam-6641	156	80	)	)	PUNCT
ejpam-6641	156	81	.	.	PUNCT
ejpam-6641	157	1	(	(	PUNCT
ejpam-6641	157	2	4.3	4.3	NUM
ejpam-6641	157	3	)	)	PUNCT
ejpam-6641	157	4	we	we	PRON
ejpam-6641	157	5	first	first	ADV
ejpam-6641	157	6	estimate	estimate	VERB
ejpam-6641	157	7	∥sβg∥lp(·)(o(0,2+θ	∥sβg∥lp(·)(o(0,2+θ	NOUN
ejpam-6641	157	8	)	)	PUNCT
ejpam-6641	157	9	)	)	PUNCT
ejpam-6641	157	10	,	,	PUNCT
ejpam-6641	157	11	where	where	SCONJ
ejpam-6641	157	12	we	we	PRON
ejpam-6641	157	13	choose	choose	VERB
ejpam-6641	157	14	θ	θ	PROPN
ejpam-6641	157	15	∈	∈	PROPN
ejpam-6641	157	16	(	(	PUNCT
ejpam-6641	157	17	0	0	NUM
ejpam-6641	157	18	,	,	PUNCT
ejpam-6641	157	19	1	1	NUM
ejpam-6641	157	20	)	)	PUNCT
ejpam-6641	157	21	,	,	PUNCT
ejpam-6641	157	22	and	and	CCONJ
ejpam-6641	157	23	estimate	estimate	VERB
ejpam-6641	157	24	for	for	ADP
ejpam-6641	157	25	sζg	sζg	NOUN
ejpam-6641	157	26	follows	follow	VERB
ejpam-6641	157	27	from	from	ADP
ejpam-6641	157	28	the	the	DET
ejpam-6641	157	29	boundedness	boundedness	NOUN
ejpam-6641	157	30	on	on	ADP
ejpam-6641	157	31	lp	lp	PROPN
ejpam-6641	157	32	(	(	PUNCT
ejpam-6641	157	33	·	·	PUNCT
ejpam-6641	157	34	)	)	PUNCT
ejpam-6641	157	35	of	of	ADP
ejpam-6641	157	36	sζg	sζg	NOUN
ejpam-6641	157	37	,	,	PUNCT
ejpam-6641	157	38	so	so	SCONJ
ejpam-6641	157	39	we	we	PRON
ejpam-6641	157	40	have	have	VERB
ejpam-6641	157	41	∥sζg∥lp(·)(o(0,2+θ	∥sζg∥lp(·)(o(0,2+θ	NOUN
ejpam-6641	157	42	)	)	PUNCT
ejpam-6641	157	43	)	)	PUNCT
ejpam-6641	158	1	≤	≤	NOUN
ejpam-6641	158	2	c∥g∥lp(·)(o(0,2+θ	c∥g∥lp(·)(o(0,2+θ	PROPN
ejpam-6641	158	3	)	)	PUNCT
ejpam-6641	158	4	)	)	PUNCT
ejpam-6641	159	1	≤	≤	PROPN
ejpam-6641	159	2	c∥g∥	c∥g∥	PROPN
ejpam-6641	159	3	h	h	PROPN
ejpam-6641	159	4	p(·),q	p(·),q	PROPN
ejpam-6641	159	5	,	,	PUNCT
ejpam-6641	159	6	κ	κ	X
ejpam-6641	159	7	(	(	PUNCT
ejpam-6641	159	8	·	·	PUNCT
ejpam-6641	159	9	)	)	PUNCT
ejpam-6641	159	10	2,2	2,2	NUM
ejpam-6641	159	11	.	.	PUNCT
ejpam-6641	160	1	now	now	ADV
ejpam-6641	160	2	to	to	PART
ejpam-6641	160	3	find	find	VERB
ejpam-6641	160	4	the	the	DET
ejpam-6641	160	5	estimate	estimate	NOUN
ejpam-6641	160	6	of	of	ADP
ejpam-6641	160	7	n(sζg)p∗,q	n(sζg)p∗,q	NOUN
ejpam-6641	160	8	,	,	PUNCT
ejpam-6641	160	9	κ	κ	NOUN
ejpam-6641	160	10	term	term	NOUN
ejpam-6641	160	11	,	,	PUNCT
ejpam-6641	160	12	we	we	PRON
ejpam-6641	160	13	will	will	AUX
ejpam-6641	160	14	split	split	VERB
ejpam-6641	160	15	the	the	DET
ejpam-6641	160	16	functions	function	NOUN
ejpam-6641	160	17	g(ℓ	g(ℓ	NOUN
ejpam-6641	160	18	)	)	PUNCT
ejpam-6641	160	19	as	as	ADP
ejpam-6641	160	20	g(ℓ	g(ℓ	NOUN
ejpam-6641	160	21	)	)	PUNCT
ejpam-6641	160	22	=	=	PUNCT
ejpam-6641	161	1	f0(ℓ	f0(ℓ	X
ejpam-6641	161	2	)	)	PUNCT
ejpam-6641	161	3	+	+	NUM
ejpam-6641	161	4	ft(ℓ	ft(ℓ	NUM
ejpam-6641	161	5	)	)	PUNCT
ejpam-6641	161	6	+	+	NOUN
ejpam-6641	161	7	gt(ℓ	gt(ℓ	X
ejpam-6641	161	8	)	)	PUNCT
ejpam-6641	161	9	+	+	CCONJ
ejpam-6641	161	10	ht(ℓ	ht(ℓ	NOUN
ejpam-6641	161	11	)	)	PUNCT
ejpam-6641	161	12	where	where	SCONJ
ejpam-6641	161	13	f0(ℓ	f0(ℓ	VERB
ejpam-6641	161	14	)	)	PUNCT
ejpam-6641	161	15	=	=	SYM
ejpam-6641	161	16	g(ℓ)1o(0,1)(ℓ	g(ℓ)1o(0,1)(ℓ	PROPN
ejpam-6641	161	17	)	)	PUNCT
ejpam-6641	161	18	,	,	PUNCT
ejpam-6641	161	19	ft(ℓ	ft(ℓ	NUM
ejpam-6641	161	20	)	)	PUNCT
ejpam-6641	161	21	=	=	SYM
ejpam-6641	161	22	g(ℓ)1o(0	g(ℓ)1o(0	NOUN
ejpam-6641	161	23	,	,	PUNCT
ejpam-6641	161	24	t	t	PROPN
ejpam-6641	161	25	2	2	NUM
ejpam-6641	161	26	)	)	PUNCT
ejpam-6641	161	27	\o(0,1)(ℓ	\o(0,1)(ℓ	PROPN
ejpam-6641	161	28	)	)	PUNCT
ejpam-6641	162	1	gt(ℓ	gt(ℓ	NOUN
ejpam-6641	162	2	)	)	PUNCT
ejpam-6641	163	1	=	=	SYM
ejpam-6641	163	2	g(ℓ)1o(0,8t)\o(0	g(ℓ)1o(0,8t)\o(0	NOUN
ejpam-6641	163	3	,	,	PUNCT
ejpam-6641	163	4	t	t	PROPN
ejpam-6641	163	5	2	2	NUM
ejpam-6641	163	6	)	)	PUNCT
ejpam-6641	163	7	(	(	PUNCT
ejpam-6641	163	8	ℓ	ℓ	NOUN
ejpam-6641	163	9	)	)	PUNCT
ejpam-6641	163	10	,	,	PUNCT
ejpam-6641	163	11	ht(ℓ	ht(ℓ	ADJ
ejpam-6641	163	12	)	)	PUNCT
ejpam-6641	163	13	=	=	SYM
ejpam-6641	163	14	g(ℓ)1rn\o(0,8t)(ℓ	g(ℓ)1rn\o(0,8t)(ℓ	PROPN
ejpam-6641	163	15	)	)	PUNCT
ejpam-6641	163	16	,	,	PUNCT
ejpam-6641	163	17	now	now	ADV
ejpam-6641	163	18	we	we	PRON
ejpam-6641	163	19	have	have	AUX
ejpam-6641	163	20	pointwise	pointwise	VERB
ejpam-6641	163	21	inequality	inequality	NOUN
ejpam-6641	163	22	,	,	PUNCT
ejpam-6641	163	23	|sζg(ℓ)|	|sζg(ℓ)|	NUM
ejpam-6641	163	24	≤	≤	NUM
ejpam-6641	163	25	|sζf0(ℓ)|+	|sζf0(ℓ)|+	AUX
ejpam-6641	163	26	|sζft(ℓ)|+	|sζft(ℓ)|+	PROPN
ejpam-6641	163	27	|sζgt(ℓ)|+	|sζgt(ℓ)|+	PROPN
ejpam-6641	163	28	|sζht(ℓ)|	|sζht(ℓ)|	PROPN
ejpam-6641	163	29	.	.	PUNCT
ejpam-6641	164	1	assume	assume	VERB
ejpam-6641	164	2	that	that	SCONJ
ejpam-6641	164	3	ϕ	ϕ	PROPN
ejpam-6641	164	4	∈	∈	PROPN
ejpam-6641	164	5	cζ	cζ	ADV
ejpam-6641	164	6	,	,	PUNCT
ejpam-6641	164	7	k	k	PROPN
ejpam-6641	164	8	∈	∈	PROPN
ejpam-6641	164	9	z	z	PROPN
ejpam-6641	164	10	,	,	PUNCT
ejpam-6641	164	11	ℓ	ℓ	PROPN
ejpam-6641	164	12	∈	∈	PROPN
ejpam-6641	164	13	tk	tk	PROPN
ejpam-6641	164	14	and	and	CCONJ
ejpam-6641	164	15	(	(	PUNCT
ejpam-6641	164	16	y	y	PROPN
ejpam-6641	164	17	,	,	PUNCT
ejpam-6641	164	18	t	t	PROPN
ejpam-6641	164	19	)	)	PUNCT
ejpam-6641	164	20	∈	∈	PROPN
ejpam-6641	164	21	γ(ℓ	γ(ℓ	PROPN
ejpam-6641	164	22	)	)	PUNCT
ejpam-6641	164	23	,	,	PUNCT
ejpam-6641	164	24	then	then	ADV
ejpam-6641	164	25	we	we	PRON
ejpam-6641	164	26	have	have	VERB
ejpam-6641	164	27	|g(1l	|g(1l	NUM
ejpam-6641	164	28	)	)	PUNCT
ejpam-6641	164	29	∗	∗	NOUN
ejpam-6641	164	30	ϕt(y)|	ϕt(y)|	NOUN
ejpam-6641	164	31	=	=	SYM
ejpam-6641	164	32	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-6641	164	33	∫	∫	PROPN
ejpam-6641	165	1	tl	tl	PROPN
ejpam-6641	165	2	ϕt(y)g(ℓ)dℓ	ϕt(y)g(ℓ)dℓ	PROPN
ejpam-6641	165	3	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-6641	165	4	≤ct−n	≤ct−n	SYM
ejpam-6641	165	5	∫	∫	PROPN
ejpam-6641	165	6	{	{	PUNCT
ejpam-6641	165	7	ℓ∈tl:|y−ℓ|<t	ℓ∈tl:|y−ℓ|<t	PROPN
ejpam-6641	165	8	}	}	PUNCT
ejpam-6641	165	9	|g(ℓ)|dℓ.	|g(ℓ)|dℓ.	NOUN
ejpam-6641	165	10	g.	g.	PROPN
ejpam-6641	165	11	a.	a.	PROPN
ejpam-6641	165	12	basendwah	basendwah	PROPN
ejpam-6641	165	13	et	et	PROPN
ejpam-6641	165	14	al	al	PROPN
ejpam-6641	165	15	.	.	PUNCT
ejpam-6641	165	16	/	/	SYM
ejpam-6641	165	17	eur	eur	PROPN
ejpam-6641	165	18	.	.	PUNCT
ejpam-6641	166	1	j.	j.	PROPN
ejpam-6641	166	2	pure	pure	PROPN
ejpam-6641	166	3	appl	appl	PROPN
ejpam-6641	166	4	.	.	PROPN
ejpam-6641	166	5	math	math	PROPN
ejpam-6641	166	6	,	,	PUNCT
ejpam-6641	166	7	18	18	NUM
ejpam-6641	166	8	(	(	PUNCT
ejpam-6641	166	9	4	4	NUM
ejpam-6641	166	10	)	)	PUNCT
ejpam-6641	166	11	(	(	PUNCT
ejpam-6641	166	12	2025	2025	NUM
ejpam-6641	166	13	)	)	PUNCT
ejpam-6641	166	14	,	,	PUNCT
ejpam-6641	166	15	6641	6641	NUM
ejpam-6641	166	16	9	9	NUM
ejpam-6641	166	17	of	of	ADP
ejpam-6641	166	18	16	16	NUM
ejpam-6641	166	19	let	let	VERB
ejpam-6641	166	20	ℓ	ℓ	PROPN
ejpam-6641	166	21	∈	∈	PROPN
ejpam-6641	166	22	tl	tl	PROPN
ejpam-6641	166	23	with	with	ADP
ejpam-6641	166	24	|y	|y	NOUN
ejpam-6641	166	25	−	−	PUNCT
ejpam-6641	166	26	ℓ|	ℓ|	PROPN
ejpam-6641	166	27	<	<	X
ejpam-6641	166	28	t	t	X
ejpam-6641	167	1	we	we	PRON
ejpam-6641	167	2	obtain	obtain	VERB
ejpam-6641	167	3	t	t	NOUN
ejpam-6641	167	4	=	=	SYM
ejpam-6641	167	5	1	1	NUM
ejpam-6641	167	6	2	2	NUM
ejpam-6641	167	7	(	(	PUNCT
ejpam-6641	167	8	t+	t+	NOUN
ejpam-6641	167	9	t	t	NOUN
ejpam-6641	167	10	)	)	PUNCT
ejpam-6641	167	11	>	>	X
ejpam-6641	167	12	1	1	NUM
ejpam-6641	167	13	2	2	NUM
ejpam-6641	167	14	(	(	PUNCT
ejpam-6641	167	15	|ℓ−	|ℓ−	NOUN
ejpam-6641	167	16	y|+	y|+	PROPN
ejpam-6641	167	17	|y	|y	NOUN
ejpam-6641	167	18	−	−	PROPN
ejpam-6641	167	19	ℓ|	ℓ|	PROPN
ejpam-6641	167	20	)	)	PUNCT
ejpam-6641	167	21	≥	≥	NOUN
ejpam-6641	167	22	1	1	NUM
ejpam-6641	167	23	2	2	NUM
ejpam-6641	167	24	|ℓ−	|ℓ−	VERB
ejpam-6641	167	25	y|	y|	NOUN
ejpam-6641	167	26	≥	≥	NOUN
ejpam-6641	167	27	1	1	NUM
ejpam-6641	167	28	2	2	NUM
ejpam-6641	167	29	(	(	PUNCT
ejpam-6641	167	30	|ℓ|	|ℓ|	PROPN
ejpam-6641	167	31	−	−	PROPN
ejpam-6641	167	32	|y|	|y|	NOUN
ejpam-6641	167	33	)	)	PUNCT
ejpam-6641	167	34	≥1	≥1	PROPN
ejpam-6641	167	35	2	2	NUM
ejpam-6641	167	36	(	(	PUNCT
ejpam-6641	167	37	|ℓ|	|ℓ|	PROPN
ejpam-6641	167	38	−	−	PROPN
ejpam-6641	167	39	2	2	NUM
ejpam-6641	167	40	t	t	NOUN
ejpam-6641	167	41	)	)	PUNCT
ejpam-6641	167	42	≥	≥	NOUN
ejpam-6641	167	43	1	1	NUM
ejpam-6641	167	44	2	2	NUM
ejpam-6641	167	45	(	(	PUNCT
ejpam-6641	167	46	|ℓ|	|ℓ|	PROPN
ejpam-6641	167	47	−	−	PROPN
ejpam-6641	167	48	2k−2	2k−2	NUM
ejpam-6641	167	49	)	)	PUNCT
ejpam-6641	167	50	≥	≥	NOUN
ejpam-6641	167	51	1	1	NUM
ejpam-6641	167	52	2	2	NUM
ejpam-6641	167	53	(	(	PUNCT
ejpam-6641	167	54	|ℓ|	|ℓ|	PROPN
ejpam-6641	167	55	−	−	PROPN
ejpam-6641	167	56	2−1|ℓ|	2−1|ℓ|	NOUN
ejpam-6641	167	57	)	)	PUNCT
ejpam-6641	167	58	=	=	SYM
ejpam-6641	167	59	|ℓ|	|ℓ|	VERB
ejpam-6641	167	60	4	4	NUM
ejpam-6641	167	61	.	.	PUNCT
ejpam-6641	168	1	as	as	ADP
ejpam-6641	168	2	a	a	DET
ejpam-6641	168	3	result	result	NOUN
ejpam-6641	168	4	we	we	PRON
ejpam-6641	168	5	get	get	VERB
ejpam-6641	168	6	|sζ(g1l)(ℓ)|	|sζ(g1l)(ℓ)|	PROPN
ejpam-6641	168	7	=	=	PUNCT
ejpam-6641	168	8	∫	∫	PROPN
ejpam-6641	168	9	∫	∫	PROPN
ejpam-6641	168	10	γ(ℓ	γ(ℓ	X
ejpam-6641	168	11	)	)	PUNCT
ejpam-6641	169	1	(	(	PUNCT
ejpam-6641	169	2	sup	sup	NOUN
ejpam-6641	169	3	ϕ∈cζ	ϕ∈cζ	PROPN
ejpam-6641	169	4	|g1l	|g1l	PROPN
ejpam-6641	169	5	∗	∗	NOUN
ejpam-6641	169	6	ϕt(y)|2	ϕt(y)|2	PROPN
ejpam-6641	169	7	dydt	dydt	PROPN
ejpam-6641	169	8	tn+1	tn+1	PROPN
ejpam-6641	169	9	)	)	PUNCT
ejpam-6641	169	10	2	2	NUM
ejpam-6641	169	11			PROPN
ejpam-6641	169	12	1/2	1/2	NUM
ejpam-6641	169	13	≤	≤	NOUN
ejpam-6641	169	14	c	c	NOUN
ejpam-6641	169	15			PROPN
ejpam-6641	169	16	∞∫	∞∫	PROPN
ejpam-6641	170	1	|ℓ|	|ℓ|	VERB
ejpam-6641	170	2	4	4	NUM
ejpam-6641	170	3	∫	∫	PROPN
ejpam-6641	170	4	{	{	PUNCT
ejpam-6641	170	5	y:|ℓ−y|<t	y:|ℓ−y|<t	PROPN
ejpam-6641	170	6	}	}	PUNCT
ejpam-6641	170	7			NOUN
ejpam-6641	170	8	1	1	NUM
ejpam-6641	170	9	tn	tn	PROPN
ejpam-6641	170	10	∫	∫	PROPN
ejpam-6641	170	11	{	{	PUNCT
ejpam-6641	170	12	ℓ∈tl:|y−ℓ|<t	ℓ∈tl:|y−ℓ|<t	PROPN
ejpam-6641	170	13	}	}	PUNCT
ejpam-6641	170	14	|g(ℓ)|dℓ	|g(ℓ)|dℓ	PUNCT
ejpam-6641	170	15			PROPN
ejpam-6641	170	16	2	2	NUM
ejpam-6641	170	17	dydt	dydt	NOUN
ejpam-6641	170	18	tn+1	tn+1	NOUN
ejpam-6641	170	19			NOUN
ejpam-6641	170	20	1/2	1/2	NUM
ejpam-6641	170	21	≤	≤	NOUN
ejpam-6641	170	22	c	c	NOUN
ejpam-6641	170	23	∫	∫	PROPN
ejpam-6641	170	24	tl	tl	PROPN
ejpam-6641	170	25	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	170	26			PROPN
ejpam-6641	170	27			PROPN
ejpam-6641	170	28	∞∫	∞∫	PROPN
ejpam-6641	170	29	|ℓ|	|ℓ|	VERB
ejpam-6641	170	30	4	4	NUM
ejpam-6641	170	31			PROPN
ejpam-6641	170	32	∫	∫	PROPN
ejpam-6641	170	33	{	{	PUNCT
ejpam-6641	170	34	y:|ℓ−y|<t	y:|ℓ−y|<t	PROPN
ejpam-6641	170	35	}	}	PUNCT
ejpam-6641	170	36	dy	dy	NOUN
ejpam-6641	170	37			PROPN
ejpam-6641	170	38	dt	dt	PROPN
ejpam-6641	170	39	t3n+1	t3n+1	PROPN
ejpam-6641	170	40			NOUN
ejpam-6641	171	1	1/2	1/2	NUM
ejpam-6641	171	2	=	=	SYM
ejpam-6641	171	3	c	c	PROPN
ejpam-6641	171	4	∫	∫	PROPN
ejpam-6641	171	5	tl	tl	PROPN
ejpam-6641	171	6	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	171	7			PROPN
ejpam-6641	171	8			PROPN
ejpam-6641	171	9	∞∫	∞∫	PROPN
ejpam-6641	171	10	|ℓ|	|ℓ|	VERB
ejpam-6641	171	11	4	4	NUM
ejpam-6641	171	12	dt	dt	NOUN
ejpam-6641	171	13	t2n+1	t2n+1	NOUN
ejpam-6641	171	14			NOUN
ejpam-6641	171	15	1/2	1/2	NUM
ejpam-6641	171	16	=	=	SYM
ejpam-6641	171	17	c	c	PROPN
ejpam-6641	171	18	∫	∫	PROPN
ejpam-6641	171	19	tl	tl	PROPN
ejpam-6641	171	20	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	171	21			PROPN
ejpam-6641	171	22	|ℓ|−n	|ℓ|−n	PROPN
ejpam-6641	171	23	.	.	PUNCT
ejpam-6641	172	1	estimation	estimation	NOUN
ejpam-6641	172	2	of	of	ADP
ejpam-6641	172	3	sζf0(ℓ	sζf0(ℓ	NOUN
ejpam-6641	172	4	)	)	PUNCT
ejpam-6641	172	5	.	.	PUNCT
ejpam-6641	173	1	for	for	ADP
ejpam-6641	173	2	ℓ	ℓ	PROPN
ejpam-6641	173	3	∈	∈	PROPN
ejpam-6641	173	4	o(0	o(0	NOUN
ejpam-6641	173	5	,	,	PUNCT
ejpam-6641	173	6	1	1	NUM
ejpam-6641	173	7	)	)	PUNCT
ejpam-6641	173	8	,	,	PUNCT
ejpam-6641	173	9	ℓ	ℓ	PROPN
ejpam-6641	173	10	∈	∈	PROPN
ejpam-6641	173	11	tt,2	tt,2	PROPN
ejpam-6641	173	12	t	t	PROPN
ejpam-6641	173	13	|sζ(f0)(ℓ)|	|sζ(f0)(ℓ)|	NUM
ejpam-6641	173	14	≤	≤	NUM
ejpam-6641	173	15	ct−n	ct−n	NOUN
ejpam-6641	173	16	∫	∫	PROPN
ejpam-6641	173	17	o(0,1	o(0,1	NUM
ejpam-6641	173	18	)	)	PUNCT
ejpam-6641	173	19	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	173	20	≤	≤	PROPN
ejpam-6641	173	21	ct−n∥f0∥p(·)∥1o(0,1)∥p′	ct−n∥f0∥p(·)∥1o(0,1)∥p′	PROPN
ejpam-6641	173	22	(	(	PUNCT
ejpam-6641	173	23	·	·	PUNCT
ejpam-6641	173	24	)	)	PUNCT
ejpam-6641	173	25	≤	≤	NUM
ejpam-6641	173	26	ct−n∥f0∥p	ct−n∥f0∥p	NOUN
ejpam-6641	173	27	(	(	PUNCT
ejpam-6641	173	28	·	·	PUNCT
ejpam-6641	173	29	)	)	PUNCT
ejpam-6641	173	30	.	.	PUNCT
ejpam-6641	174	1	n(sζf0)p	n(sζf0)p	PROPN
ejpam-6641	174	2	,	,	PUNCT
ejpam-6641	174	3	q	q	X
ejpam-6641	174	4	,	,	PUNCT
ejpam-6641	174	5	κ	κ	PROPN
ejpam-6641	174	6	≤	≤	PROPN
ejpam-6641	174	7	c∥tκ∞−n∥1tt,2t∥lp(·)∥lq((2,∞	c∥tκ∞−n∥1tt,2t∥lp(·)∥lq((2,∞	NOUN
ejpam-6641	174	8	)	)	PUNCT
ejpam-6641	174	9	;	;	PUNCT
ejpam-6641	174	10	dt	dt	PROPN
ejpam-6641	174	11	t	t	PROPN
ejpam-6641	174	12	)	)	PUNCT
ejpam-6641	174	13	∥f0∥lp	∥f0∥lp	PROPN
ejpam-6641	174	14	(	(	PUNCT
ejpam-6641	174	15	·	·	PUNCT
ejpam-6641	174	16	)	)	PUNCT
ejpam-6641	174	17	≤	≤	NOUN
ejpam-6641	175	1	c∥tκ∞−	c∥tκ∞−	NOUN
ejpam-6641	175	2	n	n	CCONJ
ejpam-6641	175	3	p′∞	p′∞	ADJ
ejpam-6641	175	4	∥lq((2,∞	∥lq((2,∞	NUM
ejpam-6641	175	5	)	)	PUNCT
ejpam-6641	175	6	;	;	PUNCT
ejpam-6641	175	7	dt	dt	PROPN
ejpam-6641	175	8	t	t	PROPN
ejpam-6641	175	9	)	)	PUNCT
ejpam-6641	175	10	∥f0∥lp	∥f0∥lp	PROPN
ejpam-6641	175	11	(	(	PUNCT
ejpam-6641	175	12	·	·	PUNCT
ejpam-6641	175	13	)	)	PUNCT
ejpam-6641	175	14	≤	≤	NOUN
ejpam-6641	175	15	c∥f0∥lp	c∥f0∥lp	PUNCT
ejpam-6641	175	16	(	(	PUNCT
ejpam-6641	175	17	·	·	PUNCT
ejpam-6641	175	18	)	)	PUNCT
ejpam-6641	175	19	.	.	PUNCT
ejpam-6641	176	1	estimation	estimation	NOUN
ejpam-6641	176	2	of	of	ADP
ejpam-6641	176	3	sζft(ℓ	sζft(ℓ	NOUN
ejpam-6641	176	4	)	)	PUNCT
ejpam-6641	176	5	.	.	PUNCT
ejpam-6641	177	1	let	let	VERB
ejpam-6641	177	2	ℓ	ℓ	PROPN
ejpam-6641	177	3	∈	∈	PROPN
ejpam-6641	177	4	tt,2	tt,2	PROPN
ejpam-6641	177	5	t	t	PROPN
ejpam-6641	177	6	|sζft(ℓ)|	|sζft(ℓ)|	PROPN
ejpam-6641	177	7	≤	≤	PROPN
ejpam-6641	177	8	c	c	PROPN
ejpam-6641	177	9	∫	∫	PROPN
ejpam-6641	177	10	o(0	o(0	PROPN
ejpam-6641	177	11	,	,	PUNCT
ejpam-6641	177	12	t	t	PROPN
ejpam-6641	177	13	2	2	NUM
ejpam-6641	177	14	)	)	PUNCT
ejpam-6641	177	15	\o(0,1	\o(0,1	NOUN
ejpam-6641	177	16	)	)	PUNCT
ejpam-6641	177	17	t−ng(ℓ)dℓ.	t−ng(ℓ)dℓ.	NOUN
ejpam-6641	177	18	g.	g.	PROPN
ejpam-6641	177	19	a.	a.	PROPN
ejpam-6641	177	20	basendwah	basendwah	PROPN
ejpam-6641	177	21	et	et	PROPN
ejpam-6641	177	22	al	al	PROPN
ejpam-6641	178	1	.	.	PUNCT
ejpam-6641	178	2	/	/	SYM
ejpam-6641	178	3	eur	eur	PROPN
ejpam-6641	178	4	.	.	PUNCT
ejpam-6641	179	1	j.	j.	PROPN
ejpam-6641	179	2	pure	pure	PROPN
ejpam-6641	179	3	appl	appl	PROPN
ejpam-6641	179	4	.	.	PROPN
ejpam-6641	179	5	math	math	PROPN
ejpam-6641	179	6	,	,	PUNCT
ejpam-6641	179	7	18	18	NUM
ejpam-6641	179	8	(	(	PUNCT
ejpam-6641	179	9	4	4	NUM
ejpam-6641	179	10	)	)	PUNCT
ejpam-6641	179	11	(	(	PUNCT
ejpam-6641	179	12	2025	2025	NUM
ejpam-6641	179	13	)	)	PUNCT
ejpam-6641	179	14	,	,	PUNCT
ejpam-6641	179	15	6641	6641	NUM
ejpam-6641	179	16	10	10	NUM
ejpam-6641	179	17	of	of	ADP
ejpam-6641	179	18	16	16	NUM
ejpam-6641	179	19	in	in	ADP
ejpam-6641	179	20	this	this	DET
ejpam-6641	179	21	context	context	NOUN
ejpam-6641	179	22	,	,	PUNCT
ejpam-6641	179	23	utilizing	utilize	VERB
ejpam-6641	179	24	hölder	hölder	NOUN
ejpam-6641	179	25	’s	’s	PART
ejpam-6641	179	26	inequality	inequality	NOUN
ejpam-6641	179	27	alongside	alongside	ADP
ejpam-6641	179	28	lemma	lemma	PROPN
ejpam-6641	179	29	(	(	PUNCT
ejpam-6641	179	30	2	2	NUM
ejpam-6641	179	31	)	)	PUNCT
ejpam-6641	179	32	,	,	PUNCT
ejpam-6641	179	33	we	we	PRON
ejpam-6641	179	34	derive	derive	VERB
ejpam-6641	179	35	,	,	PUNCT
ejpam-6641	179	36	|sβft(ℓ)|	|sβft(ℓ)|	NOUN
ejpam-6641	179	37	≤	≤	NUM
ejpam-6641	179	38	c	c	PROPN
ejpam-6641	179	39	tn	tn	PROPN
ejpam-6641	179	40	∫	∫	PROPN
ejpam-6641	179	41	1<|y|	1<|y|	NUM
ejpam-6641	179	42	<	<	X
ejpam-6641	179	43	t	t	PROPN
ejpam-6641	180	1	2	2	NUM
ejpam-6641	180	2	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	180	3	≤	≤	PROPN
ejpam-6641	180	4	c	c	PROPN
ejpam-6641	180	5	tn	tn	NOUN
ejpam-6641	180	6	t∫	t∫	NOUN
ejpam-6641	180	7	1	1	NUM
ejpam-6641	180	8	dρ	dρ	NOUN
ejpam-6641	180	9	ρ	ρ	PROPN
ejpam-6641	180	10	∫	∫	PROPN
ejpam-6641	180	11	ρ	ρ	PROPN
ejpam-6641	180	12	2	2	NUM
ejpam-6641	180	13	<	<	X
ejpam-6641	180	14	|y|<ρ	|y|<ρ	PROPN
ejpam-6641	180	15	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	180	16	≤	≤	PROPN
ejpam-6641	180	17	c	c	PROPN
ejpam-6641	180	18	tn	tn	NOUN
ejpam-6641	181	1	t∫	t∫	NOUN
ejpam-6641	181	2	1	1	NUM
ejpam-6641	181	3	dρ	dρ	ADJ
ejpam-6641	181	4	ρ	ρ	NOUN
ejpam-6641	181	5	∥g1	∥g1	NOUN
ejpam-6641	181	6	t	t	PROPN
ejpam-6641	181	7	ρ	ρ	NUM
ejpam-6641	181	8	2	2	NUM
ejpam-6641	181	9	,	,	PUNCT
ejpam-6641	181	10	ρ	ρ	PROPN
ejpam-6641	181	11	∥p(·)∥1	∥p(·)∥1	PROPN
ejpam-6641	181	12	t	t	PROPN
ejpam-6641	181	13	ρ	ρ	PROPN
ejpam-6641	181	14	2	2	NUM
ejpam-6641	181	15	,	,	PUNCT
ejpam-6641	181	16	ρ	ρ	PROPN
ejpam-6641	181	17	∥p′	∥p′	PROPN
ejpam-6641	181	18	(	(	PUNCT
ejpam-6641	181	19	·	·	PUNCT
ejpam-6641	181	20	)	)	PUNCT
ejpam-6641	181	21	≤	≤	NUM
ejpam-6641	182	1	c	c	NOUN
ejpam-6641	182	2	tn	tn	NOUN
ejpam-6641	182	3	t∫	t∫	ADJ
ejpam-6641	182	4	1	1	NUM
ejpam-6641	182	5	∥g1	∥g1	NOUN
ejpam-6641	182	6	t	t	PROPN
ejpam-6641	182	7	ρ	ρ	NUM
ejpam-6641	182	8	2	2	NUM
ejpam-6641	182	9	,	,	PUNCT
ejpam-6641	182	10	ρ	ρ	PROPN
ejpam-6641	182	11	∥p(·)ρ	∥p(·)ρ	NOUN
ejpam-6641	182	12	n	n	CCONJ
ejpam-6641	182	13	p′∞	p′∞	ADV
ejpam-6641	182	14	−1	−1	NOUN
ejpam-6641	182	15	dρ	dρ	PROPN
ejpam-6641	182	16	.	.	PUNCT
ejpam-6641	183	1	tκ∞∥|sζft(ℓ).1tt,2t∥p	tκ∞∥|sζft(ℓ).1tt,2t∥p	PROPN
ejpam-6641	183	2	(	(	PUNCT
ejpam-6641	183	3	·	·	PUNCT
ejpam-6641	183	4	)	)	PUNCT
ejpam-6641	183	5	≤	≤	NUM
ejpam-6641	184	1	ct	ct	NUM
ejpam-6641	184	2	κ∞−n+	κ∞−n+	NOUN
ejpam-6641	184	3	n	n	NOUN
ejpam-6641	184	4	p∞	p∞	X
ejpam-6641	184	5	t∫	t∫	DET
ejpam-6641	184	6	1	1	NUM
ejpam-6641	184	7	∥g1	∥g1	NOUN
ejpam-6641	184	8	t	t	PROPN
ejpam-6641	184	9	ρ	ρ	NUM
ejpam-6641	184	10	2	2	NUM
ejpam-6641	184	11	,	,	PUNCT
ejpam-6641	184	12	ρ	ρ	PROPN
ejpam-6641	184	13	∥p(·)ρ	∥p(·)ρ	NOUN
ejpam-6641	184	14	n	n	CCONJ
ejpam-6641	184	15	p′∞	p′∞	ADV
ejpam-6641	184	16	−1	−1	NOUN
ejpam-6641	184	17	dρ	dρ	ADJ
ejpam-6641	184	18	≤	≤	NUM
ejpam-6641	184	19	ct	ct	NUM
ejpam-6641	184	20	κ∞+	κ∞+	PROPN
ejpam-6641	184	21	n	n	CCONJ
ejpam-6641	184	22	p′∞	p′∞	X
ejpam-6641	184	23	t∫	t∫	DET
ejpam-6641	184	24	1	1	NUM
ejpam-6641	184	25	∥g1	∥g1	NOUN
ejpam-6641	184	26	t	t	NOUN
ejpam-6641	184	27	ρ	ρ	NUM
ejpam-6641	184	28	2	2	NUM
ejpam-6641	184	29	,	,	PUNCT
ejpam-6641	184	30	ρ	ρ	PROPN
ejpam-6641	184	31	∥p(·)ρ	∥p(·)ρ	NOUN
ejpam-6641	184	32	n	n	CCONJ
ejpam-6641	184	33	p′∞	p′∞	ADV
ejpam-6641	184	34	−1	−1	NOUN
ejpam-6641	184	35	dρ	dρ	ADJ
ejpam-6641	184	36	≤	≤	NOUN
ejpam-6641	184	37	t∫	t∫	DET
ejpam-6641	184	38	1	1	NUM
ejpam-6641	184	39	(	(	PUNCT
ejpam-6641	184	40	t	t	PROPN
ejpam-6641	184	41	ρ	ρ	PROPN
ejpam-6641	184	42	)	)	PUNCT
ejpam-6641	184	43	κ∞−	κ∞−	NUM
ejpam-6641	184	44	n	n	CCONJ
ejpam-6641	184	45	p′∞	p′∞	ADJ
ejpam-6641	184	46	ω(ρ	ω(ρ	NOUN
ejpam-6641	184	47	)	)	PUNCT
ejpam-6641	184	48	dρ	dρ	PROPN
ejpam-6641	184	49	ρ	ρ	NOUN
ejpam-6641	184	50	,	,	PUNCT
ejpam-6641	184	51	where	where	SCONJ
ejpam-6641	184	52	ω(ρ	ω(ρ	NOUN
ejpam-6641	184	53	)	)	PUNCT
ejpam-6641	184	54	=	=	PRON
ejpam-6641	184	55	ρκ∞∥g1r	ρκ∞∥g1r	VERB
ejpam-6641	184	56	ρ	ρ	PROPN
ejpam-6641	184	57	2	2	NUM
ejpam-6641	184	58	,	,	PUNCT
ejpam-6641	184	59	ρ	ρ	PROPN
ejpam-6641	184	60	∥p	∥p	X
ejpam-6641	184	61	(	(	PUNCT
ejpam-6641	184	62	·	·	PUNCT
ejpam-6641	184	63	)	)	PUNCT
ejpam-6641	184	64	.	.	PUNCT
ejpam-6641	185	1	define	define	VERB
ejpam-6641	185	2	k(t	k(t	PROPN
ejpam-6641	185	3	)	)	PUNCT
ejpam-6641	185	4	as	as	ADP
ejpam-6641	185	5	k(t	k(t	X
ejpam-6641	185	6	)	)	PUNCT
ejpam-6641	186	1	=	=	PRON
ejpam-6641	186	2	{	{	PUNCT
ejpam-6641	186	3	t	t	PROPN
ejpam-6641	186	4	κ∞−	κ∞−	NUM
ejpam-6641	186	5	n	n	CCONJ
ejpam-6641	186	6	p′∞	p′∞	NOUN
ejpam-6641	186	7	,	,	PUNCT
ejpam-6641	186	8	t	t	X
ejpam-6641	186	9	>	>	X
ejpam-6641	186	10	1	1	NUM
ejpam-6641	186	11	,	,	PUNCT
ejpam-6641	186	12	0	0	NUM
ejpam-6641	186	13	,	,	PUNCT
ejpam-6641	186	14	0	0	NUM
ejpam-6641	186	15	<	<	X
ejpam-6641	186	16	t	t	X
ejpam-6641	186	17	<	<	X
ejpam-6641	186	18	1	1	NUM
ejpam-6641	186	19	,	,	PUNCT
ejpam-6641	186	20	(	(	PUNCT
ejpam-6641	186	21	4.4	4.4	NUM
ejpam-6641	186	22	)	)	PUNCT
ejpam-6641	186	23	by	by	ADP
ejpam-6641	186	24	defining	define	VERB
ejpam-6641	186	25	,	,	PUNCT
ejpam-6641	186	26	the	the	DET
ejpam-6641	186	27	operator	operator	NOUN
ejpam-6641	186	28	hω(t	hω(t	NOUN
ejpam-6641	186	29	)	)	PUNCT
ejpam-6641	187	1	=	=	SYM
ejpam-6641	187	2	∞∫	∞∫	NOUN
ejpam-6641	187	3	0	0	PUNCT
ejpam-6641	188	1	k	k	PROPN
ejpam-6641	188	2	(	(	PUNCT
ejpam-6641	188	3	tρ)ω(ρ	tρ)ω(ρ	NOUN
ejpam-6641	188	4	)	)	PUNCT
ejpam-6641	188	5	dρ	dρ	PROPN
ejpam-6641	188	6	ρ	ρ	PROPN
ejpam-6641	188	7	,	,	PUNCT
ejpam-6641	188	8	as	as	ADP
ejpam-6641	188	9	a	a	DET
ejpam-6641	188	10	result	result	NOUN
ejpam-6641	188	11	we	we	PRON
ejpam-6641	188	12	get	get	VERB
ejpam-6641	188	13	n	n	PRON
ejpam-6641	188	14	(	(	PUNCT
ejpam-6641	188	15	sζft)p	sζft)p	PROPN
ejpam-6641	188	16	,	,	PUNCT
ejpam-6641	188	17	q	q	X
ejpam-6641	188	18	,	,	PUNCT
ejpam-6641	188	19	κ	κ	PROPN
ejpam-6641	188	20	≤	≤	NUM
ejpam-6641	188	21	∥hω∥lq((2,∞	∥hω∥lq((2,∞	NOUN
ejpam-6641	188	22	)	)	PUNCT
ejpam-6641	188	23	)	)	PUNCT
ejpam-6641	189	1	;	;	PUNCT
ejpam-6641	190	1	dt	dt	PROPN
ejpam-6641	190	2	t	t	PROPN
ejpam-6641	190	3	)	)	PUNCT
ejpam-6641	190	4	≤	≤	PROPN
ejpam-6641	190	5	∥ω∥lq((2,∞	∥ω∥lq((2,∞	PROPN
ejpam-6641	190	6	)	)	PUNCT
ejpam-6641	190	7	)	)	PUNCT
ejpam-6641	190	8	;	;	PUNCT
ejpam-6641	191	1	dt	dt	PROPN
ejpam-6641	191	2	t	t	PROPN
ejpam-6641	191	3	)	)	PUNCT
ejpam-6641	191	4	≤	≤	PROPN
ejpam-6641	191	5	∥tκ∞∥g1tt,2t∥p(·)∥lq((1,2	∥tκ∞∥g1tt,2t∥p(·)∥lq((1,2	PROPN
ejpam-6641	191	6	)	)	PUNCT
ejpam-6641	191	7	)	)	PUNCT
ejpam-6641	191	8	;	;	PUNCT
ejpam-6641	191	9	dt	dt	PROPN
ejpam-6641	191	10	t	t	PROPN
ejpam-6641	191	11	)	)	PUNCT
ejpam-6641	191	12	+	+	CCONJ
ejpam-6641	191	13	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	NUM
ejpam-6641	191	14	)	)	PUNCT
ejpam-6641	191	15	)	)	PUNCT
ejpam-6641	191	16	;	;	PUNCT
ejpam-6641	192	1	dt	dt	PROPN
ejpam-6641	192	2	t	t	PROPN
ejpam-6641	192	3	)	)	PUNCT
ejpam-6641	192	4	≤	≤	ADV
ejpam-6641	192	5	∥g∥lp(·)(o(0,4)\o(0,1	∥g∥lp(·)(o(0,4)\o(0,1	NOUN
ejpam-6641	192	6	)	)	PUNCT
ejpam-6641	192	7	)	)	PUNCT
ejpam-6641	193	1	+	+	CCONJ
ejpam-6641	193	2	∥tκ∞∥g1tt,2t∥p(·)∥lq((2,∞	∥tκ∞∥g1tt,2t∥p(·)∥lq((2,∞	VERB
ejpam-6641	193	3	)	)	PUNCT
ejpam-6641	193	4	)	)	PUNCT
ejpam-6641	193	5	;	;	PUNCT
ejpam-6641	193	6	dt	dt	PROPN
ejpam-6641	193	7	t	t	PROPN
ejpam-6641	193	8	)	)	PUNCT
ejpam-6641	193	9	≤	≤	PUNCT
ejpam-6641	194	1	∥g∥	∥g∥	PROPN
ejpam-6641	194	2	h	h	PROPN
ejpam-6641	194	3	p(·),q	p(·),q	PROPN
ejpam-6641	194	4	,	,	PUNCT
ejpam-6641	194	5	κ	κ	X
ejpam-6641	194	6	(	(	PUNCT
ejpam-6641	194	7	·	·	PUNCT
ejpam-6641	194	8	)	)	PUNCT
ejpam-6641	194	9	2	2	NUM
ejpam-6641	194	10	.	.	PUNCT
ejpam-6641	195	1	g.	g.	PROPN
ejpam-6641	195	2	a.	a.	PROPN
ejpam-6641	195	3	basendwah	basendwah	PROPN
ejpam-6641	195	4	et	et	PROPN
ejpam-6641	195	5	al	al	PROPN
ejpam-6641	195	6	.	.	PUNCT
ejpam-6641	195	7	/	/	SYM
ejpam-6641	195	8	eur	eur	PROPN
ejpam-6641	195	9	.	.	PUNCT
ejpam-6641	196	1	j.	j.	PROPN
ejpam-6641	196	2	pure	pure	PROPN
ejpam-6641	196	3	appl	appl	PROPN
ejpam-6641	196	4	.	.	PROPN
ejpam-6641	196	5	math	math	PROPN
ejpam-6641	196	6	,	,	PUNCT
ejpam-6641	196	7	18	18	NUM
ejpam-6641	196	8	(	(	PUNCT
ejpam-6641	196	9	4	4	NUM
ejpam-6641	196	10	)	)	PUNCT
ejpam-6641	196	11	(	(	PUNCT
ejpam-6641	196	12	2025	2025	NUM
ejpam-6641	196	13	)	)	PUNCT
ejpam-6641	196	14	,	,	PUNCT
ejpam-6641	196	15	6641	6641	NUM
ejpam-6641	196	16	11	11	NUM
ejpam-6641	196	17	of	of	ADP
ejpam-6641	196	18	16	16	NUM
ejpam-6641	196	19	by	by	ADP
ejpam-6641	196	20	employing	employ	VERB
ejpam-6641	196	21	(	(	PUNCT
ejpam-6641	196	22	[	[	X
ejpam-6641	196	23	13	13	NUM
ejpam-6641	196	24	]	]	PUNCT
ejpam-6641	196	25	,	,	PUNCT
ejpam-6641	196	26	corollary	corollary	ADJ
ejpam-6641	196	27	4.5	4.5	NUM
ejpam-6641	196	28	)	)	PUNCT
ejpam-6641	196	29	,	,	PUNCT
ejpam-6641	196	30	the	the	DET
ejpam-6641	196	31	inequality	inequality	NOUN
ejpam-6641	196	32	κ∞	κ∞	PROPN
ejpam-6641	196	33	−	−	PROPN
ejpam-6641	196	34	n	n	CCONJ
ejpam-6641	196	35	p′∞	p′∞	ADV
ejpam-6641	196	36	≤	≤	NOUN
ejpam-6641	196	37	0	0	NUM
ejpam-6641	196	38	,	,	PUNCT
ejpam-6641	196	39	incorporating	incorporate	VERB
ejpam-6641	196	40	embedding	embed	VERB
ejpam-6641	196	41	in	in	ADP
ejpam-6641	196	42	the	the	DET
ejpam-6641	196	43	last	last	ADJ
ejpam-6641	196	44	inequality	inequality	NOUN
ejpam-6641	196	45	o(0	o(0	NOUN
ejpam-6641	196	46	,	,	PUNCT
ejpam-6641	196	47	4	4	NUM
ejpam-6641	196	48	)	)	PUNCT
ejpam-6641	196	49	\	\	NOUN
ejpam-6641	197	1	o(0	o(0	PROPN
ejpam-6641	197	2	,	,	PUNCT
ejpam-6641	197	3	1	1	NUM
ejpam-6641	197	4	)	)	PUNCT
ejpam-6641	197	5	⊂	⊂	PROPN
ejpam-6641	198	1	o(0	o(0	ADJ
ejpam-6641	198	2	,	,	PUNCT
ejpam-6641	198	3	2	2	NUM
ejpam-6641	198	4	+	+	SYM
ejpam-6641	198	5	θ	θ	NOUN
ejpam-6641	198	6	)	)	PUNCT
ejpam-6641	198	7	∪o(0	∪o(0	NUM
ejpam-6641	198	8	,	,	PUNCT
ejpam-6641	198	9	4	4	NUM
ejpam-6641	198	10	)	)	PUNCT
ejpam-6641	198	11	\	\	NOUN
ejpam-6641	198	12	o(0	o(0	PROPN
ejpam-6641	198	13	,	,	PUNCT
ejpam-6641	198	14	2	2	NUM
ejpam-6641	198	15	+	+	SYM
ejpam-6641	198	16	θ	θ	NOUN
ejpam-6641	198	17	)	)	PUNCT
ejpam-6641	198	18	,	,	PUNCT
ejpam-6641	198	19	and	and	CCONJ
ejpam-6641	198	20	with	with	ADP
ejpam-6641	198	21	the	the	DET
ejpam-6641	198	22	assistance	assistance	NOUN
ejpam-6641	198	23	of	of	ADP
ejpam-6641	198	24	lemma	lemma	PROPN
ejpam-6641	198	25	(	(	PUNCT
ejpam-6641	198	26	4	4	NUM
ejpam-6641	198	27	)	)	PUNCT
ejpam-6641	198	28	.	.	PUNCT
ejpam-6641	199	1	estimation	estimation	NOUN
ejpam-6641	199	2	of	of	ADP
ejpam-6641	199	3	sζgt(ℓ	sζgt(ℓ	NOUN
ejpam-6641	199	4	)	)	PUNCT
ejpam-6641	199	5	.	.	PUNCT
ejpam-6641	200	1	by	by	ADP
ejpam-6641	200	2	the	the	DET
ejpam-6641	200	3	lp	lp	PROPN
ejpam-6641	200	4	(	(	PUNCT
ejpam-6641	200	5	·	·	PUNCT
ejpam-6641	200	6	)	)	PUNCT
ejpam-6641	200	7	−→	−→	NOUN
ejpam-6641	200	8	lp	lp	PROPN
ejpam-6641	200	9	(	(	PUNCT
ejpam-6641	200	10	·	·	PUNCT
ejpam-6641	200	11	)	)	PUNCT
ejpam-6641	200	12	boundedness	boundedness	NOUN
ejpam-6641	200	13	of	of	ADP
ejpam-6641	200	14	sζ	sζ	PROPN
ejpam-6641	200	15	,	,	PUNCT
ejpam-6641	200	16	we	we	PRON
ejpam-6641	200	17	obtain	obtain	VERB
ejpam-6641	200	18	∥sζgt)1rt,2t∥p	∥sζgt)1rt,2t∥p	NOUN
ejpam-6641	200	19	(	(	PUNCT
ejpam-6641	200	20	·	·	PUNCT
ejpam-6641	200	21	)	)	PUNCT
ejpam-6641	200	22	≤	≤	NUM
ejpam-6641	201	1	∥gt∥lp	∥gt∥lp	X
ejpam-6641	201	2	(	(	PUNCT
ejpam-6641	201	3	·	·	PUNCT
ejpam-6641	201	4	)	)	PUNCT
ejpam-6641	201	5	≤	≤	NUM
ejpam-6641	201	6	2∑	2∑	NUM
ejpam-6641	201	7	j=−1	j=−1	NOUN
ejpam-6641	201	8	∥g1r	∥g1r	NOUN
ejpam-6641	201	9	2jt,2j+1	2jt,2j+1	NUM
ejpam-6641	201	10	t	t	NOUN
ejpam-6641	201	11	∥p	∥p	VERB
ejpam-6641	201	12	(	(	PUNCT
ejpam-6641	201	13	·	·	PUNCT
ejpam-6641	201	14	)	)	PUNCT
ejpam-6641	201	15	.	.	PUNCT
ejpam-6641	202	1	n(sζgt)p	n(sζgt)p	PROPN
ejpam-6641	202	2	,	,	PUNCT
ejpam-6641	202	3	q	q	NOUN
ejpam-6641	202	4	,	,	PUNCT
ejpam-6641	202	5	κ	κ	PROPN
ejpam-6641	202	6	≤	≤	PROPN
ejpam-6641	202	7	c∥tκ∞∥g1r	c∥tκ∞∥g1r	PROPN
ejpam-6641	202	8	t	t	PROPN
ejpam-6641	202	9	2	2	NUM
ejpam-6641	202	10	,	,	PUNCT
ejpam-6641	202	11	t	t	PROPN
ejpam-6641	202	12	∥p(·)∥lq((2,∞	∥p(·)∥lq((2,∞	PROPN
ejpam-6641	202	13	)	)	PUNCT
ejpam-6641	202	14	;	;	PUNCT
ejpam-6641	202	15	dt	dt	PROPN
ejpam-6641	202	16	t	t	PROPN
ejpam-6641	202	17	)	)	PUNCT
ejpam-6641	202	18	+	+	CCONJ
ejpam-6641	202	19	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	VERB
ejpam-6641	202	20	)	)	PUNCT
ejpam-6641	202	21	;	;	PUNCT
ejpam-6641	202	22	dt	dt	PROPN
ejpam-6641	202	23	t	t	PROPN
ejpam-6641	202	24	)	)	PUNCT
ejpam-6641	202	25	≤	≤	NUM
ejpam-6641	202	26	c∥tκ∞∥g1rt,2t∥p(·)∥lq(·)((1,2	c∥tκ∞∥g1rt,2t∥p(·)∥lq(·)((1,2	NOUN
ejpam-6641	202	27	)	)	PUNCT
ejpam-6641	202	28	;	;	PUNCT
ejpam-6641	202	29	dt	dt	PROPN
ejpam-6641	202	30	t	t	PROPN
ejpam-6641	202	31	)	)	PUNCT
ejpam-6641	202	32	+	+	CCONJ
ejpam-6641	202	33	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	VERB
ejpam-6641	202	34	)	)	PUNCT
ejpam-6641	202	35	;	;	PUNCT
ejpam-6641	202	36	dt	dt	PROPN
ejpam-6641	202	37	t	t	PROPN
ejpam-6641	202	38	)	)	PUNCT
ejpam-6641	202	39	≤	≤	PUNCT
ejpam-6641	203	1	∥g∥	∥g∥	PROPN
ejpam-6641	203	2	h	h	PROPN
ejpam-6641	203	3	p(·),q	p(·),q	PROPN
ejpam-6641	203	4	,	,	PUNCT
ejpam-6641	203	5	κ	κ	X
ejpam-6641	203	6	(	(	PUNCT
ejpam-6641	203	7	·	·	PUNCT
ejpam-6641	203	8	)	)	PUNCT
ejpam-6641	203	9	2	2	NUM
ejpam-6641	203	10	here	here	ADV
ejpam-6641	203	11	we	we	PRON
ejpam-6641	203	12	used	use	VERB
ejpam-6641	203	13	the	the	DET
ejpam-6641	203	14	facts	fact	NOUN
ejpam-6641	203	15	,	,	PUNCT
ejpam-6641	203	16	∥tκ∞∥g1	∥tκ∞∥g1	PROPN
ejpam-6641	203	17	t	t	PROPN
ejpam-6641	203	18	2jt,2j+1	2jt,2j+1	NUM
ejpam-6641	203	19	t	t	PROPN
ejpam-6641	203	20	∥p(·)∥lq((2,∞	∥p(·)∥lq((2,∞	PROPN
ejpam-6641	203	21	)	)	PUNCT
ejpam-6641	203	22	;	;	PUNCT
ejpam-6641	203	23	dt	dt	PROPN
ejpam-6641	203	24	t	t	PROPN
ejpam-6641	203	25	)	)	PUNCT
ejpam-6641	203	26	≤	≤	NUM
ejpam-6641	203	27	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	∥tκ∞∥g1rt,2t∥p(·)∥lq((2,∞	VERB
ejpam-6641	203	28	)	)	PUNCT
ejpam-6641	203	29	;	;	PUNCT
ejpam-6641	203	30	dt	dt	PROPN
ejpam-6641	203	31	t	t	PROPN
ejpam-6641	203	32	)	)	PUNCT
ejpam-6641	203	33	,	,	PUNCT
ejpam-6641	203	34	j	j	PROPN
ejpam-6641	204	1	=	=	SYM
ejpam-6641	204	2	1	1	NUM
ejpam-6641	204	3	,	,	PUNCT
ejpam-6641	204	4	2	2	NUM
ejpam-6641	204	5	,	,	PUNCT
ejpam-6641	204	6	and	and	CCONJ
ejpam-6641	204	7	∥g1rt,2t∥lp	∥g1rt,2t∥lp	PROPN
ejpam-6641	204	8	(	(	PUNCT
ejpam-6641	204	9	·	·	PUNCT
ejpam-6641	204	10	)	)	PUNCT
ejpam-6641	204	11	≤	≤	NUM
ejpam-6641	204	12	∥g1r0,4∥p	∥g1r0,4∥p	PROPN
ejpam-6641	204	13	(	(	PUNCT
ejpam-6641	204	14	·	·	PUNCT
ejpam-6641	204	15	)	)	PUNCT
ejpam-6641	204	16	.	.	PUNCT
ejpam-6641	205	1	estimation	estimation	NOUN
ejpam-6641	205	2	of	of	ADP
ejpam-6641	205	3	sζht(ℓ	sζht(ℓ	NOUN
ejpam-6641	205	4	)	)	PUNCT
ejpam-6641	205	5	.	.	PUNCT
ejpam-6641	206	1	since	since	SCONJ
ejpam-6641	206	2	ℓ	ℓ	PROPN
ejpam-6641	206	3	∈	∈	PROPN
ejpam-6641	206	4	tt,2	tt,2	PROPN
ejpam-6641	206	5	t	t	PROPN
ejpam-6641	206	6	,	,	PUNCT
ejpam-6641	206	7	and	and	CCONJ
ejpam-6641	206	8	hölder	hölder	PROPN
ejpam-6641	206	9	’s	’s	PART
ejpam-6641	206	10	inequality	inequality	NOUN
ejpam-6641	206	11	,	,	PUNCT
ejpam-6641	206	12	we	we	PRON
ejpam-6641	206	13	get	get	VERB
ejpam-6641	206	14	|sβht(ℓ)|	|sβht(ℓ)|	PROPN
ejpam-6641	206	15	≤	≤	NUM
ejpam-6641	207	1	c	c	NOUN
ejpam-6641	207	2	ρn	ρn	NOUN
ejpam-6641	207	3	∫	∫	PROPN
ejpam-6641	207	4	|y>8t|	|y>8t|	PROPN
ejpam-6641	207	5	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	207	6	≤	≤	PROPN
ejpam-6641	207	7	c	c	NOUN
ejpam-6641	207	8	ρn	ρn	ADP
ejpam-6641	208	1	t∫	t∫	DET
ejpam-6641	208	2	1	1	NUM
ejpam-6641	208	3	dρ	dρ	NOUN
ejpam-6641	208	4	ρ	ρ	PROPN
ejpam-6641	208	5	∫	∫	PROPN
ejpam-6641	208	6	ρ	ρ	PROPN
ejpam-6641	208	7	2	2	NUM
ejpam-6641	208	8	<	<	X
ejpam-6641	208	9	|y|<ρ	|y|<ρ	PROPN
ejpam-6641	208	10	g(ℓ)dℓ	g(ℓ)dℓ	PROPN
ejpam-6641	208	11	≤	≤	PROPN
ejpam-6641	208	12	c	c	PROPN
ejpam-6641	208	13	tn	tn	NOUN
ejpam-6641	208	14	∞∫	∞∫	PROPN
ejpam-6641	208	15	4	4	NUM
ejpam-6641	208	16	t	t	NOUN
ejpam-6641	208	17	dρ	dρ	PROPN
ejpam-6641	208	18	ρ	ρ	PROPN
ejpam-6641	208	19	∥g1tρ,2ρ∥p(·)∥1tρ,2ρ∥p′	∥g1tρ,2ρ∥p(·)∥1tρ,2ρ∥p′	X
ejpam-6641	208	20	(	(	PUNCT
ejpam-6641	208	21	·	·	PUNCT
ejpam-6641	208	22	)	)	PUNCT
ejpam-6641	208	23	≤	≤	NUM
ejpam-6641	208	24	c	c	NOUN
ejpam-6641	208	25	tn	tn	NOUN
ejpam-6641	208	26	t∫	t∫	PROPN
ejpam-6641	208	27	1	1	NUM
ejpam-6641	208	28	∥g1ρ,2ρ∥p(·)ρ	∥g1ρ,2ρ∥p(·)ρ	VERB
ejpam-6641	208	29	n	n	PRON
ejpam-6641	208	30	p′∞	p′∞	ADJ
ejpam-6641	208	31	−1	−1	NOUN
ejpam-6641	208	32	dρ	dρ	PROPN
ejpam-6641	208	33	.	.	PUNCT
ejpam-6641	209	1	tκ∞∥|sζht(ℓ).1tt,2t∥lp	tκ∞∥|sζht(ℓ).1tt,2t∥lp	PROPN
ejpam-6641	209	2	(	(	PUNCT
ejpam-6641	209	3	·	·	PUNCT
ejpam-6641	209	4	)	)	PUNCT
ejpam-6641	209	5	≤	≤	NOUN
ejpam-6641	209	6	ct	ct	PROPN
ejpam-6641	209	7	κ∞+	κ∞+	PROPN
ejpam-6641	209	8	n	n	CCONJ
ejpam-6641	209	9	p∞	p∞	PROPN
ejpam-6641	209	10	∞∫	∞∫	PROPN
ejpam-6641	209	11	4	4	NUM
ejpam-6641	209	12	t	t	NOUN
ejpam-6641	209	13	∥g1tρ,2ρ∥p(·)ρ	∥g1tρ,2ρ∥p(·)ρ	NOUN
ejpam-6641	209	14	n	n	CCONJ
ejpam-6641	209	15	p′∞	p′∞	ADV
ejpam-6641	209	16	−1	−1	NOUN
ejpam-6641	209	17	dρ	dρ	ADJ
ejpam-6641	209	18	≤	≤	PROPN
ejpam-6641	209	19	∞∫	∞∫	PROPN
ejpam-6641	209	20	t	t	PROPN
ejpam-6641	209	21	(	(	PUNCT
ejpam-6641	209	22	t	t	PROPN
ejpam-6641	209	23	ρ	ρ	PROPN
ejpam-6641	209	24	)	)	PUNCT
ejpam-6641	209	25	κ∞+	κ∞+	PROPN
ejpam-6641	209	26	n	n	PRON
ejpam-6641	209	27	p∞	p∞	PROPN
ejpam-6641	209	28	ω(ρ	ω(ρ	NOUN
ejpam-6641	209	29	)	)	PUNCT
ejpam-6641	209	30	dρ	dρ	PROPN
ejpam-6641	209	31	ρ	ρ	NOUN
ejpam-6641	209	32	,	,	PUNCT
ejpam-6641	209	33	where	where	SCONJ
ejpam-6641	209	34	ω(ρ	ω(ρ	NOUN
ejpam-6641	209	35	)	)	PUNCT
ejpam-6641	209	36	=	=	PUNCT
ejpam-6641	209	37	ρκ∞∥g1ρ,2ρ∥p(·)1(2,∞	ρκ∞∥g1ρ,2ρ∥p(·)1(2,∞	NOUN
ejpam-6641	209	38	)	)	PUNCT
ejpam-6641	209	39	,	,	PUNCT
ejpam-6641	209	40	above	above	ADP
ejpam-6641	209	41	inequality	inequality	NOUN
ejpam-6641	209	42	is	be	AUX
ejpam-6641	209	43	the	the	DET
ejpam-6641	209	44	hardy	hardy	ADJ
ejpam-6641	209	45	type	type	NOUN
ejpam-6641	209	46	inequality	inequality	NOUN
ejpam-6641	209	47	,	,	PUNCT
ejpam-6641	209	48	by	by	ADP
ejpam-6641	209	49	using	use	VERB
ejpam-6641	209	50	the	the	DET
ejpam-6641	209	51	fact	fact	NOUN
ejpam-6641	209	52	κ∞	κ∞	PROPN
ejpam-6641	209	53	+	+	CCONJ
ejpam-6641	209	54	n	n	CCONJ
ejpam-6641	209	55	/	/	SYM
ejpam-6641	209	56	p∞	p∞	PROPN
ejpam-6641	209	57	>	>	X
ejpam-6641	209	58	0	0	PROPN
ejpam-6641	209	59	and	and	CCONJ
ejpam-6641	209	60	lemma	lemma	PROPN
ejpam-6641	209	61	(	(	PUNCT
ejpam-6641	209	62	2	2	NUM
ejpam-6641	209	63	)	)	PUNCT
ejpam-6641	209	64	,	,	PUNCT
ejpam-6641	209	65	get	get	VERB
ejpam-6641	209	66	∥tκ∞∥1rt,2tsζht(y)∥p(·)∥lq((2,∞	∥tκ∞∥1rt,2tsζht(y)∥p(·)∥lq((2,∞	PUNCT
ejpam-6641	209	67	)	)	PUNCT
ejpam-6641	209	68	;	;	PUNCT
ejpam-6641	209	69	dt	dt	PROPN
ejpam-6641	209	70	t	t	PROPN
ejpam-6641	209	71	≤	≤	PROPN
ejpam-6641	209	72	c∥ω∥lq((2,∞	c∥ω∥lq((2,∞	PROPN
ejpam-6641	209	73	)	)	PUNCT
ejpam-6641	209	74	;	;	PUNCT
ejpam-6641	209	75	dt	dt	PROPN
ejpam-6641	209	76	t	t	PROPN
ejpam-6641	209	77	≤	≤	NUM
ejpam-6641	209	78	∥g∥	∥g∥	PROPN
ejpam-6641	209	79	h	h	PROPN
ejpam-6641	209	80	p(·),q	p(·),q	PROPN
ejpam-6641	209	81	,	,	PUNCT
ejpam-6641	209	82	κ	κ	X
ejpam-6641	209	83	(	(	PUNCT
ejpam-6641	209	84	·	·	PUNCT
ejpam-6641	209	85	)	)	PUNCT
ejpam-6641	209	86	2	2	NUM
ejpam-6641	209	87	.	.	PUNCT
ejpam-6641	210	1	g.	g.	PROPN
ejpam-6641	210	2	a.	a.	PROPN
ejpam-6641	210	3	basendwah	basendwah	PROPN
ejpam-6641	210	4	et	et	PROPN
ejpam-6641	210	5	al	al	PROPN
ejpam-6641	210	6	.	.	PUNCT
ejpam-6641	210	7	/	/	SYM
ejpam-6641	210	8	eur	eur	PROPN
ejpam-6641	210	9	.	.	PUNCT
ejpam-6641	211	1	j.	j.	PROPN
ejpam-6641	211	2	pure	pure	PROPN
ejpam-6641	211	3	appl	appl	PROPN
ejpam-6641	211	4	.	.	PROPN
ejpam-6641	211	5	math	math	PROPN
ejpam-6641	211	6	,	,	PUNCT
ejpam-6641	211	7	18	18	NUM
ejpam-6641	211	8	(	(	PUNCT
ejpam-6641	211	9	4	4	NUM
ejpam-6641	211	10	)	)	PUNCT
ejpam-6641	211	11	(	(	PUNCT
ejpam-6641	211	12	2025	2025	NUM
ejpam-6641	211	13	)	)	PUNCT
ejpam-6641	211	14	,	,	PUNCT
ejpam-6641	211	15	6641	6641	NUM
ejpam-6641	211	16	12	12	NUM
ejpam-6641	211	17	of	of	ADP
ejpam-6641	211	18	16	16	NUM
ejpam-6641	211	19	now	now	ADV
ejpam-6641	211	20	,	,	PUNCT
ejpam-6641	211	21	let	let	VERB
ejpam-6641	211	22	’s	’s	PRON
ejpam-6641	211	23	explore	explore	VERB
ejpam-6641	211	24	the	the	DET
ejpam-6641	211	25	scenario	scenario	NOUN
ejpam-6641	211	26	where	where	SCONJ
ejpam-6641	211	27	q	q	ADJ
ejpam-6641	211	28	varies	vary	VERB
ejpam-6641	211	29	.	.	PUNCT
ejpam-6641	212	1	once	once	ADV
ejpam-6641	212	2	again	again	ADV
ejpam-6641	212	3	,	,	PUNCT
ejpam-6641	212	4	we	we	PRON
ejpam-6641	212	5	set	set	VERB
ejpam-6641	212	6	µ	µ	NOUN
ejpam-6641	212	7	=	=	SYM
ejpam-6641	212	8	2	2	NUM
ejpam-6641	212	9	,	,	PUNCT
ejpam-6641	212	10	γ	γ	NOUN
ejpam-6641	212	11	=	=	SYM
ejpam-6641	212	12	1	1	NUM
ejpam-6641	212	13	,	,	PUNCT
ejpam-6641	212	14	and	and	CCONJ
ejpam-6641	213	1	δ	δ	PROPN
ejpam-6641	213	2	=	=	SYM
ejpam-6641	213	3	2	2	X
ejpam-6641	213	4	.	.	PUNCT
ejpam-6641	214	1	the	the	DET
ejpam-6641	214	2	proof	proof	NOUN
ejpam-6641	214	3	follows	follow	VERB
ejpam-6641	214	4	a	a	DET
ejpam-6641	214	5	similar	similar	ADJ
ejpam-6641	214	6	pattern	pattern	NOUN
ejpam-6641	214	7	,	,	PUNCT
ejpam-6641	214	8	thus	thus	ADV
ejpam-6641	214	9	we	we	PRON
ejpam-6641	214	10	’ll	’ll	AUX
ejpam-6641	214	11	omit	omit	VERB
ejpam-6641	214	12	the	the	DET
ejpam-6641	214	13	details	detail	NOUN
ejpam-6641	214	14	.	.	PUNCT
ejpam-6641	215	1	our	our	PRON
ejpam-6641	215	2	objective	objective	NOUN
ejpam-6641	215	3	is	be	AUX
ejpam-6641	215	4	to	to	PART
ejpam-6641	215	5	establish	establish	VERB
ejpam-6641	215	6	that	that	DET
ejpam-6641	215	7	∥sζg∥lp∗(·)(o(0,2+θ	∥sζg∥lp∗(·)(o(0,2+θ	NOUN
ejpam-6641	215	8	)	)	PUNCT
ejpam-6641	215	9	)	)	PUNCT
ejpam-6641	216	1	+	+	ADP
ejpam-6641	216	2	n	n	DET
ejpam-6641	216	3	p∗,q	p∗,q	NOUN
ejpam-6641	216	4	,	,	PUNCT
ejpam-6641	216	5	κ	κ	PROPN
ejpam-6641	216	6	1,2	1,2	NUM
ejpam-6641	216	7	(	(	PUNCT
ejpam-6641	216	8	sζg	sζg	NOUN
ejpam-6641	216	9	)	)	PUNCT
ejpam-6641	216	10	≤	≤	NOUN
ejpam-6641	216	11	∥g∥lp(·)(o(0,2+θ	∥g∥lp(·)(o(0,2+θ	NUM
ejpam-6641	216	12	)	)	PUNCT
ejpam-6641	216	13	)	)	PUNCT
ejpam-6641	217	1	+	+	PUNCT
ejpam-6641	217	2	n	n	PRON
ejpam-6641	217	3	p	p	X
ejpam-6641	217	4	,	,	PUNCT
ejpam-6641	217	5	q	q	ADJ
ejpam-6641	217	6	,	,	PUNCT
ejpam-6641	217	7	κ	κ	PRON
ejpam-6641	217	8	λ′,δ′	λ′,δ′	PROPN
ejpam-6641	217	9	(	(	PUNCT
ejpam-6641	217	10	g	g	NOUN
ejpam-6641	217	11	)	)	PUNCT
ejpam-6641	217	12	with	with	ADP
ejpam-6641	217	13	λ′	λ′	X
ejpam-6641	217	14	<	<	X
ejpam-6641	217	15	1	1	NUM
ejpam-6641	217	16	,	,	PUNCT
ejpam-6641	217	17	δ′	δ′	NOUN
ejpam-6641	217	18	>	>	X
ejpam-6641	217	19	2	2	NUM
ejpam-6641	217	20	,	,	PUNCT
ejpam-6641	217	21	n	n	PRON
ejpam-6641	217	22	p	p	NOUN
ejpam-6641	217	23	,	,	PUNCT
ejpam-6641	217	24	q	q	ADJ
ejpam-6641	217	25	,	,	PUNCT
ejpam-6641	217	26	κ	κ	PROPN
ejpam-6641	217	27	λ	λ	PROPN
ejpam-6641	217	28	,	,	PUNCT
ejpam-6641	217	29	δ	δ	PROPN
ejpam-6641	217	30	(	(	PUNCT
ejpam-6641	217	31	g	g	NOUN
ejpam-6641	217	32	)	)	PUNCT
ejpam-6641	217	33	:	:	PUNCT
ejpam-6641	217	34	=	=	SYM
ejpam-6641	217	35	∥tκ∞∥g1tλt	∥tκ∞∥g1tλt	PROPN
ejpam-6641	217	36	,	,	PUNCT
ejpam-6641	217	37	δt∥p(·)∥lq(·)((2,∞	δt∥p(·)∥lq(·)((2,∞	NOUN
ejpam-6641	217	38	)	)	PUNCT
ejpam-6641	217	39	,	,	PUNCT
ejpam-6641	217	40	dt	dt	PROPN
ejpam-6641	217	41	t	t	PROPN
ejpam-6641	217	42	)	)	PUNCT
ejpam-6641	217	43	.	.	PUNCT
ejpam-6641	218	1	the	the	DET
ejpam-6641	218	2	estimation	estimation	NOUN
ejpam-6641	218	3	for	for	ADP
ejpam-6641	218	4	∥sζg∥lp(·)(o(0,2+θ	∥sζg∥lp(·)(o(0,2+θ	NOUN
ejpam-6641	218	5	)	)	PUNCT
ejpam-6641	218	6	)	)	PUNCT
ejpam-6641	218	7	can	can	AUX
ejpam-6641	218	8	be	be	AUX
ejpam-6641	218	9	calculated	calculate	VERB
ejpam-6641	218	10	similarly	similarly	ADV
ejpam-6641	218	11	as	as	SCONJ
ejpam-6641	218	12	we	we	PRON
ejpam-6641	218	13	done	do	VERB
ejpam-6641	218	14	in	in	ADP
ejpam-6641	218	15	the	the	DET
ejpam-6641	218	16	case	case	NOUN
ejpam-6641	218	17	of	of	ADP
ejpam-6641	218	18	constant	constant	ADJ
ejpam-6641	218	19	q.	q.	NOUN
ejpam-6641	218	20	to	to	PART
ejpam-6641	218	21	estimate	estimate	VERB
ejpam-6641	218	22	n	n	PROPN
ejpam-6641	218	23	(	(	PUNCT
ejpam-6641	218	24	sζg	sζg	PROPN
ejpam-6641	218	25	)	)	PUNCT
ejpam-6641	218	26	p∗,q	p∗,q	NOUN
ejpam-6641	218	27	,	,	PUNCT
ejpam-6641	218	28	κ	κ	NOUN
ejpam-6641	218	29	1,2	1,2	NUM
ejpam-6641	218	30	,	,	PUNCT
ejpam-6641	218	31	by	by	ADP
ejpam-6641	218	32	splitting	split	VERB
ejpam-6641	218	33	the	the	DET
ejpam-6641	218	34	function	function	NOUN
ejpam-6641	218	35	g(ℓ	g(ℓ	NOUN
ejpam-6641	218	36	)	)	PUNCT
ejpam-6641	218	37	as	as	ADP
ejpam-6641	218	38	g(ℓ	g(ℓ	NOUN
ejpam-6641	218	39	)	)	PUNCT
ejpam-6641	218	40	=	=	PUNCT
ejpam-6641	219	1	f0(ℓ	f0(ℓ	X
ejpam-6641	219	2	)	)	PUNCT
ejpam-6641	219	3	+	+	NUM
ejpam-6641	219	4	ft(ℓ	ft(ℓ	NUM
ejpam-6641	219	5	)	)	PUNCT
ejpam-6641	219	6	+	+	NOUN
ejpam-6641	219	7	gt(ℓ	gt(ℓ	X
ejpam-6641	219	8	)	)	PUNCT
ejpam-6641	219	9	+	+	CCONJ
ejpam-6641	219	10	ht(ℓ	ht(ℓ	NOUN
ejpam-6641	219	11	)	)	PUNCT
ejpam-6641	219	12	where	where	SCONJ
ejpam-6641	219	13	f0(ℓ	f0(ℓ	VERB
ejpam-6641	219	14	)	)	PUNCT
ejpam-6641	219	15	=	=	SYM
ejpam-6641	219	16	g(ℓ)1o(0	g(ℓ)1o(0	NOUN
ejpam-6641	219	17	,	,	PUNCT
ejpam-6641	219	18	1	1	NUM
ejpam-6641	219	19	2	2	NUM
ejpam-6641	219	20	)	)	PUNCT
ejpam-6641	219	21	(	(	PUNCT
ejpam-6641	219	22	ℓ	ℓ	NOUN
ejpam-6641	219	23	)	)	PUNCT
ejpam-6641	219	24	,	,	PUNCT
ejpam-6641	219	25	ft(ℓ	ft(ℓ	NUM
ejpam-6641	219	26	)	)	PUNCT
ejpam-6641	219	27	=	=	PUNCT
ejpam-6641	219	28	g(ℓ)1o(0,γ′t)\o(0	g(ℓ)1o(0,γ′t)\o(0	NOUN
ejpam-6641	219	29	,	,	PUNCT
ejpam-6641	219	30	1	1	NUM
ejpam-6641	219	31	2	2	NUM
ejpam-6641	219	32	)	)	PUNCT
ejpam-6641	219	33	)	)	PUNCT
ejpam-6641	219	34	(	(	PUNCT
ejpam-6641	219	35	ℓ	ℓ	X
ejpam-6641	219	36	)	)	PUNCT
ejpam-6641	219	37	gt(ℓ	gt(ℓ	NOUN
ejpam-6641	219	38	)	)	PUNCT
ejpam-6641	219	39	=	=	SYM
ejpam-6641	219	40	g(ℓ)1o(δ′t)\o(0,γ′t	g(ℓ)1o(δ′t)\o(0,γ′t	PROPN
ejpam-6641	219	41	)	)	PUNCT
ejpam-6641	219	42	,	,	PUNCT
ejpam-6641	219	43	ht(ℓ	ht(ℓ	ADJ
ejpam-6641	219	44	)	)	PUNCT
ejpam-6641	219	45	=	=	SYM
ejpam-6641	219	46	g(ℓ)1rn\o(0,δ′t	g(ℓ)1rn\o(0,δ′t	NOUN
ejpam-6641	219	47	)	)	PUNCT
ejpam-6641	219	48	,	,	PUNCT
ejpam-6641	219	49	then	then	ADV
ejpam-6641	219	50	|sζg(ℓ)|	|sζg(ℓ)|	VERB
ejpam-6641	219	51	≤	≤	NOUN
ejpam-6641	219	52	|sζ(f0)(ℓ)|+	|sζ(f0)(ℓ)|+	PROPN
ejpam-6641	219	53	|sζ(ft)(ℓ)|+	|sζ(ft)(ℓ)|+	PROPN
ejpam-6641	219	54	|sζ(g)t)(ℓ)|+	|sζ(g)t)(ℓ)|+	PUNCT
ejpam-6641	220	1	|sζ(ht)(ℓ)|	|sζ(ht)(ℓ)|	X
ejpam-6641	220	2	.	.	PUNCT
ejpam-6641	220	3	estimation	estimation	NOUN
ejpam-6641	220	4	of	of	ADP
ejpam-6641	220	5	sζf0	sζf0	PROPN
ejpam-6641	220	6	.	.	PUNCT
ejpam-6641	221	1	it	it	PRON
ejpam-6641	221	2	can	can	AUX
ejpam-6641	221	3	be	be	AUX
ejpam-6641	221	4	treated	treat	VERB
ejpam-6641	221	5	similarly	similarly	ADV
ejpam-6641	221	6	as	as	ADP
ejpam-6641	221	7	in	in	ADP
ejpam-6641	221	8	the	the	DET
ejpam-6641	221	9	case	case	NOUN
ejpam-6641	221	10	of	of	ADP
ejpam-6641	221	11	constant	constant	ADJ
ejpam-6641	221	12	q.	q.	NOUN
ejpam-6641	221	13	estimation	estimation	NOUN
ejpam-6641	221	14	of	of	ADP
ejpam-6641	221	15	sζft	sζft	NOUN
ejpam-6641	221	16	.	.	PUNCT
ejpam-6641	222	1	by	by	ADP
ejpam-6641	222	2	the	the	DET
ejpam-6641	222	3	same	same	ADJ
ejpam-6641	222	4	estimation	estimation	NOUN
ejpam-6641	222	5	as	as	ADP
ejpam-6641	222	6	in	in	ADP
ejpam-6641	222	7	the	the	DET
ejpam-6641	222	8	case	case	NOUN
ejpam-6641	222	9	of	of	ADP
ejpam-6641	222	10	constant	constant	ADJ
ejpam-6641	222	11	q	q	NOUN
ejpam-6641	222	12	,	,	PUNCT
ejpam-6641	222	13	and	and	CCONJ
ejpam-6641	222	14	considering	consider	VERB
ejpam-6641	222	15	|ℓ−	|ℓ−	VERB
ejpam-6641	222	16	y|	y|	NOUN
ejpam-6641	222	17	>	>	X
ejpam-6641	222	18	(	(	PUNCT
ejpam-6641	222	19	1−	1−	NUM
ejpam-6641	222	20	γ′)t	γ′)t	NOUN
ejpam-6641	222	21	we	we	PRON
ejpam-6641	222	22	get	get	VERB
ejpam-6641	222	23	|sζft(ℓ)|	|sζft(ℓ)|	PROPN
ejpam-6641	222	24	≤	≤	NOUN
ejpam-6641	222	25	ct−n	ct−n	VERB
ejpam-6641	222	26	t∫	t∫	ADJ
ejpam-6641	222	27	1	1	NUM
ejpam-6641	222	28	2	2	NUM
ejpam-6641	222	29	∥g1r	∥g1r	NOUN
ejpam-6641	222	30	ρ	ρ	X
ejpam-6641	222	31	2	2	NUM
ejpam-6641	222	32	,	,	PUNCT
ejpam-6641	222	33	ρ	ρ	X
ejpam-6641	222	34	∥p(·)ρn	∥p(·)ρn	PRON
ejpam-6641	222	35	/	/	SYM
ejpam-6641	222	36	p	p	NOUN
ejpam-6641	222	37	′	′	NUM
ejpam-6641	222	38	∞−1dρ	∞−1dρ	NOUN
ejpam-6641	222	39	,	,	PUNCT
ejpam-6641	222	40	which	which	PRON
ejpam-6641	222	41	yields	yield	VERB
ejpam-6641	222	42	tκ∞∥sζft(ℓ).1tt,2t∥lp∗	tκ∞∥sζft(ℓ).1tt,2t∥lp∗	NUM
ejpam-6641	222	43	(	(	PUNCT
ejpam-6641	222	44	·	·	PUNCT
ejpam-6641	222	45	)	)	PUNCT
ejpam-6641	222	46	≤	≤	NOUN
ejpam-6641	223	1	ct	ct	NUM
ejpam-6641	223	2	κ∞+	κ∞+	PROPN
ejpam-6641	223	3	n	n	CCONJ
ejpam-6641	223	4	p′∞	p′∞	X
ejpam-6641	223	5	t∫	t∫	PRON
ejpam-6641	223	6	1/2	1/2	NUM
ejpam-6641	223	7	∥g1	∥g1	NOUN
ejpam-6641	223	8	t	t	NOUN
ejpam-6641	223	9	ρ	ρ	NUM
ejpam-6641	223	10	2	2	NUM
ejpam-6641	223	11	,	,	PUNCT
ejpam-6641	223	12	ρ	ρ	PROPN
ejpam-6641	223	13	∥p(·)ρ	∥p(·)ρ	NOUN
ejpam-6641	223	14	n	n	CCONJ
ejpam-6641	223	15	p′∞	p′∞	ADV
ejpam-6641	223	16	−1	−1	NOUN
ejpam-6641	223	17	dρ	dρ	ADJ
ejpam-6641	223	18	≤	≤	NOUN
ejpam-6641	223	19	t∫	t∫	NUM
ejpam-6641	223	20	1/2	1/2	NUM
ejpam-6641	223	21	(	(	PUNCT
ejpam-6641	223	22	t	t	PROPN
ejpam-6641	223	23	ρ	ρ	PROPN
ejpam-6641	223	24	)	)	PUNCT
ejpam-6641	223	25	κ∞−	κ∞−	NUM
ejpam-6641	223	26	n	n	CCONJ
ejpam-6641	223	27	p′∞	p′∞	X
ejpam-6641	223	28	ψ(ρ	ψ(ρ	PROPN
ejpam-6641	223	29	)	)	PUNCT
ejpam-6641	223	30	dρ	dρ	PROPN
ejpam-6641	223	31	ρ	ρ	PROPN
ejpam-6641	223	32	,	,	PUNCT
ejpam-6641	224	1	where	where	SCONJ
ejpam-6641	224	2	ψ(ρ	ψ(ρ	PROPN
ejpam-6641	224	3	)	)	PUNCT
ejpam-6641	224	4	=	=	SYM
ejpam-6641	224	5	ρκ∞∥1tρ,2ρ∥p	ρκ∞∥1tρ,2ρ∥p	PROPN
ejpam-6641	224	6	(	(	PUNCT
ejpam-6641	224	7	·	·	PUNCT
ejpam-6641	224	8	)	)	PUNCT
ejpam-6641	224	9	.	.	PUNCT
ejpam-6641	225	1	left	leave	VERB
ejpam-6641	225	2	hand	hand	NOUN
ejpam-6641	225	3	side	side	NOUN
ejpam-6641	225	4	of	of	ADP
ejpam-6641	225	5	above	above	ADJ
ejpam-6641	225	6	equation	equation	NOUN
ejpam-6641	225	7	is	be	AUX
ejpam-6641	225	8	a	a	DET
ejpam-6641	225	9	hardy	hardy	ADJ
ejpam-6641	225	10	type	type	NOUN
ejpam-6641	225	11	operator	operator	NOUN
ejpam-6641	225	12	and	and	CCONJ
ejpam-6641	225	13	by	by	ADP
ejpam-6641	225	14	using	use	VERB
ejpam-6641	225	15	lemma	lemma	PROPN
ejpam-6641	225	16	(	(	PUNCT
ejpam-6641	225	17	2	2	X
ejpam-6641	225	18	)	)	PUNCT
ejpam-6641	225	19	we	we	PRON
ejpam-6641	225	20	get	get	VERB
ejpam-6641	225	21	n	n	PRON
ejpam-6641	225	22	p∗,q	p∗,q	NOUN
ejpam-6641	225	23	,	,	PUNCT
ejpam-6641	225	24	κ	κ	PROPN
ejpam-6641	225	25	1,2	1,2	NUM
ejpam-6641	225	26	(	(	PUNCT
ejpam-6641	225	27	sζft	sζft	NOUN
ejpam-6641	225	28	)	)	PUNCT
ejpam-6641	225	29	≤	≤	NUM
ejpam-6641	225	30	∥γψ∥lq(·)((2,∞	∥γψ∥lq(·)((2,∞	PROPN
ejpam-6641	225	31	)	)	PUNCT
ejpam-6641	225	32	;	;	PUNCT
ejpam-6641	226	1	dt	dt	PROPN
ejpam-6641	226	2	t	t	PROPN
ejpam-6641	226	3	)	)	PUNCT
ejpam-6641	226	4	≤	≤	PROPN
ejpam-6641	226	5	∥ψ∥lq(·)((2,∞	∥ψ∥lq(·)((2,∞	PROPN
ejpam-6641	226	6	)	)	PUNCT
ejpam-6641	226	7	;	;	PUNCT
ejpam-6641	226	8	dt	dt	PROPN
ejpam-6641	226	9	t	t	PROPN
ejpam-6641	226	10	)	)	PUNCT
ejpam-6641	226	11	≤	≤	PUNCT
ejpam-6641	227	1	∥g∥	∥g∥	PROPN
ejpam-6641	227	2	h	h	PROPN
ejpam-6641	227	3	p(·),q(·),κ	p(·),q(·),κ	PROPN
ejpam-6641	227	4	(	(	PUNCT
ejpam-6641	227	5	·	·	PUNCT
ejpam-6641	227	6	)	)	PUNCT
ejpam-6641	227	7	2;(γ′,δ′	2;(γ′,δ′	NUM
ejpam-6641	227	8	)	)	PUNCT
ejpam-6641	227	9	(	(	PUNCT
ejpam-6641	227	10	rn	rn	NOUN
ejpam-6641	227	11	)	)	PUNCT
ejpam-6641	227	12	,	,	PUNCT
ejpam-6641	227	13	g.	g.	PROPN
ejpam-6641	227	14	a.	a.	PROPN
ejpam-6641	227	15	basendwah	basendwah	PROPN
ejpam-6641	227	16	et	et	PROPN
ejpam-6641	227	17	al	al	PROPN
ejpam-6641	227	18	.	.	PUNCT
ejpam-6641	227	19	/	/	SYM
ejpam-6641	227	20	eur	eur	PROPN
ejpam-6641	227	21	.	.	PUNCT
ejpam-6641	228	1	j.	j.	PROPN
ejpam-6641	228	2	pure	pure	PROPN
ejpam-6641	228	3	appl	appl	PROPN
ejpam-6641	228	4	.	.	PROPN
ejpam-6641	228	5	math	math	PROPN
ejpam-6641	228	6	,	,	PUNCT
ejpam-6641	228	7	18	18	NUM
ejpam-6641	228	8	(	(	PUNCT
ejpam-6641	228	9	4	4	NUM
ejpam-6641	228	10	)	)	PUNCT
ejpam-6641	228	11	(	(	PUNCT
ejpam-6641	228	12	2025	2025	NUM
ejpam-6641	228	13	)	)	PUNCT
ejpam-6641	228	14	,	,	PUNCT
ejpam-6641	228	15	6641	6641	NUM
ejpam-6641	228	16	13	13	NUM
ejpam-6641	228	17	of	of	ADP
ejpam-6641	228	18	16	16	NUM
ejpam-6641	228	19	by	by	ADP
ejpam-6641	228	20	following	follow	VERB
ejpam-6641	228	21	same	same	ADJ
ejpam-6641	228	22	reasoning	reasoning	NOUN
ejpam-6641	228	23	as	as	ADP
ejpam-6641	228	24	in	in	ADP
ejpam-6641	228	25	the	the	DET
ejpam-6641	228	26	case	case	NOUN
ejpam-6641	228	27	of	of	ADP
ejpam-6641	228	28	constant	constant	ADJ
ejpam-6641	228	29	q.	q.	NOUN
ejpam-6641	228	30	estimation	estimation	NOUN
ejpam-6641	228	31	of	of	ADP
ejpam-6641	228	32	sζgt	sζgt	PROPN
ejpam-6641	228	33	.	.	PUNCT
ejpam-6641	229	1	by	by	ADP
ejpam-6641	229	2	the	the	DET
ejpam-6641	229	3	boundedness	boundedness	NOUN
ejpam-6641	229	4	of	of	ADP
ejpam-6641	229	5	the	the	DET
ejpam-6641	229	6	operator	operator	NOUN
ejpam-6641	229	7	sζ	sζ	VERB
ejpam-6641	229	8	in	in	ADP
ejpam-6641	229	9	the	the	DET
ejpam-6641	229	10	space	space	NOUN
ejpam-6641	229	11	lp(·)(rn	lp(·)(rn	PROPN
ejpam-6641	229	12	)	)	PUNCT
ejpam-6641	229	13	→	→	SYM
ejpam-6641	229	14	lp∗(·)(rn	lp∗(·)(rn	X
ejpam-6641	229	15	)	)	PUNCT
ejpam-6641	229	16	we	we	PRON
ejpam-6641	229	17	obtain	obtain	VERB
ejpam-6641	229	18	∥(sζgt)1tt,2t∥p	∥(sζgt)1tt,2t∥p	ADP
ejpam-6641	229	19	(	(	PUNCT
ejpam-6641	229	20	·	·	PUNCT
ejpam-6641	229	21	)	)	PUNCT
ejpam-6641	229	22	≤	≤	NOUN
ejpam-6641	229	23	c∥gt∥p	c∥gt∥p	X
ejpam-6641	229	24	(	(	PUNCT
ejpam-6641	229	25	·	·	PUNCT
ejpam-6641	229	26	)	)	PUNCT
ejpam-6641	230	1	=	=	SYM
ejpam-6641	230	2	c∥g1rγ′t	c∥g1rγ′t	NOUN
ejpam-6641	230	3	,	,	PUNCT
ejpam-6641	230	4	δ′t∥p	δ′t∥p	X
ejpam-6641	230	5	(	(	PUNCT
ejpam-6641	230	6	·	·	PUNCT
ejpam-6641	230	7	)	)	PUNCT
ejpam-6641	230	8	which	which	PRON
ejpam-6641	230	9	implies	imply	VERB
ejpam-6641	230	10	n	n	PRON
ejpam-6641	230	11	p∗,q	p∗,q	NOUN
ejpam-6641	230	12	,	,	PUNCT
ejpam-6641	230	13	κ	κ	PROPN
ejpam-6641	230	14	1,2	1,2	NUM
ejpam-6641	230	15	(	(	PUNCT
ejpam-6641	230	16	sζgt	sζgt	PROPN
ejpam-6641	230	17	)	)	PUNCT
ejpam-6641	230	18	≤	≤	PROPN
ejpam-6641	230	19	c∥g1rγ′t	c∥g1rγ′t	NOUN
ejpam-6641	230	20	,	,	PUNCT
ejpam-6641	230	21	δ′t∥hp(·),q(·),κ	δ′t∥hp(·),q(·),κ	ADV
ejpam-6641	230	22	(	(	PUNCT
ejpam-6641	230	23	·	·	PUNCT
ejpam-6641	230	24	)	)	PUNCT
ejpam-6641	230	25	2;(γ′,δ′	2;(γ′,δ′	NUM
ejpam-6641	230	26	)	)	PUNCT
ejpam-6641	230	27	(	(	PUNCT
ejpam-6641	230	28	rn	rn	NOUN
ejpam-6641	230	29	)	)	PUNCT
ejpam-6641	230	30	.	.	PUNCT
ejpam-6641	231	1	estimation	estimation	NOUN
ejpam-6641	231	2	of	of	ADP
ejpam-6641	231	3	sζht	sζht	NOUN
ejpam-6641	231	4	.	.	PUNCT
ejpam-6641	232	1	the	the	DET
ejpam-6641	232	2	estimate	estimate	NOUN
ejpam-6641	232	3	of	of	ADP
ejpam-6641	232	4	sζ	sζ	PROPN
ejpam-6641	232	5	can	can	AUX
ejpam-6641	232	6	be	be	AUX
ejpam-6641	232	7	obtained	obtain	VERB
ejpam-6641	232	8	similarly	similarly	ADV
ejpam-6641	232	9	from	from	ADP
ejpam-6641	232	10	the	the	DET
ejpam-6641	232	11	constant	constant	ADJ
ejpam-6641	232	12	q	q	NOUN
ejpam-6641	232	13	case	case	NOUN
ejpam-6641	232	14	,	,	PUNCT
ejpam-6641	232	15	we	we	PRON
ejpam-6641	232	16	get	get	VERB
ejpam-6641	232	17	∥tκ∞∥1rt,2tsζht(ℓ)∥p(·)∥lq(·)((2,∞	∥tκ∞∥1rt,2tsζht(ℓ)∥p(·)∥lq(·)((2,∞	NOUN
ejpam-6641	232	18	)	)	PUNCT
ejpam-6641	232	19	;	;	PUNCT
ejpam-6641	232	20	dt	dt	PROPN
ejpam-6641	232	21	t	t	PROPN
ejpam-6641	232	22	)	)	PUNCT
ejpam-6641	232	23	≤	≤	PUNCT
ejpam-6641	233	1	c∥g∥	c∥g∥	PROPN
ejpam-6641	233	2	h	h	PROPN
ejpam-6641	233	3	p(·),q(·),κ	p(·),q(·),κ	PROPN
ejpam-6641	233	4	(	(	PUNCT
ejpam-6641	233	5	·	·	PUNCT
ejpam-6641	233	6	)	)	PUNCT
ejpam-6641	233	7	2;(γ′,δ′	2;(γ′,δ′	NUM
ejpam-6641	233	8	)	)	PUNCT
ejpam-6641	233	9	(	(	PUNCT
ejpam-6641	233	10	rn	rn	NOUN
ejpam-6641	233	11	)	)	PUNCT
ejpam-6641	233	12	.	.	PUNCT
ejpam-6641	234	1	by	by	ADP
ejpam-6641	234	2	taking	take	VERB
ejpam-6641	234	3	into	into	ADP
ejpam-6641	234	4	consideration	consideration	NOUN
ejpam-6641	234	5	we	we	PRON
ejpam-6641	234	6	obtained	obtain	VERB
ejpam-6641	234	7	our	our	PRON
ejpam-6641	234	8	desired	desire	VERB
ejpam-6641	234	9	result	result	NOUN
ejpam-6641	234	10	.	.	PUNCT
ejpam-6641	235	1	5	5	X
ejpam-6641	235	2	.	.	X
ejpam-6641	235	3	conclusion	conclusion	NOUN
ejpam-6641	235	4	this	this	DET
ejpam-6641	235	5	manuscript	manuscript	NOUN
ejpam-6641	235	6	contributes	contribute	VERB
ejpam-6641	235	7	significantly	significantly	ADV
ejpam-6641	235	8	to	to	ADP
ejpam-6641	235	9	the	the	DET
ejpam-6641	235	10	field	field	NOUN
ejpam-6641	235	11	of	of	ADP
ejpam-6641	235	12	mathematical	mathematical	ADJ
ejpam-6641	235	13	analysis	analysis	NOUN
ejpam-6641	235	14	by	by	ADP
ejpam-6641	235	15	introducing	introduce	VERB
ejpam-6641	235	16	new	new	ADJ
ejpam-6641	235	17	results	result	NOUN
ejpam-6641	235	18	within	within	ADP
ejpam-6641	235	19	the	the	DET
ejpam-6641	235	20	framework	framework	NOUN
ejpam-6641	235	21	of	of	ADP
ejpam-6641	235	22	continual	continual	ADJ
ejpam-6641	235	23	herz	herz	PROPN
ejpam-6641	235	24	spaces	space	NOUN
ejpam-6641	235	25	.	.	PUNCT
ejpam-6641	236	1	the	the	DET
ejpam-6641	236	2	study	study	NOUN
ejpam-6641	236	3	deepens	deepen	VERB
ejpam-6641	236	4	our	our	PRON
ejpam-6641	236	5	understanding	understanding	NOUN
ejpam-6641	236	6	of	of	ADP
ejpam-6641	236	7	boundedness	boundedness	NOUN
ejpam-6641	236	8	of	of	ADP
ejpam-6641	236	9	the	the	DET
ejpam-6641	236	10	intrinsic	intrinsic	ADJ
ejpam-6641	236	11	square	square	ADJ
ejpam-6641	236	12	function	function	NOUN
ejpam-6641	236	13	on	on	ADP
ejpam-6641	236	14	continual	continual	ADJ
ejpam-6641	236	15	herz	herz	PROPN
ejpam-6641	236	16	spaces	space	NOUN
ejpam-6641	236	17	by	by	ADP
ejpam-6641	236	18	building	build	VERB
ejpam-6641	236	19	on	on	ADP
ejpam-6641	236	20	previous	previous	ADJ
ejpam-6641	236	21	findings	finding	NOUN
ejpam-6641	236	22	.	.	PUNCT
ejpam-6641	237	1	the	the	DET
ejpam-6641	237	2	application	application	NOUN
ejpam-6641	237	3	of	of	ADP
ejpam-6641	237	4	these	these	DET
ejpam-6641	237	5	results	result	NOUN
ejpam-6641	237	6	to	to	PART
ejpam-6641	237	7	establish	establish	VERB
ejpam-6641	237	8	the	the	DET
ejpam-6641	237	9	existence	existence	NOUN
ejpam-6641	237	10	of	of	ADP
ejpam-6641	237	11	the	the	DET
ejpam-6641	237	12	regularity	regularity	NOUN
ejpam-6641	237	13	solutions	solution	NOUN
ejpam-6641	237	14	of	of	ADP
ejpam-6641	237	15	some	some	DET
ejpam-6641	237	16	elliptic	elliptic	ADJ
ejpam-6641	237	17	pdes	pde	NOUN
ejpam-6641	237	18	with	with	ADP
ejpam-6641	237	19	smooth	smooth	ADJ
ejpam-6641	237	20	boundaries	boundary	NOUN
ejpam-6641	237	21	in	in	ADP
ejpam-6641	237	22	these	these	DET
ejpam-6641	237	23	spaces	space	NOUN
ejpam-6641	237	24	.	.	PUNCT
ejpam-6641	238	1	there	there	PRON
ejpam-6641	238	2	are	be	VERB
ejpam-6641	238	3	a	a	DET
ejpam-6641	238	4	number	number	NOUN
ejpam-6641	238	5	of	of	ADP
ejpam-6641	238	6	exciting	exciting	ADJ
ejpam-6641	238	7	avenues	avenue	NOUN
ejpam-6641	238	8	for	for	ADP
ejpam-6641	238	9	further	further	ADJ
ejpam-6641	238	10	study	study	NOUN
ejpam-6641	238	11	in	in	ADP
ejpam-6641	238	12	continual	continual	ADJ
ejpam-6641	238	13	weighted	weight	VERB
ejpam-6641	238	14	herz	herz	PROPN
ejpam-6641	238	15	-	-	PUNCT
ejpam-6641	238	16	morrey	morrey	PROPN
ejpam-6641	238	17	spaces	space	NOUN
ejpam-6641	238	18	in	in	ADP
ejpam-6641	238	19	the	the	DET
ejpam-6641	238	20	future	future	NOUN
ejpam-6641	238	21	.	.	PUNCT
ejpam-6641	239	1	extending	extend	VERB
ejpam-6641	239	2	these	these	DET
ejpam-6641	239	3	results	result	NOUN
ejpam-6641	239	4	to	to	ADP
ejpam-6641	239	5	two	two	NUM
ejpam-6641	239	6	weighted	weight	VERB
ejpam-6641	239	7	continual	continual	ADJ
ejpam-6641	239	8	herz	herz	PROPN
ejpam-6641	239	9	-	-	PUNCT
ejpam-6641	239	10	morrey	morrey	PROPN
ejpam-6641	239	11	spaces	space	VERB
ejpam-6641	239	12	with	with	ADP
ejpam-6641	239	13	variable	variable	ADJ
ejpam-6641	239	14	exponents	exponent	NOUN
ejpam-6641	239	15	in	in	ADP
ejpam-6641	239	16	solving	solve	VERB
ejpam-6641	239	17	pdes	pde	NOUN
ejpam-6641	239	18	within	within	ADP
ejpam-6641	239	19	such	such	ADJ
ejpam-6641	239	20	spaces	space	NOUN
ejpam-6641	239	21	could	could	AUX
ejpam-6641	239	22	be	be	AUX
ejpam-6641	239	23	particularly	particularly	ADV
ejpam-6641	239	24	valuable	valuable	ADJ
ejpam-6641	239	25	.	.	PUNCT
ejpam-6641	240	1	6	6	X
ejpam-6641	240	2	.	.	PUNCT
ejpam-6641	240	3	ethics	ethic	NOUN
ejpam-6641	240	4	declarations	declaration	NOUN
ejpam-6641	240	5	conflict	conflict	NOUN
ejpam-6641	240	6	of	of	ADP
ejpam-6641	240	7	interest	interest	NOUN
ejpam-6641	240	8	the	the	DET
ejpam-6641	240	9	authors	author	NOUN
ejpam-6641	240	10	declare	declare	VERB
ejpam-6641	240	11	that	that	SCONJ
ejpam-6641	240	12	they	they	PRON
ejpam-6641	240	13	have	have	VERB
ejpam-6641	240	14	no	no	DET
ejpam-6641	240	15	known	know	VERB
ejpam-6641	240	16	competing	compete	VERB
ejpam-6641	240	17	financial	financial	ADJ
ejpam-6641	240	18	interests	interest	NOUN
ejpam-6641	240	19	or	or	CCONJ
ejpam-6641	240	20	personal	personal	ADJ
ejpam-6641	240	21	relationships	relationship	NOUN
ejpam-6641	240	22	that	that	PRON
ejpam-6641	240	23	could	could	AUX
ejpam-6641	240	24	have	have	AUX
ejpam-6641	240	25	appeared	appear	VERB
ejpam-6641	240	26	to	to	PART
ejpam-6641	240	27	influence	influence	VERB
ejpam-6641	240	28	the	the	DET
ejpam-6641	240	29	work	work	NOUN
ejpam-6641	240	30	reported	report	VERB
ejpam-6641	240	31	in	in	ADP
ejpam-6641	240	32	this	this	DET
ejpam-6641	240	33	paper	paper	NOUN
ejpam-6641	240	34	.	.	PUNCT
ejpam-6641	241	1	ethics	ethic	NOUN
ejpam-6641	241	2	approval	approval	NOUN
ejpam-6641	241	3	and	and	CCONJ
ejpam-6641	241	4	consent	consent	NOUN
ejpam-6641	241	5	to	to	PART
ejpam-6641	241	6	participate	participate	VERB
ejpam-6641	241	7	this	this	DET
ejpam-6641	241	8	manuscript	manuscript	NOUN
ejpam-6641	241	9	has	have	VERB
ejpam-6641	241	10	not	not	PART
ejpam-6641	241	11	and	and	CCONJ
ejpam-6641	241	12	will	will	AUX
ejpam-6641	241	13	not	not	PART
ejpam-6641	241	14	be	be	AUX
ejpam-6641	241	15	submitted	submit	VERB
ejpam-6641	241	16	to	to	ADP
ejpam-6641	241	17	more	more	ADJ
ejpam-6641	241	18	than	than	ADP
ejpam-6641	241	19	one	one	NUM
ejpam-6641	241	20	journal	journal	NOUN
ejpam-6641	241	21	for	for	ADP
ejpam-6641	241	22	simultaneous	simultaneous	ADJ
ejpam-6641	241	23	consideration	consideration	NOUN
ejpam-6641	241	24	.	.	PUNCT
ejpam-6641	242	1	the	the	DET
ejpam-6641	242	2	submitted	submit	VERB
ejpam-6641	242	3	work	work	NOUN
ejpam-6641	242	4	is	be	AUX
ejpam-6641	242	5	original	original	ADJ
ejpam-6641	242	6	and	and	CCONJ
ejpam-6641	242	7	will	will	AUX
ejpam-6641	242	8	not	not	PART
ejpam-6641	242	9	be	be	AUX
ejpam-6641	242	10	published	publish	VERB
ejpam-6641	242	11	elsewhere	elsewhere	ADV
ejpam-6641	242	12	.	.	PUNCT
ejpam-6641	243	1	funding	funding	NOUN
ejpam-6641	243	2	authors	author	NOUN
ejpam-6641	243	3	state	state	VERB
ejpam-6641	243	4	no	no	DET
ejpam-6641	243	5	funding	funding	NOUN
ejpam-6641	243	6	involved	involve	VERB
ejpam-6641	243	7	.	.	PUNCT
ejpam-6641	244	1	g.	g.	PROPN
ejpam-6641	244	2	a.	a.	PROPN
ejpam-6641	244	3	basendwah	basendwah	PROPN
ejpam-6641	244	4	et	et	PROPN
ejpam-6641	244	5	al	al	PROPN
ejpam-6641	244	6	.	.	PUNCT
ejpam-6641	244	7	/	/	SYM
ejpam-6641	244	8	eur	eur	PROPN
ejpam-6641	244	9	.	.	PUNCT
ejpam-6641	245	1	j.	j.	PROPN
ejpam-6641	245	2	pure	pure	PROPN
ejpam-6641	245	3	appl	appl	PROPN
ejpam-6641	245	4	.	.	PROPN
ejpam-6641	245	5	math	math	PROPN
ejpam-6641	245	6	,	,	PUNCT
ejpam-6641	245	7	18	18	NUM
ejpam-6641	245	8	(	(	PUNCT
ejpam-6641	245	9	4	4	NUM
ejpam-6641	245	10	)	)	PUNCT
ejpam-6641	245	11	(	(	PUNCT
ejpam-6641	245	12	2025	2025	NUM
ejpam-6641	245	13	)	)	PUNCT
ejpam-6641	245	14	,	,	PUNCT
ejpam-6641	245	15	6641	6641	NUM
ejpam-6641	245	16	14	14	NUM
ejpam-6641	245	17	of	of	ADP
ejpam-6641	245	18	16	16	NUM
ejpam-6641	245	19	availability	availability	NOUN
ejpam-6641	245	20	of	of	ADP
ejpam-6641	245	21	data	datum	NOUN
ejpam-6641	245	22	no	no	DET
ejpam-6641	245	23	data	data	NOUN
ejpam-6641	245	24	is	be	AUX
ejpam-6641	245	25	available	available	ADJ
ejpam-6641	245	26	for	for	ADP
ejpam-6641	245	27	this	this	DET
ejpam-6641	245	28	study	study	NOUN
ejpam-6641	245	29	.	.	PUNCT
ejpam-6641	246	1	references	reference	NOUN
ejpam-6641	246	2	[	[	X
ejpam-6641	246	3	1	1	NUM
ejpam-6641	246	4	]	]	X
ejpam-6641	246	5	l.	l.	PROPN
ejpam-6641	246	6	diening	diening	PROPN
ejpam-6641	246	7	,	,	PUNCT
ejpam-6641	246	8	p.	p.	PROPN
ejpam-6641	246	9	harjulehto	harjulehto	PROPN
ejpam-6641	246	10	,	,	PUNCT
ejpam-6641	246	11	p.	p.	PROPN
ejpam-6641	246	12	h”ast”o	h”ast”o	PROPN
ejpam-6641	246	13	and	and	CCONJ
ejpam-6641	246	14	m.	m.	PROPN
ejpam-6641	246	15	ružička	ružička	PROPN
ejpam-6641	246	16	,	,	PUNCT
ejpam-6641	246	17	lebesgue	lebesgue	NOUN
ejpam-6641	246	18	and	and	CCONJ
ejpam-6641	246	19	sobolev	sobolev	NOUN
ejpam-6641	246	20	spaces	space	NOUN
ejpam-6641	246	21	with	with	ADP
ejpam-6641	246	22	variable	variable	ADJ
ejpam-6641	246	23	exponents	exponent	NOUN
ejpam-6641	246	24	,	,	PUNCT
ejpam-6641	246	25	lecture	lecture	NOUN
ejpam-6641	246	26	notes	note	NOUN
ejpam-6641	246	27	in	in	ADP
ejpam-6641	246	28	mathematics	mathematic	NOUN
ejpam-6641	246	29	.	.	PUNCT
ejpam-6641	247	1	vol	vol	NOUN
ejpam-6641	247	2	.	.	PROPN
ejpam-6641	248	1	2017	2017	NUM
ejpam-6641	248	2	,	,	PUNCT
ejpam-6641	248	3	springer	springer	NOUN
ejpam-6641	248	4	,	,	PUNCT
ejpam-6641	248	5	heidelberg	heidelberg	PROPN
ejpam-6641	248	6	(	(	PUNCT
ejpam-6641	248	7	2011	2011	NUM
ejpam-6641	248	8	)	)	PUNCT
ejpam-6641	249	1	.	.	PUNCT
ejpam-6641	250	1	[	[	X
ejpam-6641	250	2	2	2	X
ejpam-6641	250	3	]	]	PUNCT
ejpam-6641	250	4	v.	v.	ADP
ejpam-6641	250	5	kokilashvili	kokilashvili	PROPN
ejpam-6641	250	6	,	,	PUNCT
ejpam-6641	250	7	a.	a.	PROPN
ejpam-6641	250	8	meskhi	meskhi	PROPN
ejpam-6641	250	9	,	,	PUNCT
ejpam-6641	250	10	h.	h.	PROPN
ejpam-6641	250	11	rafeiro	rafeiro	PROPN
ejpam-6641	250	12	and	and	CCONJ
ejpam-6641	250	13	s.	s.	PROPN
ejpam-6641	250	14	samko	samko	PROPN
ejpam-6641	250	15	,	,	PUNCT
ejpam-6641	250	16	integral	integral	ADJ
ejpam-6641	250	17	operators	operator	NOUN
ejpam-6641	250	18	in	in	ADP
ejpam-6641	250	19	nonstandard	nonstandard	ADJ
ejpam-6641	250	20	function	function	NOUN
ejpam-6641	250	21	spaces	space	NOUN
ejpam-6641	250	22	.	.	PUNCT
ejpam-6641	251	1	vol	vol	NOUN
ejpam-6641	251	2	.	.	NOUN
ejpam-6641	252	1	1	1	NUM
ejpam-6641	252	2	:	:	PUNCT
ejpam-6641	252	3	variable	variable	ADJ
ejpam-6641	252	4	exponent	exponent	NOUN
ejpam-6641	252	5	lebesgue	lebesgue	NOUN
ejpam-6641	252	6	and	and	CCONJ
ejpam-6641	252	7	amalgam	amalgam	NOUN
ejpam-6641	252	8	spaces	space	NOUN
ejpam-6641	252	9	.	.	PUNCT
ejpam-6641	253	1	oper	oper	PROPN
ejpam-6641	253	2	.	.	PROPN
ejpam-6641	253	3	theory	theory	PROPN
ejpam-6641	253	4	adv	adv	PROPN
ejpam-6641	253	5	.	.	PUNCT
ejpam-6641	253	6	appl	appl	PROPN
ejpam-6641	253	7	.	.	PROPN
ejpam-6641	254	1	248	248	NUM
ejpam-6641	254	2	,	,	PUNCT
ejpam-6641	254	3	birkhuser	birkhuser	NOUN
ejpam-6641	254	4	/	/	SYM
ejpam-6641	254	5	springer	springer	NOUN
ejpam-6641	254	6	,	,	PUNCT
ejpam-6641	254	7	cham	cham	NOUN
ejpam-6641	254	8	,	,	PUNCT
ejpam-6641	254	9	2016	2016	NUM
ejpam-6641	254	10	.	.	PUNCT
ejpam-6641	255	1	[	[	X
ejpam-6641	255	2	3	3	X
ejpam-6641	255	3	]	]	X
ejpam-6641	255	4	v.	v.	ADP
ejpam-6641	255	5	kokilashvili	kokilashvili	PROPN
ejpam-6641	255	6	,	,	PUNCT
ejpam-6641	255	7	a.	a.	PROPN
ejpam-6641	255	8	meskhi	meskhi	PROPN
ejpam-6641	255	9	,	,	PUNCT
ejpam-6641	255	10	h.	h.	PROPN
ejpam-6641	255	11	rafeiro	rafeiro	PROPN
ejpam-6641	255	12	and	and	CCONJ
ejpam-6641	255	13	s.	s.	PROPN
ejpam-6641	255	14	samko	samko	PROPN
ejpam-6641	255	15	,	,	PUNCT
ejpam-6641	255	16	integral	integral	ADJ
ejpam-6641	255	17	operators	operator	NOUN
ejpam-6641	255	18	in	in	ADP
ejpam-6641	255	19	nonstandard	nonstandard	ADJ
ejpam-6641	255	20	function	function	NOUN
ejpam-6641	255	21	spaces	space	NOUN
ejpam-6641	255	22	.	.	PUNCT
ejpam-6641	256	1	vol	vol	NOUN
ejpam-6641	256	2	.	.	PUNCT
ejpam-6641	257	1	2	2	NUM
ejpam-6641	257	2	:	:	PUNCT
ejpam-6641	257	3	variable	variable	ADJ
ejpam-6641	257	4	exponent	exponent	NOUN
ejpam-6641	257	5	h”older	h”older	PROPN
ejpam-6641	257	6	,	,	PUNCT
ejpam-6641	257	7	morrey	morrey	NOUN
ejpam-6641	257	8	-	-	PUNCT
ejpam-6641	257	9	campanato	campanato	NOUN
ejpam-6641	257	10	and	and	CCONJ
ejpam-6641	257	11	grand	grand	ADJ
ejpam-6641	257	12	spaces	space	NOUN
ejpam-6641	257	13	.	.	PUNCT
ejpam-6641	258	1	theory	theory	PROPN
ejpam-6641	258	2	adv	adv	PROPN
ejpam-6641	258	3	.	.	PUNCT
ejpam-6641	258	4	appl	appl	PROPN
ejpam-6641	258	5	.	.	PUNCT
ejpam-6641	259	1	249	249	NUM
ejpam-6641	259	2	,	,	PUNCT
ejpam-6641	259	3	birkhuser	birkhuser	NOUN
ejpam-6641	259	4	/	/	SYM
ejpam-6641	259	5	springer	springer	NOUN
ejpam-6641	259	6	,	,	PUNCT
ejpam-6641	259	7	cham	cham	NOUN
ejpam-6641	259	8	,	,	PUNCT
ejpam-6641	259	9	2016	2016	NUM
ejpam-6641	259	10	.	.	PUNCT
ejpam-6641	260	1	[	[	X
ejpam-6641	260	2	4	4	NUM
ejpam-6641	260	3	]	]	X
ejpam-6641	260	4	y.	y.	PROPN
ejpam-6641	260	5	sawano	sawano	PROPN
ejpam-6641	260	6	,	,	PUNCT
ejpam-6641	260	7	g.	g.	PROPN
ejpam-6641	260	8	di	di	PROPN
ejpam-6641	260	9	fazio	fazio	PROPN
ejpam-6641	260	10	,	,	PUNCT
ejpam-6641	260	11	d.	d.	PROPN
ejpam-6641	260	12	i.	i.	PROPN
ejpam-6641	260	13	hakim	hakim	PROPN
ejpam-6641	260	14	,	,	PUNCT
ejpam-6641	260	15	morrey	morrey	PROPN
ejpam-6641	260	16	spaces	space	VERB
ejpam-6641	260	17	introduction	introduction	NOUN
ejpam-6641	260	18	and	and	CCONJ
ejpam-6641	260	19	applications	application	NOUN
ejpam-6641	260	20	to	to	ADP
ejpam-6641	260	21	integral	integral	ADJ
ejpam-6641	260	22	operators	operator	NOUN
ejpam-6641	260	23	and	and	CCONJ
ejpam-6641	260	24	pde	pde	NOUN
ejpam-6641	260	25	’s	’s	PART
ejpam-6641	260	26	,	,	PUNCT
ejpam-6641	260	27	volumes	volume	NOUN
ejpam-6641	260	28	i	i	PRON
ejpam-6641	260	29	,	,	PUNCT
ejpam-6641	260	30	ii	ii	PROPN
ejpam-6641	260	31	,	,	PUNCT
ejpam-6641	260	32	crc	crc	NOUN
ejpam-6641	260	33	press	press	PROPN
ejpam-6641	260	34	,	,	PUNCT
ejpam-6641	260	35	taylor	taylor	PROPN
ejpam-6641	260	36	and	and	CCONJ
ejpam-6641	260	37	francis	francis	PROPN
ejpam-6641	260	38	,	,	PUNCT
ejpam-6641	260	39	2020	2020	NUM
ejpam-6641	260	40	.	.	PUNCT
ejpam-6641	261	1	[	[	X
ejpam-6641	261	2	5	5	NUM
ejpam-6641	261	3	]	]	PUNCT
ejpam-6641	261	4	m.	m.	NOUN
ejpam-6641	261	5	sultan	sultan	PROPN
ejpam-6641	261	6	,	,	PUNCT
ejpam-6641	261	7	b.	b.	PROPN
ejpam-6641	261	8	sultan	sultan	PROPN
ejpam-6641	261	9	,	,	PUNCT
ejpam-6641	261	10	a.	a.	NOUN
ejpam-6641	261	11	hussain	hussain	PROPN
ejpam-6641	261	12	,	,	PUNCT
ejpam-6641	261	13	grand	grand	ADJ
ejpam-6641	261	14	herz	herz	PROPN
ejpam-6641	261	15	–	–	PUNCT
ejpam-6641	261	16	morrey	morrey	PROPN
ejpam-6641	261	17	spaces	space	VERB
ejpam-6641	261	18	with	with	ADP
ejpam-6641	261	19	variable	variable	ADJ
ejpam-6641	261	20	exponent	exponent	NOUN
ejpam-6641	261	21	,	,	PUNCT
ejpam-6641	261	22	math	math	NOUN
ejpam-6641	261	23	.	.	PUNCT
ejpam-6641	262	1	notes	note	NOUN
ejpam-6641	262	2	.	.	PUNCT
ejpam-6641	263	1	114	114	NUM
ejpam-6641	263	2	(	(	PUNCT
ejpam-6641	263	3	5	5	NUM
ejpam-6641	263	4	)	)	PUNCT
ejpam-6641	263	5	(	(	PUNCT
ejpam-6641	263	6	2023	2023	NUM
ejpam-6641	263	7	)	)	PUNCT
ejpam-6641	263	8	,	,	PUNCT
ejpam-6641	263	9	957–977	957–977	NUM
ejpam-6641	263	10	.	.	PUNCT
ejpam-6641	264	1	[	[	X
ejpam-6641	264	2	6	6	NUM
ejpam-6641	264	3	]	]	PUNCT
ejpam-6641	264	4	a.	a.	NOUN
ejpam-6641	264	5	hussain	hussain	PROPN
ejpam-6641	264	6	,	,	PUNCT
ejpam-6641	264	7	g.	g.	PROPN
ejpam-6641	264	8	gao	gao	PROPN
ejpam-6641	264	9	,	,	PUNCT
ejpam-6641	264	10	multilinear	multilinear	PROPN
ejpam-6641	264	11	singular	singular	PROPN
ejpam-6641	264	12	integrals	integral	NOUN
ejpam-6641	264	13	and	and	CCONJ
ejpam-6641	264	14	commutators	commutator	NOUN
ejpam-6641	264	15	on	on	ADP
ejpam-6641	264	16	herz	herz	ADJ
ejpam-6641	264	17	space	space	NOUN
ejpam-6641	264	18	with	with	ADP
ejpam-6641	264	19	variable	variable	ADJ
ejpam-6641	264	20	exponent	exponent	NOUN
ejpam-6641	264	21	,	,	PUNCT
ejpam-6641	264	22	isrn	isrn	PROPN
ejpam-6641	264	23	math	math	NOUN
ejpam-6641	264	24	.	.	PUNCT
ejpam-6641	265	1	anal	anal	PROPN
ejpam-6641	265	2	.	.	PUNCT
ejpam-6641	266	1	2014	2014	NUM
ejpam-6641	266	2	(	(	PUNCT
ejpam-6641	266	3	2014	2014	NUM
ejpam-6641	266	4	)	)	PUNCT
ejpam-6641	266	5	,	,	PUNCT
ejpam-6641	266	6	1	1	NUM
ejpam-6641	266	7	-	-	SYM
ejpam-6641	266	8	10	10	NUM
ejpam-6641	266	9	.	.	PUNCT
ejpam-6641	267	1	[	[	X
ejpam-6641	267	2	7	7	X
ejpam-6641	267	3	]	]	PUNCT
ejpam-6641	267	4	a.	a.	NOUN
ejpam-6641	267	5	hussain	hussain	PROPN
ejpam-6641	267	6	,	,	PUNCT
ejpam-6641	267	7	i.	i.	PROPN
ejpam-6641	267	8	khan	khan	PROPN
ejpam-6641	267	9	.	.	PUNCT
ejpam-6641	268	1	and	and	CCONJ
ejpam-6641	268	2	a.	a.	PROPN
ejpam-6641	268	3	mohamed	mohamed	PROPN
ejpam-6641	268	4	,	,	PUNCT
ejpam-6641	268	5	variable	variable	ADJ
ejpam-6641	268	6	her	her	PRON
ejpam-6641	268	7	-	-	PUNCT
ejpam-6641	268	8	morrey	morrey	PROPN
ejpam-6641	268	9	estimates	estimate	NOUN
ejpam-6641	268	10	for	for	ADP
ejpam-6641	268	11	rough	rough	ADJ
ejpam-6641	268	12	fractional	fractional	ADJ
ejpam-6641	268	13	hausdorff	hausdorff	NOUN
ejpam-6641	268	14	operator	operator	NOUN
ejpam-6641	268	15	,	,	PUNCT
ejpam-6641	268	16	j.	j.	PROPN
ejpam-6641	268	17	inequal	inequal	PROPN
ejpam-6641	268	18	.	.	PUNCT
ejpam-6641	269	1	appl	appl	PROPN
ejpam-6641	269	2	.	.	PUNCT
ejpam-6641	270	1	33	33	NUM
ejpam-6641	270	2	(	(	PUNCT
ejpam-6641	270	3	2024	2024	NUM
ejpam-6641	270	4	)	)	PUNCT
ejpam-6641	270	5	.	.	PUNCT
ejpam-6641	271	1	[	[	X
ejpam-6641	271	2	8	8	NUM
ejpam-6641	271	3	]	]	X
ejpam-6641	271	4	a.	a.	NOUN
ejpam-6641	271	5	ajaib	ajaib	PROPN
ejpam-6641	271	6	,	,	PUNCT
ejpam-6641	271	7	and	and	CCONJ
ejpam-6641	271	8	a.	a.	NOUN
ejpam-6641	271	9	hussain	hussain	PROPN
ejpam-6641	271	10	,	,	PUNCT
ejpam-6641	271	11	weighted	weight	VERB
ejpam-6641	271	12	cbmo	cbmo	NOUN
ejpam-6641	271	13	estimates	estimate	NOUN
ejpam-6641	271	14	for	for	ADP
ejpam-6641	271	15	commutators	commutator	NOUN
ejpam-6641	271	16	of	of	ADP
ejpam-6641	271	17	matrix	matrix	NOUN
ejpam-6641	271	18	hausdorff	hausdorff	NOUN
ejpam-6641	271	19	operator	operator	NOUN
ejpam-6641	271	20	on	on	ADP
ejpam-6641	271	21	the	the	DET
ejpam-6641	271	22	heisenberg	heisenberg	PROPN
ejpam-6641	271	23	group	group	NOUN
ejpam-6641	271	24	.	.	PUNCT
ejpam-6641	272	1	open	open	ADJ
ejpam-6641	272	2	math	math	NOUN
ejpam-6641	272	3	.	.	PUNCT
ejpam-6641	273	1	18(1	18(1	X
ejpam-6641	273	2	)	)	PUNCT
ejpam-6641	273	3	(	(	PUNCT
ejpam-6641	273	4	2020	2020	NUM
ejpam-6641	273	5	)	)	PUNCT
ejpam-6641	273	6	,	,	PUNCT
ejpam-6641	273	7	496	496	NUM
ejpam-6641	273	8	-	-	SYM
ejpam-6641	273	9	511	511	NUM
ejpam-6641	273	10	.	.	PUNCT
ejpam-6641	274	1	[	[	X
ejpam-6641	274	2	9	9	X
ejpam-6641	274	3	]	]	X
ejpam-6641	274	4	j.	j.	PROPN
ejpam-6641	274	5	younas	younas	PROPN
ejpam-6641	274	6	,	,	PUNCT
ejpam-6641	274	7	a.	a.	NOUN
ejpam-6641	274	8	hussain	hussain	PROPN
ejpam-6641	274	9	,	,	PUNCT
ejpam-6641	274	10	h.	h.	PROPN
ejpam-6641	274	11	alhazmi	alhazmi	PROPN
ejpam-6641	274	12	,	,	PUNCT
ejpam-6641	274	13	a.f	a.f	PROPN
ejpam-6641	274	14	.	.	PROPN
ejpam-6641	274	15	aljohani	aljohani	PROPN
ejpam-6641	274	16	,	,	PUNCT
ejpam-6641	274	17	i.	i.	PROPN
ejpam-6641	274	18	khan	khan	PROPN
ejpam-6641	274	19	,	,	PUNCT
ejpam-6641	274	20	bmo	bmo	NOUN
ejpam-6641	274	21	estimates	estimate	NOUN
ejpam-6641	274	22	for	for	ADP
ejpam-6641	274	23	commutators	commutator	NOUN
ejpam-6641	274	24	of	of	ADP
ejpam-6641	274	25	the	the	DET
ejpam-6641	274	26	rough	rough	ADJ
ejpam-6641	274	27	fractional	fractional	ADJ
ejpam-6641	274	28	hausdorff	hausdorff	NOUN
ejpam-6641	274	29	operator	operator	NOUN
ejpam-6641	274	30	on	on	ADP
ejpam-6641	274	31	grand	grand	ADJ
ejpam-6641	274	32	-	-	PUNCT
ejpam-6641	274	33	variable	variable	ADJ
ejpam-6641	274	34	-	-	PUNCT
ejpam-6641	274	35	herz	herz	ADJ
ejpam-6641	274	36	-	-	PUNCT
ejpam-6641	274	37	morrey	morrey	PROPN
ejpam-6641	274	38	spaces	space	NOUN
ejpam-6641	274	39	,	,	PUNCT
ejpam-6641	274	40	aims	aim	VERB
ejpam-6641	274	41	math	math	NOUN
ejpam-6641	274	42	.	.	PUNCT
ejpam-6641	275	1	9(9	9(9	X
ejpam-6641	275	2	)	)	PUNCT
ejpam-6641	275	3	(	(	PUNCT
ejpam-6641	275	4	2024	2024	NUM
ejpam-6641	275	5	)	)	PUNCT
ejpam-6641	275	6	,	,	PUNCT
ejpam-6641	275	7	23434	23434	NUM
ejpam-6641	275	8	-	-	SYM
ejpam-6641	275	9	23448	23448	NUM
ejpam-6641	275	10	.	.	PUNCT
ejpam-6641	276	1	[	[	X
ejpam-6641	276	2	10	10	NUM
ejpam-6641	276	3	]	]	PUNCT
ejpam-6641	276	4	s.	s.	PROPN
ejpam-6641	276	5	lu	lu	PROPN
ejpam-6641	276	6	,	,	PUNCT
ejpam-6641	276	7	d.	d.	PROPN
ejpam-6641	276	8	yang	yang	PROPN
ejpam-6641	276	9	,	,	PUNCT
ejpam-6641	276	10	g.	g.	PROPN
ejpam-6641	276	11	hu	hu	PROPN
ejpam-6641	276	12	,	,	PUNCT
ejpam-6641	276	13	herz	herz	PROPN
ejpam-6641	276	14	type	type	NOUN
ejpam-6641	276	15	spaces	space	NOUN
ejpam-6641	276	16	and	and	CCONJ
ejpam-6641	276	17	their	their	PRON
ejpam-6641	276	18	applications	application	NOUN
ejpam-6641	276	19	,	,	PUNCT
ejpam-6641	276	20	science	science	NOUN
ejpam-6641	276	21	press	press	NOUN
ejpam-6641	276	22	.	.	PUNCT
ejpam-6641	277	1	beijing	beijing	PROPN
ejpam-6641	277	2	(	(	PUNCT
ejpam-6641	277	3	2008	2008	NUM
ejpam-6641	277	4	)	)	PUNCT
ejpam-6641	278	1	[	[	X
ejpam-6641	278	2	11	11	NUM
ejpam-6641	278	3	]	]	PUNCT
ejpam-6641	278	4	m.	m.	NOUN
ejpam-6641	278	5	ragusa	ragusa	PROPN
ejpam-6641	278	6	,	,	PUNCT
ejpam-6641	278	7	homogeneous	homogeneous	ADJ
ejpam-6641	278	8	herz	herz	ADJ
ejpam-6641	278	9	spaces	space	NOUN
ejpam-6641	278	10	and	and	CCONJ
ejpam-6641	278	11	regularity	regularity	NOUN
ejpam-6641	278	12	results	result	NOUN
ejpam-6641	278	13	,	,	PUNCT
ejpam-6641	278	14	nonlinear	nonlinear	ADJ
ejpam-6641	278	15	anal	anal	NOUN
ejpam-6641	278	16	.	.	PUNCT
ejpam-6641	279	1	71	71	NUM
ejpam-6641	279	2	(	(	PUNCT
ejpam-6641	279	3	2009	2009	NUM
ejpam-6641	279	4	)	)	PUNCT
ejpam-6641	279	5	,	,	PUNCT
ejpam-6641	279	6	1909–1914	1909–1914	NUM
ejpam-6641	279	7	.	.	PUNCT
ejpam-6641	280	1	[	[	X
ejpam-6641	280	2	12	12	NUM
ejpam-6641	280	3	]	]	PUNCT
ejpam-6641	280	4	m.	m.	NOUN
ejpam-6641	280	5	izuki	izuki	PROPN
ejpam-6641	280	6	,	,	PUNCT
ejpam-6641	280	7	boundedness	boundedness	NOUN
ejpam-6641	280	8	of	of	ADP
ejpam-6641	280	9	sublinear	sublinear	NOUN
ejpam-6641	280	10	operators	operator	NOUN
ejpam-6641	280	11	on	on	ADP
ejpam-6641	280	12	herz	herz	PROPN
ejpam-6641	280	13	spaces	space	NOUN
ejpam-6641	280	14	with	with	ADP
ejpam-6641	280	15	variable	variable	ADJ
ejpam-6641	280	16	exponent	exponent	NOUN
ejpam-6641	280	17	and	and	CCONJ
ejpam-6641	280	18	application	application	NOUN
ejpam-6641	280	19	to	to	ADP
ejpam-6641	280	20	wavelet	wavelet	NOUN
ejpam-6641	280	21	characterization	characterization	NOUN
ejpam-6641	280	22	,	,	PUNCT
ejpam-6641	280	23	anal	anal	NOUN
ejpam-6641	280	24	.	.	PUNCT
ejpam-6641	280	25	math	math	NOUN
ejpam-6641	280	26	.	.	PUNCT
ejpam-6641	281	1	36(1	36(1	NUM
ejpam-6641	281	2	)	)	PUNCT
ejpam-6641	281	3	(	(	PUNCT
ejpam-6641	281	4	2010	2010	NUM
ejpam-6641	281	5	)	)	PUNCT
ejpam-6641	281	6	,	,	PUNCT
ejpam-6641	281	7	33	33	NUM
ejpam-6641	281	8	-	-	SYM
ejpam-6641	281	9	50	50	NUM
ejpam-6641	281	10	.	.	PUNCT
ejpam-6641	282	1	[	[	X
ejpam-6641	282	2	13	13	NUM
ejpam-6641	282	3	]	]	PUNCT
ejpam-6641	282	4	s.	s.	PROPN
ejpam-6641	282	5	samko	samko	PROPN
ejpam-6641	282	6	,	,	PUNCT
ejpam-6641	282	7	variable	variable	ADJ
ejpam-6641	282	8	exponent	exponent	NOUN
ejpam-6641	282	9	herz	herz	PROPN
ejpam-6641	282	10	spaces	space	NOUN
ejpam-6641	282	11	,	,	PUNCT
ejpam-6641	282	12	mediterr	mediterr	PROPN
ejpam-6641	282	13	.	.	PUNCT
ejpam-6641	283	1	j.	j.	PROPN
ejpam-6641	283	2	math	math	PROPN
ejpam-6641	283	3	.	.	PUNCT
ejpam-6641	284	1	10(4	10(4	NUM
ejpam-6641	284	2	)	)	PUNCT
ejpam-6641	284	3	(	(	PUNCT
ejpam-6641	284	4	2013	2013	NUM
ejpam-6641	284	5	)	)	PUNCT
ejpam-6641	284	6	,	,	PUNCT
ejpam-6641	284	7	20072025	20072025	NUM
ejpam-6641	284	8	.	.	PUNCT
ejpam-6641	285	1	[	[	X
ejpam-6641	285	2	14	14	NUM
ejpam-6641	285	3	]	]	X
ejpam-6641	285	4	k.p	k.p	PROPN
ejpam-6641	285	5	.	.	PROPN
ejpam-6641	285	6	ho	ho	PROPN
ejpam-6641	285	7	,	,	PUNCT
ejpam-6641	285	8	intrinsic	intrinsic	ADJ
ejpam-6641	285	9	square	square	ADJ
ejpam-6641	285	10	functions	function	NOUN
ejpam-6641	285	11	on	on	ADP
ejpam-6641	285	12	morrey	morrey	NOUN
ejpam-6641	285	13	and	and	CCONJ
ejpam-6641	285	14	block	block	NOUN
ejpam-6641	285	15	spaces	space	NOUN
ejpam-6641	285	16	with	with	ADP
ejpam-6641	285	17	variable	variable	ADJ
ejpam-6641	285	18	exponents	exponent	NOUN
ejpam-6641	285	19	,	,	PUNCT
ejpam-6641	285	20	bull	bull	NOUN
ejpam-6641	285	21	.	.	PUNCT
ejpam-6641	286	1	malays	malays	PROPN
ejpam-6641	286	2	.	.	PUNCT
ejpam-6641	287	1	math	math	NOUN
ejpam-6641	287	2	.	.	PUNCT
ejpam-6641	288	1	sci	sci	PROPN
ejpam-6641	288	2	.	.	PROPN
ejpam-6641	288	3	soc	soc	PROPN
ejpam-6641	288	4	.	.	PUNCT
ejpam-6641	289	1	40(3	40(3	NUM
ejpam-6641	289	2	)	)	PUNCT
ejpam-6641	289	3	(	(	PUNCT
ejpam-6641	289	4	2017	2017	NUM
ejpam-6641	289	5	)	)	PUNCT
ejpam-6641	289	6	,	,	PUNCT
ejpam-6641	289	7	995	995	NUM
ejpam-6641	289	8	-	-	SYM
ejpam-6641	289	9	1010	1010	NUM
ejpam-6641	289	10	.	.	PUNCT
ejpam-6641	290	1	[	[	X
ejpam-6641	290	2	15	15	NUM
ejpam-6641	290	3	]	]	X
ejpam-6641	290	4	h.	h.	PROPN
ejpam-6641	290	5	rafeiro	rafeiro	PROPN
ejpam-6641	290	6	and	and	CCONJ
ejpam-6641	290	7	s.	s.	PROPN
ejpam-6641	290	8	samko	samko	PROPN
ejpam-6641	290	9	,	,	PUNCT
ejpam-6641	290	10	riesz	riesz	VERB
ejpam-6641	290	11	potential	potential	ADJ
ejpam-6641	290	12	operator	operator	NOUN
ejpam-6641	290	13	in	in	ADP
ejpam-6641	290	14	continual	continual	ADJ
ejpam-6641	290	15	variable	variable	NOUN
ejpam-6641	290	16	ex	ex	X
ejpam-6641	290	17	ponents	ponent	NOUN
ejpam-6641	290	18	herz	herz	PROPN
ejpam-6641	290	19	spaces	space	NOUN
ejpam-6641	290	20	,	,	PUNCT
ejpam-6641	290	21	math	math	NOUN
ejpam-6641	290	22	.	.	PUNCT
ejpam-6641	291	1	nachr	nachr	PROPN
ejpam-6641	291	2	.	.	PUNCT
ejpam-6641	292	1	288(4	288(4	NUM
ejpam-6641	292	2	)	)	PUNCT
ejpam-6641	292	3	(	(	PUNCT
ejpam-6641	292	4	2015	2015	NUM
ejpam-6641	292	5	)	)	PUNCT
ejpam-6641	292	6	,	,	PUNCT
ejpam-6641	292	7	465	465	NUM
ejpam-6641	292	8	-	-	SYM
ejpam-6641	292	9	475	475	NUM
ejpam-6641	292	10	.	.	PUNCT
ejpam-6641	293	1	[	[	X
ejpam-6641	293	2	16	16	NUM
ejpam-6641	293	3	]	]	PUNCT
ejpam-6641	293	4	a.	a.	NOUN
ejpam-6641	293	5	meskhi	meskhi	PROPN
ejpam-6641	293	6	,	,	PUNCT
ejpam-6641	293	7	h.	h.	PROPN
ejpam-6641	293	8	rafeiro	rafeiro	PROPN
ejpam-6641	293	9	,	,	PUNCT
ejpam-6641	293	10	and	and	CCONJ
ejpam-6641	293	11	m.a	m.a	PROPN
ejpam-6641	293	12	.	.	PROPN
ejpam-6641	293	13	zaighum	zaighum	NOUN
ejpam-6641	293	14	,	,	PUNCT
ejpam-6641	293	15	on	on	ADP
ejpam-6641	293	16	the	the	DET
ejpam-6641	293	17	boundedness	boundedness	NOUN
ejpam-6641	293	18	of	of	ADP
ejpam-6641	293	19	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6641	293	20	integrals	integral	NOUN
ejpam-6641	293	21	on	on	ADP
ejpam-6641	293	22	continual	continual	ADJ
ejpam-6641	293	23	variable	variable	ADJ
ejpam-6641	293	24	exponent	exponent	NOUN
ejpam-6641	293	25	herz	herz	PROPN
ejpam-6641	293	26	spaces	space	VERB
ejpam-6641	293	27	,	,	PUNCT
ejpam-6641	293	28	georgian	georgian	PROPN
ejpam-6641	293	29	math	math	NOUN
ejpam-6641	293	30	.	.	PUNCT
ejpam-6641	294	1	j.	j.	PROPN
ejpam-6641	294	2	26(1	26(1	PROPN
ejpam-6641	294	3	)	)	PUNCT
ejpam-6641	294	4	(	(	PUNCT
ejpam-6641	294	5	2019	2019	NUM
ejpam-6641	294	6	)	)	PUNCT
ejpam-6641	294	7	,	,	PUNCT
ejpam-6641	294	8	105	105	NUM
ejpam-6641	294	9	-	-	SYM
ejpam-6641	294	10	116	116	NUM
ejpam-6641	294	11	.	.	PUNCT
ejpam-6641	295	1	g.	g.	PROPN
ejpam-6641	295	2	a.	a.	PROPN
ejpam-6641	295	3	basendwah	basendwah	PROPN
ejpam-6641	295	4	et	et	PROPN
ejpam-6641	295	5	al	al	PROPN
ejpam-6641	295	6	.	.	PUNCT
ejpam-6641	295	7	/	/	SYM
ejpam-6641	295	8	eur	eur	PROPN
ejpam-6641	295	9	.	.	PUNCT
ejpam-6641	296	1	j.	j.	PROPN
ejpam-6641	296	2	pure	pure	PROPN
ejpam-6641	296	3	appl	appl	PROPN
ejpam-6641	296	4	.	.	PROPN
ejpam-6641	296	5	math	math	PROPN
ejpam-6641	296	6	,	,	PUNCT
ejpam-6641	296	7	18	18	NUM
ejpam-6641	296	8	(	(	PUNCT
ejpam-6641	296	9	4	4	NUM
ejpam-6641	296	10	)	)	PUNCT
ejpam-6641	296	11	(	(	PUNCT
ejpam-6641	296	12	2025	2025	NUM
ejpam-6641	296	13	)	)	PUNCT
ejpam-6641	296	14	,	,	PUNCT
ejpam-6641	296	15	6641	6641	NUM
ejpam-6641	296	16	15	15	NUM
ejpam-6641	296	17	of	of	ADP
ejpam-6641	296	18	16	16	NUM
ejpam-6641	296	19	[	[	X
ejpam-6641	296	20	17	17	NUM
ejpam-6641	296	21	]	]	PUNCT
ejpam-6641	296	22	m.	m.	NOUN
ejpam-6641	296	23	sultan	sultan	PROPN
ejpam-6641	296	24	and	and	CCONJ
ejpam-6641	296	25	b.	b.	PROPN
ejpam-6641	296	26	sultan	sultan	PROPN
ejpam-6641	296	27	,	,	PUNCT
ejpam-6641	296	28	a	a	DET
ejpam-6641	296	29	note	note	NOUN
ejpam-6641	296	30	on	on	ADP
ejpam-6641	296	31	the	the	DET
ejpam-6641	296	32	boundedness	boundedness	NOUN
ejpam-6641	296	33	of	of	ADP
ejpam-6641	296	34	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6641	296	35	integral	integral	ADJ
ejpam-6641	296	36	operator	operator	NOUN
ejpam-6641	296	37	on	on	ADP
ejpam-6641	296	38	continual	continual	ADJ
ejpam-6641	296	39	herz	herz	PROPN
ejpam-6641	296	40	-	-	PUNCT
ejpam-6641	296	41	morrey	morrey	PROPN
ejpam-6641	296	42	spaces	space	NOUN
ejpam-6641	296	43	,	,	PUNCT
ejpam-6641	296	44	filomat	filomat	PROPN
ejpam-6641	296	45	.	.	PROPN
ejpam-6641	296	46	39	39	NUM
ejpam-6641	296	47	(	(	PUNCT
ejpam-6641	296	48	6	6	NUM
ejpam-6641	296	49	)	)	PUNCT
ejpam-6641	296	50	(	(	PUNCT
ejpam-6641	296	51	2025	2025	NUM
ejpam-6641	296	52	)	)	PUNCT
ejpam-6641	296	53	,	,	PUNCT
ejpam-6641	296	54	2017	2017	NUM
ejpam-6641	296	55	-	-	SYM
ejpam-6641	296	56	2027	2027	NUM
ejpam-6641	296	57	.	.	PUNCT
ejpam-6641	297	1	[	[	X
ejpam-6641	297	2	18	18	NUM
ejpam-6641	297	3	]	]	PUNCT
ejpam-6641	297	4	m.	m.	NOUN
ejpam-6641	297	5	izuki	izuki	PROPN
ejpam-6641	297	6	,	,	PUNCT
ejpam-6641	297	7	boundedness	boundedness	NOUN
ejpam-6641	297	8	of	of	ADP
ejpam-6641	297	9	vector	vector	NOUN
ejpam-6641	297	10	-	-	PUNCT
ejpam-6641	297	11	valued	value	VERB
ejpam-6641	297	12	sublinear	sublinear	NOUN
ejpam-6641	297	13	operators	operator	NOUN
ejpam-6641	297	14	on	on	ADP
ejpam-6641	297	15	herz	herz	ADJ
ejpam-6641	297	16	-	-	PUNCT
ejpam-6641	297	17	morrey	morrey	PROPN
ejpam-6641	297	18	spaces	space	NOUN
ejpam-6641	297	19	with	with	ADP
ejpam-6641	297	20	variable	variable	ADJ
ejpam-6641	297	21	exponents	exponent	NOUN
ejpam-6641	297	22	,	,	PUNCT
ejpam-6641	297	23	math	math	NOUN
ejpam-6641	297	24	.	.	PUNCT
ejpam-6641	298	1	sci	sci	PROPN
ejpam-6641	298	2	.	.	PUNCT
ejpam-6641	299	1	j	j	PROPN
ejpam-6641	299	2	13(10	13(10	NUM
ejpam-6641	299	3	)	)	PUNCT
ejpam-6641	299	4	(	(	PUNCT
ejpam-6641	299	5	2009	2009	NUM
ejpam-6641	299	6	)	)	PUNCT
ejpam-6641	299	7	,	,	PUNCT
ejpam-6641	299	8	243	243	NUM
ejpam-6641	299	9	-	-	SYM
ejpam-6641	299	10	253	253	NUM
ejpam-6641	299	11	.	.	PUNCT
ejpam-6641	300	1	[	[	X
ejpam-6641	300	2	19	19	NUM
ejpam-6641	300	3	]	]	X
ejpam-6641	300	4	j.l	j.l	PROPN
ejpam-6641	300	5	.	.	PROPN
ejpam-6641	300	6	wu	wu	PROPN
ejpam-6641	300	7	,	,	PUNCT
ejpam-6641	300	8	w.j	w.j	PROPN
ejpam-6641	300	9	.	.	PROPN
ejpam-6641	300	10	zhao	zhao	PROPN
ejpam-6641	300	11	,	,	PUNCT
ejpam-6641	300	12	boundedness	boundedness	NOUN
ejpam-6641	300	13	for	for	ADP
ejpam-6641	300	14	higher	high	ADJ
ejpam-6641	300	15	order	order	NOUN
ejpam-6641	300	16	commutators	commutator	NOUN
ejpam-6641	300	17	of	of	ADP
ejpam-6641	300	18	fractional	fractional	ADJ
ejpam-6641	300	19	integrals	integral	NOUN
ejpam-6641	300	20	on	on	ADP
ejpam-6641	300	21	variable	variable	ADJ
ejpam-6641	300	22	exponent	exponent	NOUN
ejpam-6641	300	23	herz	herz	PROPN
ejpam-6641	300	24	-	-	PUNCT
ejpam-6641	300	25	morrey	morrey	PROPN
ejpam-6641	300	26	spaces	space	NOUN
ejpam-6641	300	27	.	.	PUNCT
ejpam-6641	301	1	mediterr	mediterr	PROPN
ejpam-6641	301	2	.	.	PUNCT
ejpam-6641	302	1	j.	j.	PROPN
ejpam-6641	302	2	math	math	PROPN
ejpam-6641	302	3	.	.	PUNCT
ejpam-6641	303	1	14	14	NUM
ejpam-6641	303	2	(	(	PUNCT
ejpam-6641	303	3	2017	2017	NUM
ejpam-6641	303	4	)	)	PUNCT
ejpam-6641	303	5	198	198	NUM
ejpam-6641	303	6	.	.	PUNCT
ejpam-6641	304	1	[	[	X
ejpam-6641	304	2	20	20	NUM
ejpam-6641	304	3	]	]	X
ejpam-6641	304	4	r.l	r.l	PROPN
ejpam-6641	304	5	.	.	PROPN
ejpam-6641	304	6	frank	frank	PROPN
ejpam-6641	304	7	,	,	PUNCT
ejpam-6641	304	8	e.h	e.h	PROPN
ejpam-6641	304	9	.	.	PROPN
ejpam-6641	304	10	lieb	lieb	PROPN
ejpam-6641	304	11	,	,	PUNCT
ejpam-6641	304	12	and	and	CCONJ
ejpam-6641	304	13	seiringer	seiringer	NOUN
ejpam-6641	304	14	,	,	PUNCT
ejpam-6641	304	15	r.	r.	PROPN
ejpam-6641	304	16	hardy	hardy	ADV
ejpam-6641	304	17	–	–	PUNCT
ejpam-6641	304	18	lieb	lieb	PROPN
ejpam-6641	304	19	–	–	PUNCT
ejpam-6641	304	20	thirring	thirre	VERB
ejpam-6641	304	21	inequalities	inequality	NOUN
ejpam-6641	304	22	for	for	ADP
ejpam-6641	304	23	fractional	fractional	ADJ
ejpam-6641	304	24	schr”odinger	schr”odinger	PROPN
ejpam-6641	304	25	operators	operator	NOUN
ejpam-6641	304	26	,	,	PUNCT
ejpam-6641	304	27	j.	j.	PROPN
ejpam-6641	304	28	amer	amer	PROPN
ejpam-6641	304	29	.	.	PROPN
ejpam-6641	304	30	math	math	PROPN
ejpam-6641	304	31	.	.	PUNCT
ejpam-6641	305	1	soc	soc	PROPN
ejpam-6641	305	2	.	.	PUNCT
ejpam-6641	306	1	21(4)(2008	21(4)(2008	NUM
ejpam-6641	306	2	)	)	PUNCT
ejpam-6641	306	3	,	,	PUNCT
ejpam-6641	306	4	925–950	925–950	NUM
ejpam-6641	306	5	.	.	PUNCT
ejpam-6641	307	1	[	[	X
ejpam-6641	307	2	21	21	NUM
ejpam-6641	307	3	]	]	X
ejpam-6641	307	4	r.l	r.l	PROPN
ejpam-6641	307	5	.	.	PROPN
ejpam-6641	307	6	frank	frank	PROPN
ejpam-6641	307	7	,	,	PUNCT
ejpam-6641	307	8	a	a	DET
ejpam-6641	307	9	simple	simple	ADJ
ejpam-6641	307	10	proof	proof	NOUN
ejpam-6641	307	11	of	of	ADP
ejpam-6641	307	12	hardy	hardy	ADJ
ejpam-6641	307	13	-	-	PUNCT
ejpam-6641	307	14	lieb	lieb	NOUN
ejpam-6641	307	15	-	-	PUNCT
ejpam-6641	307	16	thirring	thirre	VERB
ejpam-6641	307	17	inequalities	inequality	NOUN
ejpam-6641	307	18	,	,	PUNCT
ejpam-6641	307	19	comm	comm	NOUN
ejpam-6641	307	20	.	.	PUNCT
ejpam-6641	307	21	math	math	NOUN
ejpam-6641	307	22	.	.	PUNCT
ejpam-6641	308	1	phys	phy	NOUN
ejpam-6641	308	2	.	.	PUNCT
ejpam-6641	309	1	290(2009	290(2009	NUM
ejpam-6641	309	2	)	)	PUNCT
ejpam-6641	309	3	,	,	PUNCT
ejpam-6641	310	1	789–800	789–800	NUM
ejpam-6641	310	2	.	.	PUNCT
ejpam-6641	311	1	[	[	X
ejpam-6641	311	2	22	22	NUM
ejpam-6641	311	3	]	]	X
ejpam-6641	311	4	r.l	r.l	PROPN
ejpam-6641	311	5	.	.	PROPN
ejpam-6641	311	6	frank	frank	PROPN
ejpam-6641	311	7	,	,	PUNCT
ejpam-6641	311	8	e.	e.	PROPN
ejpam-6641	311	9	lieb	lieb	PROPN
ejpam-6641	311	10	and	and	CCONJ
ejpam-6641	311	11	r.	r.	PROPN
ejpam-6641	311	12	seiringer	seiringer	PROPN
ejpam-6641	311	13	,	,	PUNCT
ejpam-6641	311	14	stability	stability	NOUN
ejpam-6641	311	15	of	of	ADP
ejpam-6641	311	16	relativistic	relativistic	ADJ
ejpam-6641	311	17	matter	matter	NOUN
ejpam-6641	311	18	with	with	ADP
ejpam-6641	311	19	magnetic	magnetic	ADJ
ejpam-6641	311	20	fields	field	NOUN
ejpam-6641	311	21	for	for	ADP
ejpam-6641	311	22	nuclear	nuclear	ADJ
ejpam-6641	311	23	charges	charge	NOUN
ejpam-6641	311	24	up	up	ADP
ejpam-6641	311	25	to	to	ADP
ejpam-6641	311	26	the	the	DET
ejpam-6641	311	27	critical	critical	ADJ
ejpam-6641	311	28	value	value	NOUN
ejpam-6641	311	29	,	,	PUNCT
ejpam-6641	311	30	comm	comm	NOUN
ejpam-6641	311	31	.	.	PUNCT
ejpam-6641	311	32	math	math	NOUN
ejpam-6641	311	33	.	.	PUNCT
ejpam-6641	312	1	phys	phy	NOUN
ejpam-6641	312	2	.	.	PUNCT
ejpam-6641	313	1	275(2)(2007	275(2)(2007	NUM
ejpam-6641	313	2	)	)	PUNCT
ejpam-6641	313	3	,	,	PUNCT
ejpam-6641	313	4	479–489	479–489	NUM
ejpam-6641	313	5	.	.	PUNCT
ejpam-6641	314	1	[	[	X
ejpam-6641	314	2	23	23	NUM
ejpam-6641	314	3	]	]	X
ejpam-6641	314	4	n.	n.	NOUN
ejpam-6641	314	5	ghoussoub	ghoussoub	PROPN
ejpam-6641	314	6	,	,	PUNCT
ejpam-6641	314	7	f.	f.	PROPN
ejpam-6641	314	8	robert	robert	PROPN
ejpam-6641	314	9	,	,	PUNCT
ejpam-6641	314	10	s.	s.	PROPN
ejpam-6641	314	11	shakerian	shakerian	PROPN
ejpam-6641	314	12	.	.	PUNCT
ejpam-6641	315	1	and	and	CCONJ
ejpam-6641	315	2	m.	m.	NOUN
ejpam-6641	315	3	zhao	zhao	PROPN
ejpam-6641	315	4	,	,	PUNCT
ejpam-6641	315	5	mass	mass	PROPN
ejpam-6641	315	6	and	and	CCONJ
ejpam-6641	315	7	asymptotics	asymptotic	NOUN
ejpam-6641	315	8	associated	associate	VERB
ejpam-6641	315	9	to	to	PART
ejpam-6641	315	10	fractional	fractional	VERB
ejpam-6641	315	11	hardy	hardy	ADJ
ejpam-6641	315	12	-	-	PUNCT
ejpam-6641	315	13	schr”odinger	schr”odinger	NOUN
ejpam-6641	315	14	operators	operator	NOUN
ejpam-6641	315	15	in	in	ADP
ejpam-6641	315	16	critical	critical	ADJ
ejpam-6641	315	17	regimes	regime	NOUN
ejpam-6641	315	18	,	,	PUNCT
ejpam-6641	315	19	comm	comm	NOUN
ejpam-6641	315	20	.	.	PUNCT
ejpam-6641	316	1	part	part	NOUN
ejpam-6641	316	2	.	.	PUNCT
ejpam-6641	317	1	diff	diff	PROPN
ejpam-6641	317	2	.	.	PUNCT
ejpam-6641	318	1	eq	eq	X
ejpam-6641	318	2	.	.	PROPN
ejpam-6641	318	3	43(6)(2018	43(6)(2018	NUM
ejpam-6641	318	4	)	)	PUNCT
ejpam-6641	318	5	,	,	PUNCT
ejpam-6641	318	6	859–892	859–892	NUM
ejpam-6641	318	7	.	.	PUNCT
ejpam-6641	319	1	[	[	X
ejpam-6641	319	2	24	24	NUM
ejpam-6641	319	3	]	]	PUNCT
ejpam-6641	319	4	k.	k.	PROPN
ejpam-6641	319	5	tzirakis	tzirakis	PROPN
ejpam-6641	319	6	,	,	PUNCT
ejpam-6641	319	7	sharp	sharp	ADJ
ejpam-6641	319	8	trace	trace	NOUN
ejpam-6641	319	9	hardy	hardy	ADJ
ejpam-6641	319	10	-	-	PUNCT
ejpam-6641	319	11	sobolev	sobolev	NOUN
ejpam-6641	319	12	inequalities	inequality	NOUN
ejpam-6641	319	13	and	and	CCONJ
ejpam-6641	319	14	fractional	fractional	ADJ
ejpam-6641	319	15	hardy	hardy	ADJ
ejpam-6641	319	16	-	-	PUNCT
ejpam-6641	319	17	sobolev	sobolev	NOUN
ejpam-6641	319	18	inequalities	inequality	NOUN
ejpam-6641	319	19	,	,	PUNCT
ejpam-6641	319	20	j.	j.	PROPN
ejpam-6641	319	21	funct	funct	PROPN
ejpam-6641	319	22	.	.	PUNCT
ejpam-6641	320	1	anal	anal	PROPN
ejpam-6641	320	2	.	.	PUNCT
ejpam-6641	321	1	270(2016	270(2016	NUM
ejpam-6641	321	2	)	)	PUNCT
ejpam-6641	321	3	,	,	PUNCT
ejpam-6641	322	1	4513–4539	4513–4539	NUM
ejpam-6641	322	2	.	.	PUNCT
ejpam-6641	323	1	[	[	X
ejpam-6641	323	2	25	25	NUM
ejpam-6641	323	3	]	]	PUNCT
ejpam-6641	323	4	b.	b.	PROPN
ejpam-6641	323	5	hasan	hasan	PROPN
ejpam-6641	323	6	,	,	PUNCT
ejpam-6641	323	7	and	and	CCONJ
ejpam-6641	323	8	s.	s.	PROPN
ejpam-6641	323	9	yalçın	yalçın	PROPN
ejpam-6641	323	10	,	,	PUNCT
ejpam-6641	323	11	convolution	convolution	NOUN
ejpam-6641	323	12	and	and	CCONJ
ejpam-6641	323	13	coefficient	coefficient	NOUN
ejpam-6641	323	14	estimates	estimate	NOUN
ejpam-6641	323	15	for	for	ADP
ejpam-6641	323	16	(	(	PUNCT
ejpam-6641	323	17	p	p	X
ejpam-6641	323	18	,	,	PUNCT
ejpam-6641	323	19	q)-convex	q)-convex	NOUN
ejpam-6641	323	20	harmonic	harmonic	ADJ
ejpam-6641	323	21	functions	function	NOUN
ejpam-6641	323	22	associated	associate	VERB
ejpam-6641	323	23	with	with	ADP
ejpam-6641	323	24	subordination	subordination	NOUN
ejpam-6641	323	25	,	,	PUNCT
ejpam-6641	323	26	journal	journal	NOUN
ejpam-6641	323	27	of	of	ADP
ejpam-6641	323	28	function	function	NOUN
ejpam-6641	323	29	spaces	space	NOUN
ejpam-6641	323	30	,	,	PUNCT
ejpam-6641	323	31	2022(1	2022(1	NUM
ejpam-6641	323	32	)	)	PUNCT
ejpam-6641	323	33	(	(	PUNCT
ejpam-6641	323	34	2022	2022	NUM
ejpam-6641	323	35	)	)	PUNCT
ejpam-6641	323	36	,	,	PUNCT
ejpam-6641	323	37	5317797	5317797	NUM
ejpam-6641	323	38	.	.	PUNCT
ejpam-6641	324	1	[	[	X
ejpam-6641	324	2	26	26	NUM
ejpam-6641	324	3	]	]	X
ejpam-6641	324	4	b.	b.	PROPN
ejpam-6641	324	5	hasan	hasan	PROPN
ejpam-6641	324	6	,	,	PUNCT
ejpam-6641	324	7	q	q	NOUN
ejpam-6641	324	8	-	-	PUNCT
ejpam-6641	324	9	analogue	analogue	NOUN
ejpam-6641	324	10	of	of	ADP
ejpam-6641	324	11	a	a	DET
ejpam-6641	324	12	new	new	ADJ
ejpam-6641	324	13	subclass	subclass	NOUN
ejpam-6641	324	14	of	of	ADP
ejpam-6641	324	15	harmonic	harmonic	ADJ
ejpam-6641	324	16	univalent	univalent	ADJ
ejpam-6641	324	17	functions	function	NOUN
ejpam-6641	324	18	associated	associate	VERB
ejpam-6641	324	19	with	with	ADP
ejpam-6641	324	20	subordination	subordination	NOUN
ejpam-6641	324	21	,	,	PUNCT
ejpam-6641	324	22	symmetry	symmetry	NOUN
ejpam-6641	324	23	,	,	PUNCT
ejpam-6641	324	24	14(4	14(4	NUM
ejpam-6641	324	25	)	)	PUNCT
ejpam-6641	324	26	(	(	PUNCT
ejpam-6641	324	27	2022	2022	NUM
ejpam-6641	324	28	)	)	PUNCT
ejpam-6641	324	29	,	,	PUNCT
ejpam-6641	324	30	708	708	NUM
ejpam-6641	324	31	.	.	PUNCT
ejpam-6641	325	1	[	[	X
ejpam-6641	325	2	27	27	NUM
ejpam-6641	325	3	]	]	PUNCT
ejpam-6641	325	4	m.	m.	NOUN
ejpam-6641	325	5	izuki	izuki	PROPN
ejpam-6641	325	6	and	and	CCONJ
ejpam-6641	325	7	t.	t.	PROPN
ejpam-6641	325	8	noi	noi	PROPN
ejpam-6641	325	9	,	,	PUNCT
ejpam-6641	325	10	an	an	DET
ejpam-6641	325	11	intrinsic	intrinsic	ADJ
ejpam-6641	325	12	square	square	ADJ
ejpam-6641	325	13	function	function	NOUN
ejpam-6641	325	14	on	on	ADP
ejpam-6641	325	15	weighted	weight	VERB
ejpam-6641	325	16	herz	herz	PROPN
ejpam-6641	325	17	spaces	space	NOUN
ejpam-6641	325	18	with	with	ADP
ejpam-6641	325	19	variable	variable	ADJ
ejpam-6641	325	20	exponents	exponent	NOUN
ejpam-6641	325	21	,	,	PUNCT
ejpam-6641	325	22	j.	j.	PROPN
ejpam-6641	325	23	math	math	PROPN
ejpam-6641	325	24	.	.	PUNCT
ejpam-6641	326	1	inequal	inequal	ADJ
ejpam-6641	326	2	.	.	PUNCT
ejpam-6641	327	1	11(3	11(3	NUM
ejpam-6641	327	2	)	)	PUNCT
ejpam-6641	327	3	(	(	PUNCT
ejpam-6641	327	4	2017	2017	NUM
ejpam-6641	327	5	)	)	PUNCT
ejpam-6641	327	6	,	,	PUNCT
ejpam-6641	327	7	799	799	NUM
ejpam-6641	327	8	-	-	SYM
ejpam-6641	327	9	816	816	NUM
ejpam-6641	327	10	.	.	PUNCT
ejpam-6641	328	1	[	[	X
ejpam-6641	328	2	28	28	NUM
ejpam-6641	328	3	]	]	X
ejpam-6641	328	4	b.	b.	PROPN
ejpam-6641	328	5	sultan	sultan	PROPN
ejpam-6641	328	6	,	,	PUNCT
ejpam-6641	328	7	atomic	atomic	ADJ
ejpam-6641	328	8	decomposition	decomposition	NOUN
ejpam-6641	328	9	of	of	ADP
ejpam-6641	328	10	anisotropic	anisotropic	NOUN
ejpam-6641	328	11	grand	grand	ADJ
ejpam-6641	328	12	variable	variable	NOUN
ejpam-6641	328	13	weighted	weight	VERB
ejpam-6641	328	14	herz	herz	PROPN
ejpam-6641	328	15	spaces	space	NOUN
ejpam-6641	328	16	and	and	CCONJ
ejpam-6641	328	17	applications	application	NOUN
ejpam-6641	328	18	.	.	PUNCT
ejpam-6641	329	1	j.	j.	PROPN
ejpam-6641	329	2	pseudo	pseudo	PROPN
ejpam-6641	329	3	-	-	PUNCT
ejpam-6641	329	4	differ	differ	VERB
ejpam-6641	329	5	.	.	PUNCT
ejpam-6641	330	1	oper	oper	PROPN
ejpam-6641	330	2	.	.	PUNCT
ejpam-6641	330	3	appl	appl	PROPN
ejpam-6641	330	4	.	.	PROPN
ejpam-6641	331	1	16	16	NUM
ejpam-6641	331	2	,	,	PUNCT
ejpam-6641	331	3	53	53	NUM
ejpam-6641	331	4	(	(	PUNCT
ejpam-6641	331	5	2025	2025	NUM
ejpam-6641	331	6	)	)	PUNCT
ejpam-6641	331	7	.	.	PUNCT
ejpam-6641	332	1	[	[	X
ejpam-6641	332	2	29	29	NUM
ejpam-6641	332	3	]	]	PUNCT
ejpam-6641	332	4	b.	b.	PROPN
ejpam-6641	332	5	sultan	sultan	PROPN
ejpam-6641	332	6	,	,	PUNCT
ejpam-6641	332	7	f.	f.	PROPN
ejpam-6641	332	8	azmi	azmi	PROPN
ejpam-6641	332	9	,	,	PUNCT
ejpam-6641	332	10	m.	m.	NOUN
ejpam-6641	332	11	sultan	sultan	PROPN
ejpam-6641	332	12	,	,	PUNCT
ejpam-6641	332	13	m.	m.	PROPN
ejpam-6641	332	14	mehmood	mehmood	PROPN
ejpam-6641	332	15	,	,	PUNCT
ejpam-6641	332	16	n.	n.	PROPN
ejpam-6641	332	17	mlaiki	mlaiki	PROPN
ejpam-6641	332	18	,	,	PUNCT
ejpam-6641	332	19	boundedness	boundedness	NOUN
ejpam-6641	332	20	of	of	ADP
ejpam-6641	332	21	riesz	riesz	PROPN
ejpam-6641	332	22	potential	potential	ADJ
ejpam-6641	332	23	operator	operator	NOUN
ejpam-6641	332	24	on	on	ADP
ejpam-6641	332	25	grand	grand	ADJ
ejpam-6641	332	26	herz	herz	PROPN
ejpam-6641	332	27	-	-	PUNCT
ejpam-6641	332	28	morrey	morrey	PROPN
ejpam-6641	332	29	spaces	space	NOUN
ejpam-6641	332	30	,	,	PUNCT
ejpam-6641	332	31	axioms	axiom	NOUN
ejpam-6641	332	32	.	.	PUNCT
ejpam-6641	333	1	11(11	11(11	NUM
ejpam-6641	333	2	)	)	PUNCT
ejpam-6641	333	3	,	,	PUNCT
ejpam-6641	333	4	2022	2022	NUM
ejpam-6641	333	5	,	,	PUNCT
ejpam-6641	333	6	583	583	NUM
ejpam-6641	333	7	.	.	PUNCT
ejpam-6641	334	1	[	[	X
ejpam-6641	334	2	30	30	NUM
ejpam-6641	334	3	]	]	X
ejpam-6641	334	4	b.	b.	PROPN
ejpam-6641	334	5	sultan	sultan	PROPN
ejpam-6641	334	6	,	,	PUNCT
ejpam-6641	334	7	m.	m.	NOUN
ejpam-6641	334	8	sultan	sultan	PROPN
ejpam-6641	334	9	,	,	PUNCT
ejpam-6641	334	10	m.	m.	PROPN
ejpam-6641	334	11	mehmood	mehmood	PROPN
ejpam-6641	334	12	,	,	PUNCT
ejpam-6641	334	13	f.	f.	PROPN
ejpam-6641	334	14	azmi	azmi	PROPN
ejpam-6641	334	15	,	,	PUNCT
ejpam-6641	334	16	m.a	m.a	PROPN
ejpam-6641	334	17	.	.	PROPN
ejpam-6641	334	18	alghafli	alghafli	PROPN
ejpam-6641	334	19	,	,	PUNCT
ejpam-6641	334	20	n.	n.	PROPN
ejpam-6641	334	21	mlaiki	mlaiki	PROPN
ejpam-6641	334	22	.	.	PUNCT
ejpam-6641	335	1	boundedness	boundedness	PROPN
ejpam-6641	335	2	of	of	ADP
ejpam-6641	335	3	fractional	fractional	ADJ
ejpam-6641	335	4	integrals	integral	NOUN
ejpam-6641	335	5	on	on	ADP
ejpam-6641	335	6	grand	grand	ADJ
ejpam-6641	335	7	weighted	weight	VERB
ejpam-6641	335	8	herz	herz	PROPN
ejpam-6641	335	9	spaces	space	NOUN
ejpam-6641	335	10	with	with	ADP
ejpam-6641	335	11	variable	variable	ADJ
ejpam-6641	335	12	exponent	exponent	NOUN
ejpam-6641	335	13	,	,	PUNCT
ejpam-6641	335	14	aims	aim	VERB
ejpam-6641	335	15	math	math	NOUN
ejpam-6641	335	16	.	.	PUNCT
ejpam-6641	336	1	8(1	8(1	NOUN
ejpam-6641	336	2	)	)	PUNCT
ejpam-6641	336	3	,	,	PUNCT
ejpam-6641	336	4	(	(	PUNCT
ejpam-6641	336	5	2023	2023	NUM
ejpam-6641	336	6	)	)	PUNCT
ejpam-6641	336	7	,	,	PUNCT
ejpam-6641	336	8	752	752	NUM
ejpam-6641	336	9	-	-	SYM
ejpam-6641	336	10	764	764	NUM
ejpam-6641	336	11	.	.	PUNCT
ejpam-6641	337	1	doi	doi	NOUN
ejpam-6641	337	2	:	:	PUNCT
ejpam-6641	337	3	10.3934	10.3934	NUM
ejpam-6641	337	4	/	/	SYM
ejpam-6641	337	5	math.2023036	math.2023036	NOUN
ejpam-6641	337	6	.	.	PUNCT
ejpam-6641	338	1	[	[	X
ejpam-6641	338	2	31	31	NUM
ejpam-6641	338	3	]	]	PUNCT
ejpam-6641	338	4	b.	b.	PROPN
ejpam-6641	338	5	sultan	sultan	PROPN
ejpam-6641	338	6	,	,	PUNCT
ejpam-6641	338	7	f.	f.	PROPN
ejpam-6641	338	8	azmi	azmi	PROPN
ejpam-6641	338	9	,	,	PUNCT
ejpam-6641	338	10	m.	m.	NOUN
ejpam-6641	338	11	sultan	sultan	PROPN
ejpam-6641	338	12	,	,	PUNCT
ejpam-6641	338	13	t.	t.	PROPN
ejpam-6641	338	14	mahmood	mahmood	PROPN
ejpam-6641	338	15	,	,	PUNCT
ejpam-6641	338	16	n.	n.	PROPN
ejpam-6641	338	17	mlaiki	mlaiki	PROPN
ejpam-6641	338	18	,	,	PUNCT
ejpam-6641	338	19	n.	n.	NOUN
ejpam-6641	338	20	souayah	souayah	NOUN
ejpam-6641	338	21	.	.	PUNCT
ejpam-6641	339	1	boundedness	boundedness	NOUN
ejpam-6641	339	2	of	of	ADP
ejpam-6641	339	3	fractional	fractional	ADJ
ejpam-6641	339	4	integrals	integral	NOUN
ejpam-6641	339	5	on	on	ADP
ejpam-6641	339	6	grand	grand	ADJ
ejpam-6641	339	7	weighted	weight	VERB
ejpam-6641	339	8	herzmorrey	herzmorrey	NOUN
ejpam-6641	339	9	spaces	space	NOUN
ejpam-6641	339	10	with	with	ADP
ejpam-6641	339	11	variable	variable	ADJ
ejpam-6641	339	12	exponent	exponent	NOUN
ejpam-6641	339	13	.	.	PUNCT
ejpam-6641	340	1	frac	frac	PROPN
ejpam-6641	340	2	.	.	PUNCT
ejpam-6641	340	3	fract	fract	PROPN
ejpam-6641	340	4	.	.	PUNCT
ejpam-6641	341	1	6(11	6(11	NUM
ejpam-6641	341	2	)	)	PUNCT
ejpam-6641	341	3	,	,	PUNCT
ejpam-6641	341	4	(	(	PUNCT
ejpam-6641	341	5	2022	2022	NUM
ejpam-6641	341	6	)	)	PUNCT
ejpam-6641	341	7	,	,	PUNCT
ejpam-6641	341	8	660	660	NUM
ejpam-6641	341	9	-	-	SYM
ejpam-6641	341	10	670	670	NUM
ejpam-6641	341	11	.	.	PUNCT
ejpam-6641	342	1	https://doi.org/10.3390/fractalfract6110660	https://doi.org/10.3390/fractalfract6110660	PROPN
ejpam-6641	343	1	[	[	X
ejpam-6641	343	2	32	32	NUM
ejpam-6641	343	3	]	]	PUNCT
ejpam-6641	343	4	b.	b.	PROPN
ejpam-6641	343	5	sultan	sultan	PROPN
ejpam-6641	343	6	,	,	PUNCT
ejpam-6641	343	7	m.	m.	NOUN
ejpam-6641	343	8	sultan	sultan	PROPN
ejpam-6641	343	9	,	,	PUNCT
ejpam-6641	343	10	q.	q.	PROPN
ejpam-6641	343	11	q.	q.	PROPN
ejpam-6641	343	12	zhang	zhang	PROPN
ejpam-6641	343	13	,	,	PUNCT
ejpam-6641	343	14	n.	n.	PROPN
ejpam-6641	343	15	mlaiki	mlaiki	PROPN
ejpam-6641	343	16	,	,	PUNCT
ejpam-6641	343	17	boundedness	boundedness	NOUN
ejpam-6641	343	18	of	of	ADP
ejpam-6641	343	19	hardy	hardy	ADJ
ejpam-6641	343	20	operators	operator	NOUN
ejpam-6641	343	21	on	on	ADP
ejpam-6641	343	22	grand	grand	ADJ
ejpam-6641	343	23	variable	variable	NOUN
ejpam-6641	343	24	weighted	weight	VERB
ejpam-6641	343	25	herz	herz	PROPN
ejpam-6641	343	26	spaces	space	NOUN
ejpam-6641	343	27	,	,	PUNCT
ejpam-6641	343	28	aims	aim	VERB
ejpam-6641	343	29	math	math	NOUN
ejpam-6641	343	30	.	.	PUNCT
ejpam-6641	344	1	8(10	8(10	NUM
ejpam-6641	344	2	)	)	PUNCT
ejpam-6641	344	3	(	(	PUNCT
ejpam-6641	344	4	2023	2023	NUM
ejpam-6641	344	5	)	)	PUNCT
ejpam-6641	344	6	,	,	PUNCT
ejpam-6641	344	7	24515–24527	24515–24527	NUM
ejpam-6641	344	8	.	.	PUNCT
ejpam-6641	345	1	[	[	X
ejpam-6641	345	2	33	33	NUM
ejpam-6641	345	3	]	]	PUNCT
ejpam-6641	345	4	b.	b.	PROPN
ejpam-6641	345	5	sultan	sultan	PROPN
ejpam-6641	345	6	,	,	PUNCT
ejpam-6641	345	7	m.	m.	NOUN
ejpam-6641	345	8	sultan	sultan	PROPN
ejpam-6641	345	9	,	,	PUNCT
ejpam-6641	345	10	boundedness	boundedness	NOUN
ejpam-6641	345	11	of	of	ADP
ejpam-6641	345	12	commutators	commutator	NOUN
ejpam-6641	345	13	of	of	ADP
ejpam-6641	345	14	rough	rough	ADJ
ejpam-6641	345	15	hardy	hardy	ADJ
ejpam-6641	345	16	operators	operator	NOUN
ejpam-6641	345	17	on	on	ADP
ejpam-6641	345	18	grand	grand	ADJ
ejpam-6641	345	19	variable	variable	ADJ
ejpam-6641	345	20	herz	herz	PROPN
ejpam-6641	345	21	spaces	space	NOUN
ejpam-6641	345	22	,	,	PUNCT
ejpam-6641	345	23	forum	forum	PROPN
ejpam-6641	345	24	math	math	NOUN
ejpam-6641	345	25	.	.	PUNCT
ejpam-6641	346	1	(	(	PUNCT
ejpam-6641	346	2	2023	2023	NUM
ejpam-6641	346	3	)	)	PUNCT
ejpam-6641	346	4	,	,	PUNCT
ejpam-6641	346	5	https://doi	https://doi	PROPN
ejpam-6641	346	6	.org	.org	PUNCT
ejpam-6641	346	7	/10	/10	PUNCT
ejpam-6641	347	1	.1515	.1515	PROPN
ejpam-6641	347	2	/forum	/forum	PROPN
ejpam-6641	347	3	-2023	-2023	PROPN
ejpam-6641	347	4	-0152	-0152	PROPN
ejpam-6641	347	5	.	.	PUNCT
ejpam-6641	348	1	[	[	X
ejpam-6641	348	2	34	34	NUM
ejpam-6641	348	3	]	]	PUNCT
ejpam-6641	348	4	b.	b.	PROPN
ejpam-6641	348	5	sultan	sultan	PROPN
ejpam-6641	348	6	,	,	PUNCT
ejpam-6641	348	7	m.	m.	NOUN
ejpam-6641	348	8	sultan	sultan	PROPN
ejpam-6641	348	9	,	,	PUNCT
ejpam-6641	348	10	i.	i.	PROPN
ejpam-6641	348	11	khan	khan	PROPN
ejpam-6641	348	12	,	,	PUNCT
ejpam-6641	348	13	on	on	ADP
ejpam-6641	348	14	sobolev	sobolev	NOUN
ejpam-6641	348	15	theorem	theorem	NOUN
ejpam-6641	348	16	for	for	ADP
ejpam-6641	348	17	higher	high	ADJ
ejpam-6641	348	18	commutators	commutator	NOUN
ejpam-6641	348	19	of	of	ADP
ejpam-6641	348	20	fractional	fractional	ADJ
ejpam-6641	348	21	integrals	integral	NOUN
ejpam-6641	348	22	in	in	ADP
ejpam-6641	348	23	grand	grand	ADJ
ejpam-6641	348	24	variable	variable	ADJ
ejpam-6641	348	25	herz	herz	PROPN
ejpam-6641	348	26	spaces	space	NOUN
ejpam-6641	348	27	,	,	PUNCT
ejpam-6641	348	28	commun	commun	PROPN
ejpam-6641	348	29	.	.	PUNCT
ejpam-6641	349	1	nonlinear	nonlinear	PROPN
ejpam-6641	349	2	sci	sci	PROPN
ejpam-6641	349	3	.	.	PUNCT
ejpam-6641	349	4	numer	numer	PROPN
ejpam-6641	349	5	.	.	PUNCT
ejpam-6641	350	1	simul	simul	PROPN
ejpam-6641	350	2	.	.	PUNCT
ejpam-6641	351	1	126	126	NUM
ejpam-6641	351	2	(	(	PUNCT
ejpam-6641	351	3	2023	2023	NUM
ejpam-6641	351	4	)	)	PUNCT
ejpam-6641	351	5	.	.	PUNCT
ejpam-6641	352	1	g.	g.	PROPN
ejpam-6641	352	2	a.	a.	PROPN
ejpam-6641	352	3	basendwah	basendwah	PROPN
ejpam-6641	352	4	et	et	PROPN
ejpam-6641	352	5	al	al	PROPN
ejpam-6641	352	6	.	.	PUNCT
ejpam-6641	352	7	/	/	SYM
ejpam-6641	352	8	eur	eur	PROPN
ejpam-6641	352	9	.	.	PUNCT
ejpam-6641	353	1	j.	j.	PROPN
ejpam-6641	353	2	pure	pure	PROPN
ejpam-6641	353	3	appl	appl	PROPN
ejpam-6641	353	4	.	.	PROPN
ejpam-6641	353	5	math	math	PROPN
ejpam-6641	353	6	,	,	PUNCT
ejpam-6641	353	7	18	18	NUM
ejpam-6641	353	8	(	(	PUNCT
ejpam-6641	353	9	4	4	NUM
ejpam-6641	353	10	)	)	PUNCT
ejpam-6641	353	11	(	(	PUNCT
ejpam-6641	353	12	2025	2025	NUM
ejpam-6641	353	13	)	)	PUNCT
ejpam-6641	353	14	,	,	PUNCT
ejpam-6641	353	15	6641	6641	NUM
ejpam-6641	353	16	16	16	NUM
ejpam-6641	353	17	of	of	ADP
ejpam-6641	353	18	16	16	NUM
ejpam-6641	353	19	[	[	X
ejpam-6641	353	20	35	35	NUM
ejpam-6641	353	21	]	]	PUNCT
ejpam-6641	353	22	m.	m.	NOUN
ejpam-6641	353	23	sultan	sultan	PROPN
ejpam-6641	353	24	,	,	PUNCT
ejpam-6641	353	25	b.	b.	PROPN
ejpam-6641	353	26	sultan	sultan	PROPN
ejpam-6641	353	27	,	,	PUNCT
ejpam-6641	353	28	a.	a.	PROPN
ejpam-6641	353	29	khan	khan	PROPN
ejpam-6641	353	30	,	,	PUNCT
ejpam-6641	353	31	t.	t.	PROPN
ejpam-6641	353	32	abdeljawad	abdeljawad	PROPN
ejpam-6641	353	33	,	,	PUNCT
ejpam-6641	353	34	boundedness	boundedness	NOUN
ejpam-6641	353	35	of	of	ADP
ejpam-6641	353	36	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6641	353	37	integral	integral	ADJ
ejpam-6641	353	38	operator	operator	NOUN
ejpam-6641	353	39	of	of	ADP
ejpam-6641	353	40	variable	variable	ADJ
ejpam-6641	353	41	order	order	NOUN
ejpam-6641	353	42	in	in	ADP
ejpam-6641	353	43	grand	grand	ADJ
ejpam-6641	353	44	herz	herz	PROPN
ejpam-6641	353	45	-	-	PUNCT
ejpam-6641	353	46	morrey	morrey	PROPN
ejpam-6641	353	47	spaces	space	NOUN
ejpam-6641	353	48	,	,	PUNCT
ejpam-6641	353	49	aims	aim	VERB
ejpam-6641	353	50	math	math	NOUN
ejpam-6641	353	51	.	.	PUNCT
ejpam-6641	353	52	,	,	PUNCT
ejpam-6641	353	53	8(9	8(9	NUM
ejpam-6641	353	54	)	)	PUNCT
ejpam-6641	353	55	(	(	PUNCT
ejpam-6641	353	56	2023	2023	NUM
ejpam-6641	353	57	)	)	PUNCT
ejpam-6641	353	58	,	,	PUNCT
ejpam-6641	353	59	22338–22353	22338–22353	NUM
ejpam-6641	353	60	.	.	PUNCT
ejpam-6641	354	1	[	[	X
ejpam-6641	354	2	36	36	NUM
ejpam-6641	354	3	]	]	PUNCT
ejpam-6641	354	4	b.	b.	PROPN
ejpam-6641	354	5	sultan	sultan	PROPN
ejpam-6641	354	6	,	,	PUNCT
ejpam-6641	354	7	m.	m.	NOUN
ejpam-6641	354	8	sultan	sultan	PROPN
ejpam-6641	354	9	,	,	PUNCT
ejpam-6641	354	10	boundedness	boundedness	NOUN
ejpam-6641	354	11	of	of	ADP
ejpam-6641	354	12	higher	high	ADJ
ejpam-6641	354	13	order	order	NOUN
ejpam-6641	354	14	commutators	commutator	NOUN
ejpam-6641	354	15	of	of	ADP
ejpam-6641	354	16	hardy	hardy	ADJ
ejpam-6641	354	17	operators	operator	NOUN
ejpam-6641	354	18	on	on	ADP
ejpam-6641	354	19	grand	grand	ADJ
ejpam-6641	354	20	herz	herz	PROPN
ejpam-6641	354	21	-	-	PUNCT
ejpam-6641	354	22	morrey	morrey	PROPN
ejpam-6641	354	23	spaces	space	NOUN
ejpam-6641	354	24	,	,	PUNCT
ejpam-6641	354	25	bull	bull	NOUN
ejpam-6641	354	26	.	.	PUNCT
ejpam-6641	355	1	sci	sci	PROPN
ejpam-6641	355	2	.	.	PUNCT
ejpam-6641	355	3	math	math	PROPN
ejpam-6641	355	4	.	.	PUNCT
ejpam-6641	355	5	,	,	PUNCT
ejpam-6641	355	6	190	190	NUM
ejpam-6641	355	7	(	(	PUNCT
ejpam-6641	355	8	2024	2024	NUM
ejpam-6641	355	9	)	)	PUNCT
ejpam-6641	355	10	.	.	PUNCT
ejpam-6641	356	1	[	[	X
ejpam-6641	356	2	37	37	NUM
ejpam-6641	356	3	]	]	PUNCT
ejpam-6641	356	4	m.	m.	NOUN
ejpam-6641	356	5	sultan	sultan	PROPN
ejpam-6641	356	6	,	,	PUNCT
ejpam-6641	356	7	b.	b.	PROPN
ejpam-6641	356	8	sultan	sultan	PROPN
ejpam-6641	356	9	,	,	PUNCT
ejpam-6641	356	10	boundedness	boundedness	NOUN
ejpam-6641	356	11	of	of	ADP
ejpam-6641	356	12	sublinear	sublinear	NOUN
ejpam-6641	356	13	operators	operator	NOUN
ejpam-6641	356	14	on	on	ADP
ejpam-6641	356	15	grand	grand	ADJ
ejpam-6641	356	16	central	central	ADJ
ejpam-6641	356	17	orliczmorrey	orliczmorrey	NOUN
ejpam-6641	356	18	spaces	space	NOUN
ejpam-6641	356	19	,	,	PUNCT
ejpam-6641	356	20	bull	bull	NOUN
ejpam-6641	356	21	.	.	PUNCT
ejpam-6641	357	1	sci.math	sci.math	PROPN
ejpam-6641	357	2	.	.	PROPN
ejpam-6641	358	1	205	205	NUM
ejpam-6641	358	2	(	(	PUNCT
ejpam-6641	358	3	2025	2025	NUM
ejpam-6641	358	4	)	)	PUNCT
ejpam-6641	358	5	,	,	PUNCT
ejpam-6641	358	6	103704	103704	NUM
ejpam-6641	358	7	[	[	X
ejpam-6641	358	8	38	38	NUM
ejpam-6641	358	9	]	]	PUNCT
ejpam-6641	358	10	m.	m.	NOUN
ejpam-6641	358	11	sultan	sultan	PROPN
ejpam-6641	358	12	,	,	PUNCT
ejpam-6641	358	13	b.	b.	PROPN
ejpam-6641	358	14	sultan	sultan	PROPN
ejpam-6641	358	15	,	,	PUNCT
ejpam-6641	358	16	λ	λ	ADJ
ejpam-6641	358	17	-	-	ADJ
ejpam-6641	358	18	central	central	ADJ
ejpam-6641	358	19	musielak	musielak	NOUN
ejpam-6641	358	20	–	–	PUNCT
ejpam-6641	358	21	orlicz	orlicz	NUM
ejpam-6641	358	22	–	–	PUNCT
ejpam-6641	358	23	morrey	morrey	NOUN
ejpam-6641	358	24	spaces	space	NOUN
ejpam-6641	358	25	,	,	PUNCT
ejpam-6641	358	26	arab	arab	PROPN
ejpam-6641	358	27	.	.	PUNCT
ejpam-6641	359	1	j.	j.	PROPN
ejpam-6641	359	2	math	math	PROPN
ejpam-6641	359	3	.	.	PUNCT
ejpam-6641	360	1	14	14	NUM
ejpam-6641	360	2	(	(	PUNCT
ejpam-6641	360	3	2025	2025	NUM
ejpam-6641	360	4	)	)	PUNCT
ejpam-6641	360	5	,	,	PUNCT
ejpam-6641	361	1	357–363	357–363	NUM
ejpam-6641	361	2	.	.	PUNCT
ejpam-6641	362	1	[	[	X
ejpam-6641	362	2	39	39	NUM
ejpam-6641	362	3	]	]	PUNCT
ejpam-6641	362	4	b.	b.	PROPN
ejpam-6641	362	5	sultan	sultan	PROPN
ejpam-6641	362	6	,	,	PUNCT
ejpam-6641	362	7	m.	m.	NOUN
ejpam-6641	362	8	sultan	sultan	PROPN
ejpam-6641	362	9	,	,	PUNCT
ejpam-6641	362	10	a.	a.	NOUN
ejpam-6641	362	11	hussain	hussain	PROPN
ejpam-6641	362	12	,	,	PUNCT
ejpam-6641	362	13	boundedness	boundedness	NOUN
ejpam-6641	362	14	of	of	ADP
ejpam-6641	362	15	the	the	DET
ejpam-6641	362	16	bochner	bochner	NOUN
ejpam-6641	362	17	–	–	PUNCT
ejpam-6641	362	18	riesz	riesz	NOUN
ejpam-6641	362	19	operators	operator	NOUN
ejpam-6641	362	20	on	on	ADP
ejpam-6641	362	21	the	the	DET
ejpam-6641	362	22	weighted	weight	VERB
ejpam-6641	362	23	herz	herz	PROPN
ejpam-6641	362	24	–	–	PUNCT
ejpam-6641	362	25	morrey	morrey	PROPN
ejpam-6641	362	26	type	type	NOUN
ejpam-6641	362	27	hardy	hardy	ADJ
ejpam-6641	362	28	spaces	space	NOUN
ejpam-6641	362	29	,	,	PUNCT
ejpam-6641	362	30	complex	complex	ADJ
ejpam-6641	362	31	anal	anal	NOUN
ejpam-6641	362	32	.	.	PUNCT
ejpam-6641	363	1	oper	oper	PROPN
ejpam-6641	363	2	.	.	PUNCT
ejpam-6641	363	3	theory	theory	NOUN
ejpam-6641	363	4	.	.	PUNCT
ejpam-6641	364	1	19	19	NUM
ejpam-6641	364	2	(	(	PUNCT
ejpam-6641	364	3	49	49	NUM
ejpam-6641	364	4	)	)	PUNCT
ejpam-6641	364	5	(	(	PUNCT
ejpam-6641	364	6	2025	2025	NUM
ejpam-6641	364	7	)	)	PUNCT
ejpam-6641	364	8	.	.	PUNCT
ejpam-6641	365	1	[	[	X
ejpam-6641	365	2	40	40	NUM
ejpam-6641	365	3	]	]	PUNCT
ejpam-6641	365	4	b.	b.	PROPN
ejpam-6641	365	5	sultan	sultan	PROPN
ejpam-6641	365	6	,	,	PUNCT
ejpam-6641	365	7	a.	a.	NOUN
ejpam-6641	365	8	hussain	hussain	PROPN
ejpam-6641	365	9	,	,	PUNCT
ejpam-6641	365	10	m.	m.	NOUN
ejpam-6641	365	11	sultan	sultan	PROPN
ejpam-6641	365	12	,	,	PUNCT
ejpam-6641	365	13	chracterization	chracterization	NOUN
ejpam-6641	365	14	of	of	ADP
ejpam-6641	365	15	generalized	generalized	ADJ
ejpam-6641	365	16	campanato	campanato	NOUN
ejpam-6641	365	17	spaces	space	NOUN
ejpam-6641	365	18	with	with	ADP
ejpam-6641	365	19	variable	variable	ADJ
ejpam-6641	365	20	exponents	exponent	NOUN
ejpam-6641	365	21	via	via	ADP
ejpam-6641	365	22	fractional	fractional	ADJ
ejpam-6641	365	23	integrals	integral	NOUN
ejpam-6641	365	24	,	,	PUNCT
ejpam-6641	365	25	j.	j.	PROPN
ejpam-6641	365	26	pseudo	pseudo	NOUN
ejpam-6641	365	27	-	-	PUNCT
ejpam-6641	365	28	differ	differ	VERB
ejpam-6641	365	29	.	.	PUNCT
ejpam-6641	366	1	oper	oper	PROPN
ejpam-6641	366	2	.	.	PUNCT
ejpam-6641	366	3	appl	appl	PROPN
ejpam-6641	366	4	.	.	PUNCT
ejpam-6641	367	1	16	16	NUM
ejpam-6641	367	2	(	(	PUNCT
ejpam-6641	367	3	22	22	NUM
ejpam-6641	367	4	)	)	PUNCT
ejpam-6641	367	5	(	(	PUNCT
ejpam-6641	367	6	2025	2025	NUM
ejpam-6641	367	7	)	)	PUNCT
ejpam-6641	367	8	.	.	PUNCT
ejpam-6641	368	1	[	[	X
ejpam-6641	368	2	41	41	NUM
ejpam-6641	368	3	]	]	PUNCT
ejpam-6641	368	4	b.	b.	PROPN
ejpam-6641	368	5	sultan	sultan	PROPN
ejpam-6641	368	6	,	,	PUNCT
ejpam-6641	368	7	m.	m.	NOUN
ejpam-6641	368	8	sultan	sultan	PROPN
ejpam-6641	368	9	,	,	PUNCT
ejpam-6641	368	10	a.	a.	PROPN
ejpam-6641	368	11	khan	khan	PROPN
ejpam-6641	368	12	,	,	PUNCT
ejpam-6641	368	13	t.	t.	PROPN
ejpam-6641	368	14	abdeljawad	abdeljawad	PROPN
ejpam-6641	368	15	,	,	PUNCT
ejpam-6641	368	16	boundedness	boundedness	NOUN
ejpam-6641	368	17	of	of	ADP
ejpam-6641	368	18	commutators	commutator	NOUN
ejpam-6641	368	19	of	of	ADP
ejpam-6641	368	20	variable	variable	ADJ
ejpam-6641	368	21	marcinkiewicz	marcinkiewicz	ADJ
ejpam-6641	368	22	fractional	fractional	ADJ
ejpam-6641	368	23	integral	integral	ADJ
ejpam-6641	368	24	operator	operator	NOUN
ejpam-6641	368	25	in	in	ADP
ejpam-6641	368	26	grand	grand	ADJ
ejpam-6641	368	27	variable	variable	ADJ
ejpam-6641	368	28	herz	herz	PROPN
ejpam-6641	368	29	spaces	space	NOUN
ejpam-6641	368	30	,	,	PUNCT
ejpam-6641	368	31	j.	j.	PROPN
ejpam-6641	368	32	inequal	inequal	PROPN
ejpam-6641	368	33	.	.	PUNCT
ejpam-6641	369	1	appl	appl	PROPN
ejpam-6641	369	2	.	.	PUNCT
ejpam-6641	370	1	2024	2024	NUM
ejpam-6641	370	2	(	(	PUNCT
ejpam-6641	370	3	2024	2024	NUM
ejpam-6641	370	4	)	)	PUNCT
ejpam-6641	370	5	,	,	PUNCT
ejpam-6641	370	6	93	93	NUM
ejpam-6641	370	7	.	.	PUNCT
ejpam-6641	371	1	[	[	X
ejpam-6641	371	2	42	42	NUM
ejpam-6641	371	3	]	]	PUNCT
ejpam-6641	371	4	b.	b.	PROPN
ejpam-6641	371	5	sultan	sultan	PROPN
ejpam-6641	371	6	,	,	PUNCT
ejpam-6641	371	7	m.	m.	NOUN
ejpam-6641	371	8	sultan	sultan	PROPN
ejpam-6641	371	9	,	,	PUNCT
ejpam-6641	371	10	sobolev	sobolev	NOUN
ejpam-6641	371	11	-	-	PUNCT
ejpam-6641	371	12	type	type	NOUN
ejpam-6641	371	13	theorem	theorem	NOUN
ejpam-6641	371	14	for	for	ADP
ejpam-6641	371	15	commutators	commutator	NOUN
ejpam-6641	371	16	of	of	ADP
ejpam-6641	371	17	hardy	hardy	ADJ
ejpam-6641	371	18	operators	operator	NOUN
ejpam-6641	371	19	in	in	ADP
ejpam-6641	371	20	grand	grand	ADJ
ejpam-6641	371	21	herz	herz	PROPN
ejpam-6641	371	22	spaces	space	NOUN
ejpam-6641	371	23	,	,	PUNCT
ejpam-6641	371	24	ukr	ukr	PROPN
ejpam-6641	371	25	.	.	PROPN
ejpam-6641	371	26	math	math	PROPN
ejpam-6641	371	27	.	.	PUNCT
ejpam-6641	372	1	j.	j.	PROPN
ejpam-6641	372	2	76	76	NUM
ejpam-6641	372	3	(	(	PUNCT
ejpam-6641	372	4	2024	2024	NUM
ejpam-6641	372	5	)	)	PUNCT
ejpam-6641	372	6	,	,	PUNCT
ejpam-6641	372	7	1196–1213	1196–1213	NUM
ejpam-6641	372	8	.	.	PUNCT
ejpam-6641	373	1	[	[	X
ejpam-6641	373	2	43	43	NUM
ejpam-6641	373	3	]	]	PUNCT
ejpam-6641	373	4	m.	m.	NOUN
ejpam-6641	373	5	sultan	sultan	PROPN
ejpam-6641	373	6	,	,	PUNCT
ejpam-6641	373	7	b.	b.	PROPN
ejpam-6641	373	8	sultan	sultan	PROPN
ejpam-6641	373	9	,	,	PUNCT
ejpam-6641	373	10	r.e	r.e	PROPN
ejpam-6641	373	11	.	.	PROPN
ejpam-6641	373	12	castillo	castillo	PROPN
ejpam-6641	373	13	,	,	PUNCT
ejpam-6641	373	14	weighted	weight	VERB
ejpam-6641	373	15	composition	composition	NOUN
ejpam-6641	373	16	operator	operator	NOUN
ejpam-6641	373	17	on	on	ADP
ejpam-6641	373	18	gamma	gamma	NOUN
ejpam-6641	373	19	spaces	space	NOUN
ejpam-6641	373	20	with	with	ADP
ejpam-6641	373	21	variable	variable	ADJ
ejpam-6641	373	22	exponent	exponent	NOUN
ejpam-6641	373	23	,	,	PUNCT
ejpam-6641	373	24	j.	j.	PROPN
ejpam-6641	373	25	pseudo	pseudo	NOUN
ejpam-6641	373	26	-	-	PUNCT
ejpam-6641	373	27	differ	differ	VERB
ejpam-6641	373	28	.	.	PUNCT
ejpam-6641	374	1	oper	oper	PROPN
ejpam-6641	374	2	.	.	PUNCT
ejpam-6641	374	3	appl	appl	PROPN
ejpam-6641	374	4	.	.	PUNCT
ejpam-6641	375	1	15	15	NUM
ejpam-6641	375	2	(	(	PUNCT
ejpam-6641	375	3	46	46	NUM
ejpam-6641	375	4	)	)	PUNCT
ejpam-6641	375	5	(	(	PUNCT
ejpam-6641	375	6	2024	2024	NUM
ejpam-6641	375	7	)	)	PUNCT
ejpam-6641	375	8	.	.	PUNCT
ejpam-6641	376	1	[	[	X
ejpam-6641	376	2	44	44	NUM
ejpam-6641	376	3	]	]	PUNCT
ejpam-6641	376	4	m.	m.	NOUN
ejpam-6641	376	5	sultan	sultan	PROPN
ejpam-6641	376	6	,	,	PUNCT
ejpam-6641	376	7	b.	b.	PROPN
ejpam-6641	376	8	sultan	sultan	PROPN
ejpam-6641	376	9	,	,	PUNCT
ejpam-6641	376	10	a	a	DET
ejpam-6641	376	11	note	note	NOUN
ejpam-6641	376	12	on	on	ADP
ejpam-6641	376	13	the	the	DET
ejpam-6641	376	14	boundedness	boundedness	NOUN
ejpam-6641	376	15	of	of	ADP
ejpam-6641	376	16	higher	high	ADJ
ejpam-6641	376	17	order	order	NOUN
ejpam-6641	376	18	commutators	commutator	NOUN
ejpam-6641	376	19	on	on	ADP
ejpam-6641	376	20	fractional	fractional	ADJ
ejpam-6641	376	21	integrals	integral	NOUN
ejpam-6641	376	22	in	in	ADP
ejpam-6641	376	23	grand	grand	ADJ
ejpam-6641	376	24	variable	variable	ADJ
ejpam-6641	376	25	herz	herz	ADJ
ejpam-6641	376	26	-	-	PUNCT
ejpam-6641	376	27	morrey	morrey	PROPN
ejpam-6641	376	28	spaces	space	NOUN
ejpam-6641	376	29	,	,	PUNCT
ejpam-6641	376	30	kragujev	kragujev	PROPN
ejpam-6641	376	31	.	.	PUNCT
ejpam-6641	377	1	j.	j.	PROPN
ejpam-6641	377	2	math	math	PROPN
ejpam-6641	377	3	.	.	PUNCT
ejpam-6641	378	1	50(7	50(7	X
ejpam-6641	378	2	)	)	PUNCT
ejpam-6641	378	3	(	(	PUNCT
ejpam-6641	378	4	2026	2026	NUM
ejpam-6641	378	5	)	)	PUNCT
ejpam-6641	378	6	,	,	PUNCT
ejpam-6641	378	7	1063	1063	NUM
ejpam-6641	378	8	-	-	SYM
ejpam-6641	378	9	1080	1080	NUM
ejpam-6641	378	10	.	.	PUNCT
ejpam-6641	379	1	[	[	X
ejpam-6641	379	2	45	45	NUM
ejpam-6641	379	3	]	]	PUNCT
ejpam-6641	379	4	a.	a.	NOUN
ejpam-6641	379	5	hussain	hussain	PROPN
ejpam-6641	379	6	,	,	PUNCT
ejpam-6641	379	7	naqash	naqash	PROPN
ejpam-6641	379	8	sarfraz	sarfraz	PROPN
ejpam-6641	379	9	and	and	CCONJ
ejpam-6641	379	10	f.	f.	PROPN
ejpam-6641	379	11	gurbuz	gurbuz	PROPN
ejpam-6641	379	12	,	,	PUNCT
ejpam-6641	379	13	sharp	sharp	ADJ
ejpam-6641	379	14	weak	weak	ADJ
ejpam-6641	379	15	bounds	bound	NOUN
ejpam-6641	379	16	for	for	ADP
ejpam-6641	379	17	p	p	NOUN
ejpam-6641	379	18	-	-	PUNCT
ejpam-6641	379	19	adic	adic	ADJ
ejpam-6641	379	20	hardy	hardy	ADJ
ejpam-6641	379	21	operators	operator	NOUN
ejpam-6641	379	22	on	on	ADP
ejpam-6641	379	23	p	p	ADJ
ejpam-6641	379	24	-	-	PUNCT
ejpam-6641	379	25	adic	adic	ADJ
ejpam-6641	379	26	linear	linear	ADJ
ejpam-6641	379	27	spaces	space	NOUN
ejpam-6641	379	28	,	,	PUNCT
ejpam-6641	379	29	commun.fac	commun.fac	PROPN
ejpam-6641	379	30	.	.	PUNCT
ejpam-6641	379	31	sci.univ.ank.ser	sci.univ.ank.ser	NOUN
ejpam-6641	379	32	.	.	PUNCT
ejpam-6641	380	1	a1	a1	NOUN
ejpam-6641	380	2	math	math	NOUN
ejpam-6641	380	3	.	.	PUNCT
ejpam-6641	381	1	stat	stat	PROPN
ejpam-6641	381	2	.	.	PUNCT
ejpam-6641	382	1	71(4	71(4	NUM
ejpam-6641	382	2	)	)	PUNCT
ejpam-6641	382	3	(	(	PUNCT
ejpam-6641	382	4	2022	2022	NUM
ejpam-6641	382	5	)	)	PUNCT
ejpam-6641	382	6	,	,	PUNCT
ejpam-6641	382	7	919–929	919–929	NUM
ejpam-6641	382	8	.	.	PUNCT
ejpam-6641	383	1	[	[	X
ejpam-6641	383	2	46	46	NUM
ejpam-6641	383	3	]	]	PUNCT
ejpam-6641	383	4	a.	a.	NOUN
ejpam-6641	383	5	hussain	hussain	PROPN
ejpam-6641	383	6	,	,	PUNCT
ejpam-6641	383	7	n.	n.	PROPN
ejpam-6641	383	8	sarfraz	sarfraz	PROPN
ejpam-6641	383	9	et	et	PROPN
ejpam-6641	383	10	al	al	PROPN
ejpam-6641	383	11	.	.	PROPN
ejpam-6641	383	12	,	,	PUNCT
ejpam-6641	383	13	the	the	DET
ejpam-6641	383	14	boundedness	boundedness	NOUN
ejpam-6641	383	15	of	of	ADP
ejpam-6641	383	16	commutators	commutator	NOUN
ejpam-6641	383	17	of	of	ADP
ejpam-6641	383	18	rough	rough	ADJ
ejpam-6641	383	19	p	p	ADJ
ejpam-6641	383	20	-	-	PUNCT
ejpam-6641	383	21	adic	adic	ADJ
ejpam-6641	383	22	fractional	fractional	ADJ
ejpam-6641	383	23	hardy	hardy	ADJ
ejpam-6641	383	24	type	type	NOUN
ejpam-6641	383	25	operators	operator	NOUN
ejpam-6641	383	26	on	on	ADP
ejpam-6641	383	27	herz	herz	ADJ
ejpam-6641	383	28	-	-	PUNCT
ejpam-6641	383	29	type	type	NOUN
ejpam-6641	383	30	spaces	space	NOUN
ejpam-6641	383	31	,	,	PUNCT
ejpam-6641	383	32	j.	j.	PROPN
ejpam-6641	383	33	inequal	inequal	PROPN
ejpam-6641	383	34	.	.	PUNCT
ejpam-6641	384	1	appl	appl	PROPN
ejpam-6641	384	2	.	.	PUNCT
ejpam-6641	385	1	(	(	PUNCT
ejpam-6641	385	2	2021	2021	NUM
ejpam-6641	385	3	)	)	PUNCT
ejpam-6641	385	4	(	(	PUNCT
ejpam-6641	385	5	2021	2021	NUM
ejpam-6641	385	6	)	)	PUNCT
ejpam-6641	385	7	,	,	PUNCT
ejpam-6641	385	8	123	123	NUM
ejpam-6641	385	9	.	.	PUNCT
ejpam-6641	386	1	[	[	X
ejpam-6641	386	2	47	47	NUM
ejpam-6641	386	3	]	]	PUNCT
ejpam-6641	386	4	a.	a.	NOUN
ejpam-6641	386	5	hussain	hussain	PROPN
ejpam-6641	386	6	,	,	PUNCT
ejpam-6641	386	7	n.	n.	PROPN
ejpam-6641	386	8	sarfraz	sarfraz	PROPN
ejpam-6641	386	9	,	,	PUNCT
ejpam-6641	386	10	ilyas	ilyas	PROPN
ejpam-6641	386	11	khan	khan	PROPN
ejpam-6641	386	12	,	,	PUNCT
ejpam-6641	386	13	and	and	CCONJ
ejpam-6641	386	14	a.m.	a.m.	PROPN
ejpam-6641	386	15	alqahtani	alqahtani	PROPN
ejpam-6641	386	16	,	,	PUNCT
ejpam-6641	386	17	estimates	estimate	NOUN
ejpam-6641	386	18	for	for	ADP
ejpam-6641	386	19	commutators	commutator	NOUN
ejpam-6641	386	20	of	of	ADP
ejpam-6641	386	21	bilinear	bilinear	NOUN
ejpam-6641	386	22	fractional	fractional	ADJ
ejpam-6641	386	23	p	p	NOUN
ejpam-6641	386	24	-	-	PUNCT
ejpam-6641	386	25	adic	adic	ADJ
ejpam-6641	386	26	hardy	hardy	ADJ
ejpam-6641	386	27	operator	operator	NOUN
ejpam-6641	386	28	on	on	ADP
ejpam-6641	386	29	herz	herz	ADJ
ejpam-6641	386	30	-	-	PUNCT
ejpam-6641	386	31	type	type	NOUN
ejpam-6641	386	32	spaces	space	NOUN
ejpam-6641	386	33	,	,	PUNCT
ejpam-6641	386	34	j.	j.	PROPN
ejpam-6641	386	35	funct	funct	PROPN
ejpam-6641	386	36	.	.	PUNCT
ejpam-6641	387	1	spaces	space	NOUN
ejpam-6641	387	2	(	(	PUNCT
ejpam-6641	387	3	2021	2021	NUM
ejpam-6641	387	4	)	)	PUNCT
ejpam-6641	388	1	i	i	PROPN
ejpam-6641	388	2	d	d	PROPN
ejpam-6641	388	3	6615604	6615604	NUM
ejpam-6641	388	4	.	.	PUNCT
ejpam-6641	389	1	[	[	X
ejpam-6641	389	2	48	48	NUM
ejpam-6641	389	3	]	]	PUNCT
ejpam-6641	389	4	a.	a.	NOUN
ejpam-6641	389	5	hussain	hussain	PROPN
ejpam-6641	389	6	and	and	CCONJ
ejpam-6641	389	7	a.	a.	PROPN
ejpam-6641	389	8	ajaib	ajaib	PROPN
ejpam-6641	389	9	,	,	PUNCT
ejpam-6641	389	10	some	some	DET
ejpam-6641	389	11	weighted	weight	VERB
ejpam-6641	389	12	inequalities	inequality	NOUN
ejpam-6641	389	13	for	for	ADP
ejpam-6641	389	14	hausdorff	hausdorff	NOUN
ejpam-6641	389	15	operator	operator	NOUN
ejpam-6641	389	16	and	and	CCONJ
ejpam-6641	389	17	commutators	commutator	NOUN
ejpam-6641	389	18	,	,	PUNCT
ejpam-6641	389	19	j.	j.	PROPN
ejpam-6641	389	20	inequal	inequal	PROPN
ejpam-6641	389	21	.	.	PUNCT
ejpam-6641	390	1	appl	appl	PROPN
ejpam-6641	390	2	.	.	PROPN
ejpam-6641	390	3	2018	2018	NUM
ejpam-6641	390	4	,	,	PUNCT
ejpam-6641	390	5	(	(	PUNCT
ejpam-6641	390	6	2018)6	2018)6	NUM
ejpam-6641	390	7	.	.	PUNCT
ejpam-6641	391	1	introduction	introduction	NOUN
ejpam-6641	391	2	preliminaries	preliminary	NOUN
ejpam-6641	391	3	continual	continual	ADJ
ejpam-6641	391	4	herz	herz	PROPN
ejpam-6641	391	5	spaces	space	NOUN
ejpam-6641	391	6	with	with	ADP
ejpam-6641	391	7	variable	variable	ADJ
ejpam-6641	391	8	exponent	exponent	NOUN
ejpam-6641	391	9	boundedness	boundedness	NOUN
ejpam-6641	391	10	result	result	NOUN
ejpam-6641	391	11	on	on	ADP
ejpam-6641	391	12	continual	continual	ADJ
ejpam-6641	391	13	herz	herz	PROPN
ejpam-6641	391	14	spaces	space	NOUN
ejpam-6641	391	15	with	with	ADP
ejpam-6641	391	16	variable	variable	ADJ
ejpam-6641	391	17	exponent	exponent	NOUN
ejpam-6641	391	18	non	non	ADJ
ejpam-6641	391	19	-	-	ADJ
ejpam-6641	391	20	homogeneous	homogeneous	ADJ
ejpam-6641	391	21	herz	herz	NOUN
ejpam-6641	391	22	space(when	space(when	PROPN
ejpam-6641	392	1	=	=	NOUN
ejpam-6641	392	2	0	0	NUM
ejpam-6641	392	3	)	)	PUNCT
ejpam-6641	392	4	conclusion	conclusion	NOUN
ejpam-6641	392	5	ethics	ethic	NOUN
ejpam-6641	392	6	declarations	declaration	NOUN