id	sid	tid	token	lemma	pos
ejpam-5113	1	1	european	european	PROPN
ejpam-5113	1	2	journal	journal	PROPN
ejpam-5113	1	3	of	of	ADP
ejpam-5113	1	4	pure	pure	ADJ
ejpam-5113	1	5	and	and	CCONJ
ejpam-5113	1	6	applied	apply	VERB
ejpam-5113	1	7	mathematics	mathematic	NOUN
ejpam-5113	1	8	vol	vol	NOUN
ejpam-5113	1	9	.	.	PROPN
ejpam-5113	2	1	17	17	NUM
ejpam-5113	2	2	,	,	PUNCT
ejpam-5113	2	3	no	no	INTJ
ejpam-5113	2	4	.	.	NOUN
ejpam-5113	2	5	2	2	NUM
ejpam-5113	2	6	,	,	PUNCT
ejpam-5113	2	7	2024	2024	NUM
ejpam-5113	2	8	,	,	PUNCT
ejpam-5113	2	9	931	931	NUM
ejpam-5113	2	10	-	-	SYM
ejpam-5113	2	11	944	944	NUM
ejpam-5113	2	12	issn	issn	PROPN
ejpam-5113	2	13	1307	1307	NUM
ejpam-5113	2	14	-	-	SYM
ejpam-5113	2	15	5543	5543	NUM
ejpam-5113	2	16	–	–	PUNCT
ejpam-5113	2	17	ejpam.com	ejpam.com	X
ejpam-5113	2	18	published	publish	VERB
ejpam-5113	2	19	by	by	ADP
ejpam-5113	2	20	new	new	PROPN
ejpam-5113	2	21	york	york	PROPN
ejpam-5113	2	22	business	business	PROPN
ejpam-5113	2	23	global	global	PROPN
ejpam-5113	2	24	volterra	volterra	PROPN
ejpam-5113	2	25	-	-	PUNCT
ejpam-5113	2	26	composition	composition	NOUN
ejpam-5113	2	27	operators	operator	NOUN
ejpam-5113	2	28	acting	act	VERB
ejpam-5113	2	29	on	on	ADP
ejpam-5113	2	30	sp	sp	ADP
ejpam-5113	2	31	spaces	space	NOUN
ejpam-5113	2	32	and	and	CCONJ
ejpam-5113	2	33	weighted	weight	VERB
ejpam-5113	2	34	zygmund	zygmund	PROPN
ejpam-5113	2	35	spaces	space	NOUN
ejpam-5113	2	36	waleed	waleed	PROPN
ejpam-5113	2	37	al	al	PROPN
ejpam-5113	2	38	-	-	PUNCT
ejpam-5113	2	39	rawashdeh	rawashdeh	PROPN
ejpam-5113	2	40	department	department	NOUN
ejpam-5113	2	41	of	of	ADP
ejpam-5113	2	42	mathematics	mathematics	PROPN
ejpam-5113	2	43	,	,	PUNCT
ejpam-5113	2	44	zarqa	zarqa	PROPN
ejpam-5113	2	45	university	university	PROPN
ejpam-5113	2	46	,	,	PUNCT
ejpam-5113	2	47	2000	2000	NUM
ejpam-5113	2	48	zarqa	zarqa	NOUN
ejpam-5113	2	49	,	,	PUNCT
ejpam-5113	2	50	13110	13110	NUM
ejpam-5113	2	51	jordan	jordan	PROPN
ejpam-5113	2	52	abstract	abstract	PROPN
ejpam-5113	2	53	.	.	PUNCT
ejpam-5113	3	1	let	let	VERB
ejpam-5113	3	2	φ	φ	PROPN
ejpam-5113	3	3	be	be	AUX
ejpam-5113	3	4	an	an	DET
ejpam-5113	3	5	analytic	analytic	ADJ
ejpam-5113	3	6	selfmap	selfmap	NOUN
ejpam-5113	3	7	of	of	ADP
ejpam-5113	3	8	the	the	DET
ejpam-5113	3	9	open	open	ADJ
ejpam-5113	3	10	unit	unit	NOUN
ejpam-5113	3	11	disk	disk	NOUN
ejpam-5113	3	12	d	d	NOUN
ejpam-5113	3	13	and	and	CCONJ
ejpam-5113	3	14	g	g	PROPN
ejpam-5113	3	15	be	be	AUX
ejpam-5113	3	16	an	an	DET
ejpam-5113	3	17	analytic	analytic	ADJ
ejpam-5113	3	18	function	function	NOUN
ejpam-5113	3	19	on	on	ADP
ejpam-5113	3	20	d.	d.	PROPN
ejpam-5113	3	21	the	the	DET
ejpam-5113	3	22	volterra	volterra	NOUN
ejpam-5113	3	23	-	-	PUNCT
ejpam-5113	3	24	type	type	NOUN
ejpam-5113	3	25	composition	composition	NOUN
ejpam-5113	3	26	operators	operator	NOUN
ejpam-5113	3	27	induced	induce	VERB
ejpam-5113	3	28	by	by	ADP
ejpam-5113	3	29	the	the	DET
ejpam-5113	3	30	maps	map	NOUN
ejpam-5113	3	31	g	g	PROPN
ejpam-5113	3	32	and	and	CCONJ
ejpam-5113	3	33	φ	φ	PROPN
ejpam-5113	3	34	are	be	AUX
ejpam-5113	3	35	defined	define	VERB
ejpam-5113	3	36	as	as	ADP
ejpam-5113	3	37	(	(	PUNCT
ejpam-5113	3	38	iφg	iφg	NOUN
ejpam-5113	3	39	f	f	PROPN
ejpam-5113	3	40	)	)	PUNCT
ejpam-5113	4	1	(	(	PUNCT
ejpam-5113	4	2	z	z	X
ejpam-5113	4	3	)	)	PUNCT
ejpam-5113	4	4	=	=	SYM
ejpam-5113	5	1	∫	∫	PROPN
ejpam-5113	5	2	z	z	NOUN
ejpam-5113	5	3	0	0	NUM
ejpam-5113	6	1	f	f	PROPN
ejpam-5113	6	2	′(φ(ζ))g(ζ)dζ	′(φ(ζ))g(ζ)dζ	PROPN
ejpam-5113	6	3	and	and	CCONJ
ejpam-5113	6	4	(	(	PUNCT
ejpam-5113	6	5	tφ	tφ	PROPN
ejpam-5113	6	6	g	g	PROPN
ejpam-5113	6	7	f	f	PROPN
ejpam-5113	6	8	)	)	PUNCT
ejpam-5113	6	9	(	(	PUNCT
ejpam-5113	6	10	z	z	X
ejpam-5113	6	11	)	)	PUNCT
ejpam-5113	6	12	=	=	SYM
ejpam-5113	7	1	∫	∫	PROPN
ejpam-5113	7	2	z	z	NOUN
ejpam-5113	7	3	0	0	NUM
ejpam-5113	7	4	f(φ(ζ))g′(ζ)dζ	f(φ(ζ))g′(ζ)dζ	NOUN
ejpam-5113	7	5	.	.	PUNCT
ejpam-5113	8	1	for	for	ADP
ejpam-5113	8	2	1	1	NUM
ejpam-5113	8	3	≤	≤	NOUN
ejpam-5113	8	4	p	p	NOUN
ejpam-5113	8	5	<	<	X
ejpam-5113	8	6	∞	∞	PROPN
ejpam-5113	8	7	,	,	PUNCT
ejpam-5113	8	8	sp(d	sp(d	PUNCT
ejpam-5113	8	9	)	)	PUNCT
ejpam-5113	8	10	is	be	AUX
ejpam-5113	8	11	the	the	DET
ejpam-5113	8	12	space	space	NOUN
ejpam-5113	8	13	of	of	ADP
ejpam-5113	8	14	all	all	DET
ejpam-5113	8	15	analytic	analytic	ADJ
ejpam-5113	8	16	functions	function	NOUN
ejpam-5113	8	17	on	on	ADP
ejpam-5113	8	18	d	d	X
ejpam-5113	8	19	whose	whose	DET
ejpam-5113	8	20	first	first	ADJ
ejpam-5113	8	21	derivative	derivative	ADJ
ejpam-5113	8	22	f	f	NOUN
ejpam-5113	8	23	′	′	NUM
ejpam-5113	8	24	lies	lie	VERB
ejpam-5113	8	25	in	in	ADP
ejpam-5113	8	26	the	the	DET
ejpam-5113	8	27	hardy	hardy	ADJ
ejpam-5113	8	28	space	space	NOUN
ejpam-5113	8	29	hp(d	hp(d	PRON
ejpam-5113	8	30	)	)	PUNCT
ejpam-5113	8	31	,	,	PUNCT
ejpam-5113	8	32	endowed	endow	VERB
ejpam-5113	8	33	with	with	ADP
ejpam-5113	8	34	the	the	DET
ejpam-5113	8	35	norm	norm	NOUN
ejpam-5113	8	36	∥f∥sp	∥f∥sp	PROPN
ejpam-5113	8	37	=	=	SYM
ejpam-5113	8	38	|f(0)|+	|f(0)|+	VERB
ejpam-5113	9	1	∥f	∥f	PROPN
ejpam-5113	9	2	′∥hp	′∥hp	ADV
ejpam-5113	9	3	.	.	PUNCT
ejpam-5113	10	1	let	let	VERB
ejpam-5113	10	2	µ	µ	X
ejpam-5113	10	3	:	:	PUNCT
ejpam-5113	10	4	(	(	PUNCT
ejpam-5113	10	5	0	0	NUM
ejpam-5113	10	6	,	,	PUNCT
ejpam-5113	10	7	1	1	NUM
ejpam-5113	10	8	]	]	PUNCT
ejpam-5113	10	9	→	→	X
ejpam-5113	10	10	(	(	PUNCT
ejpam-5113	10	11	0,∞	0,∞	NOUN
ejpam-5113	10	12	)	)	PUNCT
ejpam-5113	10	13	be	be	VERB
ejpam-5113	10	14	a	a	DET
ejpam-5113	10	15	positive	positive	ADJ
ejpam-5113	10	16	continuous	continuous	ADJ
ejpam-5113	10	17	function	function	NOUN
ejpam-5113	10	18	on	on	ADP
ejpam-5113	10	19	d	d	PROPN
ejpam-5113	10	20	such	such	ADJ
ejpam-5113	10	21	that	that	PRON
ejpam-5113	10	22	for	for	ADP
ejpam-5113	10	23	z	z	PROPN
ejpam-5113	10	24	∈	∈	PROPN
ejpam-5113	11	1	d	d	ADP
ejpam-5113	11	2	we	we	PRON
ejpam-5113	11	3	define	define	VERB
ejpam-5113	11	4	µ(z	µ(z	NOUN
ejpam-5113	11	5	)	)	PUNCT
ejpam-5113	11	6	=	=	SYM
ejpam-5113	11	7	µ(|z|	µ(|z|	PROPN
ejpam-5113	11	8	)	)	PUNCT
ejpam-5113	11	9	.	.	PUNCT
ejpam-5113	12	1	the	the	DET
ejpam-5113	12	2	weighted	weight	VERB
ejpam-5113	12	3	zygmund	zygmund	PROPN
ejpam-5113	12	4	space	space	NOUN
ejpam-5113	12	5	zµ(d	zµ(d	NOUN
ejpam-5113	12	6	)	)	PUNCT
ejpam-5113	12	7	is	be	AUX
ejpam-5113	12	8	the	the	DET
ejpam-5113	12	9	space	space	NOUN
ejpam-5113	12	10	of	of	ADP
ejpam-5113	12	11	all	all	DET
ejpam-5113	12	12	analytic	analytic	ADJ
ejpam-5113	12	13	functions	function	NOUN
ejpam-5113	12	14	f	f	X
ejpam-5113	12	15	on	on	ADP
ejpam-5113	12	16	d	d	X
ejpam-5113	12	17	such	such	ADJ
ejpam-5113	12	18	that	that	DET
ejpam-5113	12	19	supz∈d	supz∈d	PROPN
ejpam-5113	12	20	µ(z)|f	µ(z)|f	PROPN
ejpam-5113	12	21	′′(z)|	′′(z)|	PROPN
ejpam-5113	12	22	is	be	AUX
ejpam-5113	12	23	finite	finite	ADJ
ejpam-5113	12	24	.	.	PUNCT
ejpam-5113	13	1	in	in	ADP
ejpam-5113	13	2	this	this	DET
ejpam-5113	13	3	paper	paper	NOUN
ejpam-5113	13	4	,	,	PUNCT
ejpam-5113	13	5	we	we	PRON
ejpam-5113	13	6	characterize	characterize	VERB
ejpam-5113	13	7	the	the	DET
ejpam-5113	13	8	boundedness	boundedness	NOUN
ejpam-5113	13	9	and	and	CCONJ
ejpam-5113	13	10	compactness	compactness	NOUN
ejpam-5113	13	11	of	of	ADP
ejpam-5113	13	12	the	the	DET
ejpam-5113	13	13	volterra	volterra	NOUN
ejpam-5113	13	14	-	-	PUNCT
ejpam-5113	13	15	type	type	NOUN
ejpam-5113	13	16	composition	composition	NOUN
ejpam-5113	13	17	operators	operator	NOUN
ejpam-5113	13	18	that	that	PRON
ejpam-5113	13	19	act	act	VERB
ejpam-5113	13	20	between	between	ADP
ejpam-5113	13	21	sp	sp	ADP
ejpam-5113	13	22	spaces	space	NOUN
ejpam-5113	13	23	and	and	CCONJ
ejpam-5113	13	24	weighted	weight	VERB
ejpam-5113	13	25	zygmund	zygmund	PROPN
ejpam-5113	13	26	spaces	space	NOUN
ejpam-5113	13	27	.	.	PUNCT
ejpam-5113	14	1	2020	2020	NUM
ejpam-5113	14	2	mathematics	mathematic	NOUN
ejpam-5113	14	3	subject	subject	NOUN
ejpam-5113	14	4	classifications	classification	NOUN
ejpam-5113	14	5	:	:	PUNCT
ejpam-5113	14	6	47b33	47b33	NUM
ejpam-5113	14	7	,	,	PUNCT
ejpam-5113	14	8	47b38	47b38	NUM
ejpam-5113	14	9	,	,	PUNCT
ejpam-5113	14	10	30h10	30h10	NUM
ejpam-5113	14	11	,	,	PUNCT
ejpam-5113	14	12	30h20	30h20	NUM
ejpam-5113	14	13	,	,	PUNCT
ejpam-5113	14	14	47b37	47b37	NUM
ejpam-5113	14	15	,	,	PUNCT
ejpam-5113	14	16	30h05	30h05	NUM
ejpam-5113	14	17	,	,	PUNCT
ejpam-5113	14	18	32c15	32c15	NUM
ejpam-5113	14	19	key	key	ADJ
ejpam-5113	14	20	words	word	NOUN
ejpam-5113	14	21	and	and	CCONJ
ejpam-5113	14	22	phrases	phrase	NOUN
ejpam-5113	14	23	:	:	PUNCT
ejpam-5113	14	24	weighted	weight	VERB
ejpam-5113	14	25	zygmund	zygmund	PROPN
ejpam-5113	14	26	spaces	space	NOUN
ejpam-5113	14	27	,	,	PUNCT
ejpam-5113	14	28	sp	sp	ADP
ejpam-5113	14	29	spaces	space	NOUN
ejpam-5113	14	30	,	,	PUNCT
ejpam-5113	14	31	volterra	volterra	PROPN
ejpam-5113	14	32	operators	operator	NOUN
ejpam-5113	14	33	,	,	PUNCT
ejpam-5113	14	34	composition	composition	NOUN
ejpam-5113	14	35	operators	operator	NOUN
ejpam-5113	14	36	,	,	PUNCT
ejpam-5113	14	37	bounded	bounded	ADJ
ejpam-5113	14	38	operators	operator	NOUN
ejpam-5113	14	39	,	,	PUNCT
ejpam-5113	14	40	compact	compact	ADJ
ejpam-5113	14	41	operators	operator	NOUN
ejpam-5113	14	42	1	1	NUM
ejpam-5113	14	43	.	.	PUNCT
ejpam-5113	15	1	introduction	introduction	NOUN
ejpam-5113	15	2	let	let	VERB
ejpam-5113	15	3	d	d	NOUN
ejpam-5113	15	4	be	be	AUX
ejpam-5113	15	5	the	the	DET
ejpam-5113	15	6	open	open	ADJ
ejpam-5113	15	7	unit	unit	NOUN
ejpam-5113	15	8	disk	disk	NOUN
ejpam-5113	15	9	{	{	PUNCT
ejpam-5113	15	10	z	z	NOUN
ejpam-5113	15	11	∈	∈	PROPN
ejpam-5113	15	12	d	d	NOUN
ejpam-5113	15	13	:	:	PUNCT
ejpam-5113	15	14	|z|	|z|	VERB
ejpam-5113	15	15	<	<	X
ejpam-5113	15	16	1	1	NUM
ejpam-5113	15	17	}	}	PUNCT
ejpam-5113	15	18	in	in	ADP
ejpam-5113	15	19	the	the	DET
ejpam-5113	15	20	complex	complex	ADJ
ejpam-5113	15	21	plane	plane	NOUN
ejpam-5113	15	22	c.	c.	NOUN
ejpam-5113	15	23	let	let	VERB
ejpam-5113	15	24	h(d	h(d	PRON
ejpam-5113	15	25	)	)	PUNCT
ejpam-5113	15	26	be	be	AUX
ejpam-5113	15	27	the	the	DET
ejpam-5113	15	28	space	space	NOUN
ejpam-5113	15	29	of	of	ADP
ejpam-5113	15	30	all	all	DET
ejpam-5113	15	31	analytic	analytic	ADJ
ejpam-5113	15	32	functions	function	NOUN
ejpam-5113	15	33	on	on	ADP
ejpam-5113	15	34	the	the	DET
ejpam-5113	15	35	open	open	ADJ
ejpam-5113	15	36	unit	unit	NOUN
ejpam-5113	15	37	disk	disk	NOUN
ejpam-5113	15	38	d.	d.	NOUN
ejpam-5113	15	39	for	for	ADP
ejpam-5113	15	40	1	1	NUM
ejpam-5113	15	41	≤	≤	NOUN
ejpam-5113	15	42	p	p	NOUN
ejpam-5113	15	43	<	<	X
ejpam-5113	15	44	∞	∞	PROPN
ejpam-5113	15	45	,	,	PUNCT
ejpam-5113	15	46	the	the	DET
ejpam-5113	15	47	analytic	analytic	ADJ
ejpam-5113	15	48	hardy	hardy	ADJ
ejpam-5113	15	49	space	space	NOUN
ejpam-5113	15	50	hp(d	hp(d	PUNCT
ejpam-5113	15	51	on	on	ADP
ejpam-5113	15	52	the	the	DET
ejpam-5113	15	53	unit	unit	NOUN
ejpam-5113	15	54	disk	disk	NOUN
ejpam-5113	15	55	d	d	NOUN
ejpam-5113	15	56	is	be	AUX
ejpam-5113	15	57	the	the	DET
ejpam-5113	15	58	banach	banach	NOUN
ejpam-5113	15	59	space	space	NOUN
ejpam-5113	15	60	of	of	ADP
ejpam-5113	15	61	all	all	DET
ejpam-5113	15	62	analytic	analytic	ADJ
ejpam-5113	15	63	functions	function	NOUN
ejpam-5113	15	64	f	f	PROPN
ejpam-5113	15	65	∈	∈	PROPN
ejpam-5113	15	66	h(d	h(d	PROPN
ejpam-5113	15	67	)	)	PUNCT
ejpam-5113	15	68	such	such	ADJ
ejpam-5113	15	69	that	that	SCONJ
ejpam-5113	15	70	∥f∥php	∥f∥php	VERB
ejpam-5113	15	71	=	=	NOUN
ejpam-5113	15	72	sup	sup	NOUN
ejpam-5113	15	73	0	0	NUM
ejpam-5113	15	74	<	<	NOUN
ejpam-5113	15	75	r<1	r<1	NOUN
ejpam-5113	15	76	∫	∫	NOUN
ejpam-5113	15	77	∂d	∂d	PROPN
ejpam-5113	15	78	|f(rζ)|pdσ(ζ	|f(rζ)|pdσ(ζ	NUM
ejpam-5113	15	79	)	)	PUNCT
ejpam-5113	15	80	<	<	X
ejpam-5113	15	81	∞	∞	PROPN
ejpam-5113	15	82	,	,	PUNCT
ejpam-5113	15	83	where	where	SCONJ
ejpam-5113	15	84	σ	σ	PROPN
ejpam-5113	15	85	is	be	AUX
ejpam-5113	15	86	the	the	DET
ejpam-5113	15	87	normalized	normalize	VERB
ejpam-5113	15	88	lebesgue	lebesgue	NOUN
ejpam-5113	15	89	measure	measure	NOUN
ejpam-5113	15	90	on	on	ADP
ejpam-5113	15	91	the	the	DET
ejpam-5113	15	92	boundary	boundary	NOUN
ejpam-5113	15	93	of	of	ADP
ejpam-5113	15	94	the	the	DET
ejpam-5113	15	95	unit	unit	NOUN
ejpam-5113	15	96	disk	disk	NOUN
ejpam-5113	15	97	.	.	PUNCT
ejpam-5113	16	1	for	for	SCONJ
ejpam-5113	16	2	f	f	PROPN
ejpam-5113	16	3	belongs	belong	VERB
ejpam-5113	16	4	to	to	ADP
ejpam-5113	16	5	hp(d	hp(d	NUM
ejpam-5113	16	6	)	)	PUNCT
ejpam-5113	16	7	,	,	PUNCT
ejpam-5113	16	8	it	it	PRON
ejpam-5113	16	9	is	be	AUX
ejpam-5113	16	10	well	well	ADV
ejpam-5113	16	11	known	know	VERB
ejpam-5113	16	12	from	from	ADP
ejpam-5113	16	13	fatou	fatou	NOUN
ejpam-5113	16	14	’s	’s	PART
ejpam-5113	16	15	theorem	theorem	NOUN
ejpam-5113	16	16	that	that	SCONJ
ejpam-5113	16	17	the	the	DET
ejpam-5113	16	18	radial	radial	ADJ
ejpam-5113	16	19	limit	limit	NOUN
ejpam-5113	16	20	f∗(ζ	f∗(ζ	NOUN
ejpam-5113	16	21	)	)	PUNCT
ejpam-5113	17	1	=	=	PROPN
ejpam-5113	17	2	lim	lim	PROPN
ejpam-5113	17	3	r→1−	r→1−	PROPN
ejpam-5113	17	4	f(rζ	f(rζ	PROPN
ejpam-5113	17	5	)	)	PUNCT
ejpam-5113	17	6	doi	doi	NOUN
ejpam-5113	17	7	:	:	PUNCT
ejpam-5113	17	8	https://doi.org/10.29020/nybg.ejpam.v17i2.5113	https://doi.org/10.29020/nybg.ejpam.v17i2.5113	ADJ
ejpam-5113	17	9	email	email	NOUN
ejpam-5113	17	10	address	address	NOUN
ejpam-5113	17	11	:	:	PUNCT
ejpam-5113	17	12	walrawashdeh@zu.edu.jo	walrawashdeh@zu.edu.jo	NOUN
ejpam-5113	17	13	(	(	PUNCT
ejpam-5113	17	14	w.	w.	PROPN
ejpam-5113	17	15	al	al	PROPN
ejpam-5113	17	16	-	-	PUNCT
ejpam-5113	17	17	rawashdeh	rawashdeh	PROPN
ejpam-5113	17	18	)	)	PUNCT
ejpam-5113	17	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5113	18	1	931	931	NUM
ejpam-5113	18	2	©	©	ADP
ejpam-5113	18	3	2024	2024	NUM
ejpam-5113	18	4	ejpam	ejpam	NOUN
ejpam-5113	18	5	all	all	DET
ejpam-5113	18	6	rights	right	NOUN
ejpam-5113	18	7	reserved	reserve	VERB
ejpam-5113	18	8	.	.	PUNCT
ejpam-5113	19	1	w.	w.	PROPN
ejpam-5113	19	2	al	al	PROPN
ejpam-5113	19	3	-	-	PUNCT
ejpam-5113	19	4	rawashdeh	rawashdeh	PROPN
ejpam-5113	19	5	/	/	SYM
ejpam-5113	19	6	eur	eur	PROPN
ejpam-5113	19	7	.	.	PUNCT
ejpam-5113	20	1	j.	j.	PROPN
ejpam-5113	20	2	pure	pure	PROPN
ejpam-5113	20	3	appl	appl	PROPN
ejpam-5113	20	4	.	.	PROPN
ejpam-5113	20	5	math	math	PROPN
ejpam-5113	20	6	,	,	PUNCT
ejpam-5113	20	7	17	17	NUM
ejpam-5113	20	8	(	(	PUNCT
ejpam-5113	20	9	2	2	NUM
ejpam-5113	20	10	)	)	PUNCT
ejpam-5113	20	11	(	(	PUNCT
ejpam-5113	20	12	2024	2024	NUM
ejpam-5113	20	13	)	)	PUNCT
ejpam-5113	20	14	,	,	PUNCT
ejpam-5113	20	15	931	931	NUM
ejpam-5113	20	16	-	-	SYM
ejpam-5113	20	17	944	944	NUM
ejpam-5113	20	18	932	932	NUM
ejpam-5113	20	19	exists	exist	VERB
ejpam-5113	20	20	for	for	ADP
ejpam-5113	20	21	almost	almost	ADV
ejpam-5113	20	22	all	all	PRON
ejpam-5113	20	23	ζ	ζ	NOUN
ejpam-5113	20	24	on	on	ADP
ejpam-5113	20	25	∂d	∂d	PROPN
ejpam-5113	20	26	.	.	PUNCT
ejpam-5113	21	1	moreover	moreover	ADV
ejpam-5113	21	2	,	,	PUNCT
ejpam-5113	21	3	∥f∥php	∥f∥php	PROPN
ejpam-5113	21	4	=	=	SYM
ejpam-5113	21	5	∫	∫	PROPN
ejpam-5113	21	6	∂d	∂d	PROPN
ejpam-5113	21	7	|f∗(ζ)|pdσ(ζ	|f∗(ζ)|pdσ(ζ	NOUN
ejpam-5113	21	8	)	)	PUNCT
ejpam-5113	21	9	,	,	PUNCT
ejpam-5113	21	10	for	for	ADP
ejpam-5113	21	11	all	all	DET
ejpam-5113	21	12	finite	finite	ADJ
ejpam-5113	21	13	values	value	NOUN
ejpam-5113	21	14	of	of	ADP
ejpam-5113	21	15	p.	p.	NOUN
ejpam-5113	21	16	we	we	PRON
ejpam-5113	21	17	often	often	ADV
ejpam-5113	21	18	use	use	VERB
ejpam-5113	21	19	a	a	DET
ejpam-5113	21	20	standard	standard	ADJ
ejpam-5113	21	21	synonym	synonym	NOUN
ejpam-5113	21	22	of	of	ADP
ejpam-5113	21	23	notation	notation	NOUN
ejpam-5113	21	24	of	of	ADP
ejpam-5113	21	25	writing	write	VERB
ejpam-5113	21	26	f	f	PROPN
ejpam-5113	21	27	instead	instead	ADV
ejpam-5113	21	28	of	of	ADP
ejpam-5113	21	29	f∗.	f∗.	NOUN
ejpam-5113	21	30	for	for	ADP
ejpam-5113	21	31	1	1	NUM
ejpam-5113	21	32	≤	≤	NOUN
ejpam-5113	21	33	p	p	NOUN
ejpam-5113	21	34	<	<	X
ejpam-5113	21	35	∞	∞	PROPN
ejpam-5113	21	36	,	,	PUNCT
ejpam-5113	21	37	sp(d	sp(d	PUNCT
ejpam-5113	21	38	)	)	PUNCT
ejpam-5113	21	39	is	be	AUX
ejpam-5113	21	40	the	the	DET
ejpam-5113	21	41	space	space	NOUN
ejpam-5113	21	42	of	of	ADP
ejpam-5113	21	43	all	all	DET
ejpam-5113	21	44	analytic	analytic	ADJ
ejpam-5113	21	45	functions	function	NOUN
ejpam-5113	21	46	on	on	ADP
ejpam-5113	21	47	the	the	DET
ejpam-5113	21	48	unit	unit	NOUN
ejpam-5113	21	49	disk	disk	NOUN
ejpam-5113	22	1	d	d	X
ejpam-5113	22	2	whose	whose	DET
ejpam-5113	22	3	first	first	ADJ
ejpam-5113	22	4	derivative	derivative	ADJ
ejpam-5113	22	5	f	f	NOUN
ejpam-5113	22	6	′	′	NUM
ejpam-5113	22	7	lies	lie	VERB
ejpam-5113	22	8	in	in	ADP
ejpam-5113	22	9	the	the	DET
ejpam-5113	22	10	hardy	hardy	ADJ
ejpam-5113	22	11	space	space	NOUN
ejpam-5113	22	12	hp(d	hp(d	PUNCT
ejpam-5113	22	13	)	)	PUNCT
ejpam-5113	22	14	endowed	endow	VERB
ejpam-5113	22	15	with	with	ADP
ejpam-5113	22	16	the	the	DET
ejpam-5113	22	17	norm	norm	NOUN
ejpam-5113	22	18	∥f∥sp	∥f∥sp	PROPN
ejpam-5113	22	19	=	=	SYM
ejpam-5113	22	20	|f(0)|+	|f(0)|+	VERB
ejpam-5113	23	1	∥f	∥f	PROPN
ejpam-5113	23	2	′∥hp	′∥hp	ADV
ejpam-5113	23	3	.	.	PUNCT
ejpam-5113	24	1	one	one	PRON
ejpam-5113	24	2	can	can	AUX
ejpam-5113	24	3	easily	easily	ADV
ejpam-5113	24	4	show	show	VERB
ejpam-5113	24	5	that	that	SCONJ
ejpam-5113	24	6	sp	sp	NOUN
ejpam-5113	24	7	is	be	AUX
ejpam-5113	24	8	a	a	DET
ejpam-5113	24	9	banach	banach	NOUN
ejpam-5113	24	10	space	space	NOUN
ejpam-5113	24	11	with	with	ADP
ejpam-5113	24	12	respect	respect	NOUN
ejpam-5113	24	13	to	to	ADP
ejpam-5113	24	14	this	this	DET
ejpam-5113	24	15	norm	norm	NOUN
ejpam-5113	24	16	.	.	PUNCT
ejpam-5113	25	1	it	it	PRON
ejpam-5113	25	2	is	be	AUX
ejpam-5113	25	3	well	well	ADV
ejpam-5113	25	4	known	know	VERB
ejpam-5113	25	5	that	that	SCONJ
ejpam-5113	25	6	sp	sp	ADP
ejpam-5113	25	7	is	be	AUX
ejpam-5113	25	8	a	a	DET
ejpam-5113	25	9	banach	banach	NOUN
ejpam-5113	25	10	algebra	algebra	NOUN
ejpam-5113	25	11	when	when	SCONJ
ejpam-5113	25	12	the	the	DET
ejpam-5113	25	13	norm	norm	NOUN
ejpam-5113	25	14	of	of	ADP
ejpam-5113	25	15	f	f	PROPN
ejpam-5113	25	16	∈	∈	PROPN
ejpam-5113	25	17	sp	sp	NOUN
ejpam-5113	25	18	is	be	AUX
ejpam-5113	25	19	defined	define	VERB
ejpam-5113	25	20	by	by	ADP
ejpam-5113	25	21	∥f∥∞	∥f∥∞	PUNCT
ejpam-5113	26	1	+	+	CCONJ
ejpam-5113	26	2	∥f	∥f	INTJ
ejpam-5113	26	3	′∥hp	′∥hp	ADV
ejpam-5113	26	4	.	.	PUNCT
ejpam-5113	27	1	for	for	ADP
ejpam-5113	27	2	more	more	ADJ
ejpam-5113	27	3	information	information	NOUN
ejpam-5113	27	4	about	about	ADP
ejpam-5113	27	5	these	these	DET
ejpam-5113	27	6	spaces	space	NOUN
ejpam-5113	27	7	we	we	PRON
ejpam-5113	27	8	refer	refer	VERB
ejpam-5113	27	9	the	the	DET
ejpam-5113	27	10	readers	reader	NOUN
ejpam-5113	27	11	to	to	ADP
ejpam-5113	27	12	the	the	DET
ejpam-5113	27	13	monograph	monograph	NOUN
ejpam-5113	28	1	[	[	X
ejpam-5113	28	2	5	5	NUM
ejpam-5113	28	3	]	]	PUNCT
ejpam-5113	28	4	,	,	PUNCT
ejpam-5113	28	5	the	the	DET
ejpam-5113	28	6	papers	paper	NOUN
ejpam-5113	28	7	(	(	PUNCT
ejpam-5113	28	8	[	[	X
ejpam-5113	28	9	1	1	NUM
ejpam-5113	28	10	]	]	PUNCT
ejpam-5113	28	11	,	,	PUNCT
ejpam-5113	28	12	[	[	X
ejpam-5113	28	13	2	2	NUM
ejpam-5113	28	14	]	]	NUM
ejpam-5113	28	15	)	)	PUNCT
ejpam-5113	28	16	,	,	PUNCT
ejpam-5113	28	17	and	and	CCONJ
ejpam-5113	28	18	the	the	DET
ejpam-5113	28	19	references	reference	NOUN
ejpam-5113	28	20	therein	therein	ADV
ejpam-5113	28	21	.	.	PUNCT
ejpam-5113	29	1	let	let	VERB
ejpam-5113	29	2	µ	µ	X
ejpam-5113	29	3	:	:	PUNCT
ejpam-5113	29	4	(	(	PUNCT
ejpam-5113	29	5	0	0	NUM
ejpam-5113	29	6	,	,	PUNCT
ejpam-5113	29	7	1	1	NUM
ejpam-5113	29	8	]	]	PUNCT
ejpam-5113	29	9	→	→	X
ejpam-5113	29	10	(	(	PUNCT
ejpam-5113	29	11	0,∞	0,∞	NOUN
ejpam-5113	29	12	)	)	PUNCT
ejpam-5113	29	13	be	be	VERB
ejpam-5113	29	14	a	a	DET
ejpam-5113	29	15	positive	positive	ADJ
ejpam-5113	29	16	continuous	continuous	ADJ
ejpam-5113	29	17	function	function	NOUN
ejpam-5113	29	18	on	on	ADP
ejpam-5113	29	19	d	d	PROPN
ejpam-5113	29	20	such	such	ADJ
ejpam-5113	29	21	that	that	PRON
ejpam-5113	29	22	for	for	ADP
ejpam-5113	29	23	z	z	PROPN
ejpam-5113	29	24	∈	∈	PROPN
ejpam-5113	30	1	d	d	ADP
ejpam-5113	30	2	we	we	PRON
ejpam-5113	30	3	define	define	VERB
ejpam-5113	30	4	µ(z	µ(z	NOUN
ejpam-5113	30	5	)	)	PUNCT
ejpam-5113	30	6	=	=	SYM
ejpam-5113	30	7	µ(|z|	µ(|z|	PROPN
ejpam-5113	30	8	)	)	PUNCT
ejpam-5113	30	9	.	.	PUNCT
ejpam-5113	31	1	the	the	DET
ejpam-5113	31	2	weighted	weight	VERB
ejpam-5113	31	3	zygmund	zygmund	PROPN
ejpam-5113	31	4	space	space	NOUN
ejpam-5113	31	5	zµ	zµ	PROPN
ejpam-5113	31	6	is	be	AUX
ejpam-5113	31	7	the	the	DET
ejpam-5113	31	8	space	space	NOUN
ejpam-5113	31	9	of	of	ADP
ejpam-5113	31	10	all	all	DET
ejpam-5113	31	11	analytic	analytic	ADJ
ejpam-5113	31	12	functions	function	NOUN
ejpam-5113	31	13	f	f	X
ejpam-5113	31	14	on	on	ADP
ejpam-5113	31	15	the	the	DET
ejpam-5113	31	16	open	open	ADJ
ejpam-5113	31	17	unit	unit	NOUN
ejpam-5113	31	18	disk	disk	NOUN
ejpam-5113	31	19	d	d	NOUN
ejpam-5113	31	20	such	such	ADJ
ejpam-5113	31	21	that	that	DET
ejpam-5113	31	22	sup	sup	PROPN
ejpam-5113	31	23	z∈d	z∈d	PROPN
ejpam-5113	31	24	µ(z)|f	µ(z)|f	PROPN
ejpam-5113	31	25	′′(z)|	′′(z)|	PROPN
ejpam-5113	31	26	<	<	X
ejpam-5113	31	27	∞.	∞.	PROPN
ejpam-5113	31	28	it	it	PRON
ejpam-5113	31	29	is	be	AUX
ejpam-5113	31	30	a	a	DET
ejpam-5113	31	31	banach	banach	NOUN
ejpam-5113	31	32	space	space	NOUN
ejpam-5113	31	33	with	with	ADP
ejpam-5113	31	34	the	the	DET
ejpam-5113	31	35	norm	norm	NOUN
ejpam-5113	31	36	∥f∥zµ	∥f∥zµ	NOUN
ejpam-5113	31	37	=	=	SYM
ejpam-5113	31	38	|f(0)|+	|f(0)|+	NUM
ejpam-5113	31	39	|f	|f	ADP
ejpam-5113	31	40	′(0)|+	′(0)|+	NUM
ejpam-5113	31	41	sup	sup	NOUN
ejpam-5113	31	42	z∈d	z∈d	PROPN
ejpam-5113	31	43	µ(z)|f	µ(z)|f	PROPN
ejpam-5113	31	44	′′(z)|	′′(z)|	PROPN
ejpam-5113	31	45	.	.	PUNCT
ejpam-5113	32	1	when	when	SCONJ
ejpam-5113	32	2	µ(z	µ(z	PROPN
ejpam-5113	32	3	)	)	PUNCT
ejpam-5113	32	4	=	=	SYM
ejpam-5113	32	5	1	1	NUM
ejpam-5113	32	6	−	−	PROPN
ejpam-5113	32	7	|z|2	|z|2	PROPN
ejpam-5113	32	8	,	,	PUNCT
ejpam-5113	32	9	this	this	DET
ejpam-5113	32	10	space	space	NOUN
ejpam-5113	32	11	is	be	AUX
ejpam-5113	32	12	known	know	VERB
ejpam-5113	32	13	as	as	ADP
ejpam-5113	32	14	the	the	DET
ejpam-5113	32	15	classical	classical	ADJ
ejpam-5113	32	16	zygmund	zygmund	NOUN
ejpam-5113	32	17	space	space	NOUN
ejpam-5113	32	18	z.	z.	PROPN
ejpam-5113	32	19	from	from	ADP
ejpam-5113	32	20	zygmund	zygmund	PROPN
ejpam-5113	32	21	’s	’s	PART
ejpam-5113	32	22	theorem	theorem	NOUN
ejpam-5113	32	23	(	(	PUNCT
ejpam-5113	32	24	[	[	X
ejpam-5113	32	25	6	6	NUM
ejpam-5113	32	26	]	]	PUNCT
ejpam-5113	32	27	,	,	PUNCT
ejpam-5113	32	28	theorem	theorem	VERB
ejpam-5113	32	29	5.3),we	5.3),we	PRON
ejpam-5113	32	30	know	know	VERB
ejpam-5113	32	31	that	that	SCONJ
ejpam-5113	32	32	f	f	PROPN
ejpam-5113	32	33	∈	∈	PROPN
ejpam-5113	32	34	z	z	NOUN
ejpam-5113	33	1	if	if	SCONJ
ejpam-5113	33	2	and	and	CCONJ
ejpam-5113	33	3	only	only	ADV
ejpam-5113	33	4	if	if	SCONJ
ejpam-5113	33	5	f	f	PROPN
ejpam-5113	33	6	is	be	AUX
ejpam-5113	33	7	continuous	continuous	ADJ
ejpam-5113	33	8	on	on	ADP
ejpam-5113	33	9	d	d	PROPN
ejpam-5113	33	10	and	and	CCONJ
ejpam-5113	33	11	∥f∥	∥f∥	PROPN
ejpam-5113	33	12	=	=	SYM
ejpam-5113	33	13	sup	sup	NOUN
ejpam-5113	33	14	∣∣f	∣∣f	NOUN
ejpam-5113	33	15	(	(	PUNCT
ejpam-5113	33	16	ei(θ+h	ei(θ+h	PROPN
ejpam-5113	33	17	)	)	PUNCT
ejpam-5113	33	18	)	)	PUNCT
ejpam-5113	34	1	+	+	CCONJ
ejpam-5113	34	2	f	f	X
ejpam-5113	34	3	(	(	PUNCT
ejpam-5113	34	4	ei(θ−h	ei(θ−h	PROPN
ejpam-5113	34	5	)	)	PUNCT
ejpam-5113	34	6	)	)	PUNCT
ejpam-5113	35	1	−	−	ADP
ejpam-5113	35	2	2f	2f	NUM
ejpam-5113	35	3	(	(	PUNCT
ejpam-5113	35	4	eiθ	eiθ	NOUN
ejpam-5113	35	5	)	)	PUNCT
ejpam-5113	35	6	∣∣	∣∣	PROPN
ejpam-5113	35	7	h	h	NOUN
ejpam-5113	35	8	<	<	X
ejpam-5113	35	9	∞	∞	PROPN
ejpam-5113	35	10	,	,	PUNCT
ejpam-5113	35	11	where	where	SCONJ
ejpam-5113	35	12	the	the	DET
ejpam-5113	35	13	supremum	supremum	NOUN
ejpam-5113	35	14	is	be	AUX
ejpam-5113	35	15	taken	take	VERB
ejpam-5113	35	16	over	over	ADP
ejpam-5113	35	17	all	all	DET
ejpam-5113	35	18	θ	θ	NOUN
ejpam-5113	35	19	∈	∈	NOUN
ejpam-5113	35	20	r	r	NOUN
ejpam-5113	35	21	and	and	CCONJ
ejpam-5113	35	22	h	h	NOUN
ejpam-5113	35	23	>	>	X
ejpam-5113	35	24	0	0	X
ejpam-5113	35	25	.	.	PUNCT
ejpam-5113	36	1	let	let	VERB
ejpam-5113	36	2	g	g	PRON
ejpam-5113	36	3	be	be	AUX
ejpam-5113	36	4	an	an	DET
ejpam-5113	36	5	analytic	analytic	ADJ
ejpam-5113	36	6	function	function	NOUN
ejpam-5113	36	7	on	on	ADP
ejpam-5113	36	8	d	d	PROPN
ejpam-5113	36	9	,	,	PUNCT
ejpam-5113	36	10	the	the	DET
ejpam-5113	36	11	volterra	volterra	NOUN
ejpam-5113	36	12	type	type	NOUN
ejpam-5113	36	13	operator	operator	NOUN
ejpam-5113	36	14	(	(	PUNCT
ejpam-5113	36	15	see	see	VERB
ejpam-5113	36	16	[	[	X
ejpam-5113	36	17	18	18	NUM
ejpam-5113	36	18	]	]	PUNCT
ejpam-5113	36	19	)	)	PUNCT
ejpam-5113	36	20	is	be	AUX
ejpam-5113	36	21	defined	define	VERB
ejpam-5113	36	22	as	as	ADP
ejpam-5113	36	23	(	(	PUNCT
ejpam-5113	36	24	tgf	tgf	PROPN
ejpam-5113	36	25	)	)	PUNCT
ejpam-5113	36	26	(	(	PUNCT
ejpam-5113	36	27	z	z	X
ejpam-5113	36	28	)	)	PUNCT
ejpam-5113	36	29	=	=	SYM
ejpam-5113	37	1	∫	∫	PROPN
ejpam-5113	37	2	z	z	NOUN
ejpam-5113	37	3	0	0	NUM
ejpam-5113	37	4	f(ζ)g′(ζ)dζ	f(ζ)g′(ζ)dζ	NOUN
ejpam-5113	37	5	,	,	PUNCT
ejpam-5113	37	6	where	where	SCONJ
ejpam-5113	37	7	f	f	PROPN
ejpam-5113	37	8	∈	∈	PROPN
ejpam-5113	37	9	h(d	h(d	PROPN
ejpam-5113	37	10	)	)	PUNCT
ejpam-5113	37	11	and	and	CCONJ
ejpam-5113	37	12	z	z	PROPN
ejpam-5113	37	13	∈	∈	PROPN
ejpam-5113	37	14	d.	d.	PROPN
ejpam-5113	37	15	note	note	VERB
ejpam-5113	37	16	that	that	SCONJ
ejpam-5113	37	17	tg	tg	PROPN
ejpam-5113	37	18	can	can	AUX
ejpam-5113	37	19	be	be	AUX
ejpam-5113	37	20	viewed	view	VERB
ejpam-5113	37	21	as	as	ADP
ejpam-5113	37	22	a	a	DET
ejpam-5113	37	23	generalization	generalization	NOUN
ejpam-5113	37	24	of	of	ADP
ejpam-5113	37	25	the	the	DET
ejpam-5113	37	26	cesâro	cesâro	PROPN
ejpam-5113	37	27	operator	operator	NOUN
ejpam-5113	37	28	whose	whose	DET
ejpam-5113	37	29	first	first	ADV
ejpam-5113	37	30	studied	study	VERB
ejpam-5113	37	31	by	by	ADP
ejpam-5113	37	32	aleman	aleman	NOUN
ejpam-5113	37	33	and	and	CCONJ
ejpam-5113	37	34	siskkis	siskki	NOUN
ejpam-5113	38	1	[	[	X
ejpam-5113	38	2	4	4	NUM
ejpam-5113	38	3	]	]	PUNCT
ejpam-5113	38	4	.	.	PUNCT
ejpam-5113	39	1	it	it	PRON
ejpam-5113	39	2	is	be	AUX
ejpam-5113	39	3	natural	natural	ADJ
ejpam-5113	39	4	to	to	PART
ejpam-5113	39	5	define	define	VERB
ejpam-5113	39	6	another	another	DET
ejpam-5113	39	7	volterra	volterra	NOUN
ejpam-5113	39	8	type	type	NOUN
ejpam-5113	39	9	operator	operator	NOUN
ejpam-5113	39	10	ig	ig	PROPN
ejpam-5113	39	11	as	as	SCONJ
ejpam-5113	39	12	follows	follow	VERB
ejpam-5113	39	13	(	(	PUNCT
ejpam-5113	39	14	igf	igf	PROPN
ejpam-5113	39	15	)	)	PUNCT
ejpam-5113	39	16	(	(	PUNCT
ejpam-5113	39	17	z	z	NOUN
ejpam-5113	39	18	)	)	PUNCT
ejpam-5113	39	19	=	=	SYM
ejpam-5113	40	1	∫	∫	PROPN
ejpam-5113	40	2	z	z	NOUN
ejpam-5113	40	3	0	0	NUM
ejpam-5113	41	1	f	f	PROPN
ejpam-5113	41	2	′(ζ)g(ζ)dζ	′(ζ)g(ζ)dζ	PROPN
ejpam-5113	41	3	.	.	PUNCT
ejpam-5113	42	1	w.	w.	PROPN
ejpam-5113	42	2	al	al	PROPN
ejpam-5113	42	3	-	-	PUNCT
ejpam-5113	42	4	rawashdeh	rawashdeh	PROPN
ejpam-5113	42	5	/	/	SYM
ejpam-5113	42	6	eur	eur	PROPN
ejpam-5113	42	7	.	.	PUNCT
ejpam-5113	43	1	j.	j.	PROPN
ejpam-5113	43	2	pure	pure	PROPN
ejpam-5113	43	3	appl	appl	PROPN
ejpam-5113	43	4	.	.	PROPN
ejpam-5113	43	5	math	math	PROPN
ejpam-5113	43	6	,	,	PUNCT
ejpam-5113	43	7	17	17	NUM
ejpam-5113	43	8	(	(	PUNCT
ejpam-5113	43	9	2	2	NUM
ejpam-5113	43	10	)	)	PUNCT
ejpam-5113	43	11	(	(	PUNCT
ejpam-5113	43	12	2024	2024	NUM
ejpam-5113	43	13	)	)	PUNCT
ejpam-5113	43	14	,	,	PUNCT
ejpam-5113	43	15	931	931	NUM
ejpam-5113	43	16	-	-	SYM
ejpam-5113	43	17	944	944	NUM
ejpam-5113	43	18	933	933	NUM
ejpam-5113	43	19	recently	recently	ADV
ejpam-5113	43	20	,	,	PUNCT
ejpam-5113	43	21	many	many	ADJ
ejpam-5113	43	22	researchers	researcher	NOUN
ejpam-5113	43	23	considered	consider	VERB
ejpam-5113	43	24	these	these	DET
ejpam-5113	43	25	operators	operator	NOUN
ejpam-5113	43	26	and	and	CCONJ
ejpam-5113	43	27	characterized	characterize	VERB
ejpam-5113	43	28	their	their	PRON
ejpam-5113	43	29	boundedness	boundedness	NOUN
ejpam-5113	43	30	and	and	CCONJ
ejpam-5113	43	31	compactness	compactness	NOUN
ejpam-5113	43	32	between	between	ADP
ejpam-5113	43	33	various	various	ADJ
ejpam-5113	43	34	spaces	space	NOUN
ejpam-5113	43	35	of	of	ADP
ejpam-5113	43	36	analytic	analytic	ADJ
ejpam-5113	43	37	functions	function	NOUN
ejpam-5113	43	38	,	,	PUNCT
ejpam-5113	43	39	for	for	ADP
ejpam-5113	43	40	example	example	NOUN
ejpam-5113	43	41	see	see	VERB
ejpam-5113	43	42	(	(	PUNCT
ejpam-5113	43	43	[	[	X
ejpam-5113	43	44	3	3	NUM
ejpam-5113	43	45	]	]	PUNCT
ejpam-5113	43	46	,	,	PUNCT
ejpam-5113	43	47	[	[	X
ejpam-5113	43	48	8	8	NUM
ejpam-5113	43	49	]	]	PUNCT
ejpam-5113	43	50	,	,	PUNCT
ejpam-5113	43	51	[	[	X
ejpam-5113	43	52	10	10	NUM
ejpam-5113	43	53	]	]	PUNCT
ejpam-5113	43	54	,	,	PUNCT
ejpam-5113	43	55	[	[	X
ejpam-5113	43	56	11	11	NUM
ejpam-5113	43	57	]	]	PUNCT
ejpam-5113	43	58	,	,	PUNCT
ejpam-5113	43	59	[	[	X
ejpam-5113	43	60	12	12	NUM
ejpam-5113	43	61	]	]	PUNCT
ejpam-5113	43	62	,	,	PUNCT
ejpam-5113	43	63	[	[	X
ejpam-5113	43	64	13	13	NUM
ejpam-5113	43	65	]	]	PUNCT
ejpam-5113	43	66	,	,	PUNCT
ejpam-5113	43	67	[	[	X
ejpam-5113	43	68	14	14	NUM
ejpam-5113	43	69	]	]	PUNCT
ejpam-5113	43	70	,	,	PUNCT
ejpam-5113	43	71	[	[	X
ejpam-5113	43	72	16	16	NUM
ejpam-5113	43	73	]	]	PUNCT
ejpam-5113	43	74	,	,	PUNCT
ejpam-5113	43	75	[	[	X
ejpam-5113	43	76	20	20	NUM
ejpam-5113	43	77	]	]	PUNCT
ejpam-5113	43	78	)	)	PUNCT
ejpam-5113	43	79	and	and	CCONJ
ejpam-5113	43	80	the	the	DET
ejpam-5113	43	81	references	reference	NOUN
ejpam-5113	43	82	therein	therein	ADV
ejpam-5113	43	83	.	.	PUNCT
ejpam-5113	44	1	let	let	VERB
ejpam-5113	44	2	φ	φ	PROPN
ejpam-5113	44	3	be	be	AUX
ejpam-5113	44	4	an	an	DET
ejpam-5113	44	5	analytic	analytic	ADJ
ejpam-5113	44	6	function	function	NOUN
ejpam-5113	44	7	maps	map	NOUN
ejpam-5113	44	8	d	d	NOUN
ejpam-5113	44	9	into	into	ADP
ejpam-5113	44	10	itself	itself	PRON
ejpam-5113	44	11	,	,	PUNCT
ejpam-5113	44	12	the	the	DET
ejpam-5113	44	13	composition	composition	NOUN
ejpam-5113	44	14	operator	operator	NOUN
ejpam-5113	44	15	induced	induce	VERB
ejpam-5113	44	16	by	by	ADP
ejpam-5113	44	17	φ	φ	PROPN
ejpam-5113	44	18	is	be	AUX
ejpam-5113	44	19	defined	define	VERB
ejpam-5113	44	20	on	on	ADP
ejpam-5113	44	21	the	the	DET
ejpam-5113	44	22	space	space	NOUN
ejpam-5113	44	23	h(d	h(d	PROPN
ejpam-5113	44	24	)	)	PUNCT
ejpam-5113	44	25	of	of	ADP
ejpam-5113	44	26	all	all	DET
ejpam-5113	44	27	analytic	analytic	ADJ
ejpam-5113	44	28	functions	function	NOUN
ejpam-5113	44	29	on	on	ADP
ejpam-5113	44	30	d	d	X
ejpam-5113	44	31	by	by	ADP
ejpam-5113	44	32	cφf(z	cφf(z	NOUN
ejpam-5113	44	33	)	)	PUNCT
ejpam-5113	44	34	=	=	SYM
ejpam-5113	44	35	f(φ(z	f(φ(z	NOUN
ejpam-5113	44	36	)	)	PUNCT
ejpam-5113	44	37	)	)	PUNCT
ejpam-5113	44	38	,	,	PUNCT
ejpam-5113	44	39	for	for	ADP
ejpam-5113	44	40	all	all	DET
ejpam-5113	44	41	f	f	PROPN
ejpam-5113	44	42	∈	∈	PROPN
ejpam-5113	44	43	h(d	h(d	PROPN
ejpam-5113	44	44	)	)	PUNCT
ejpam-5113	44	45	and	and	CCONJ
ejpam-5113	44	46	z	z	NOUN
ejpam-5113	44	47	∈	∈	PROPN
ejpam-5113	44	48	d.	d.	NOUN
ejpam-5113	44	49	it	it	PRON
ejpam-5113	44	50	is	be	AUX
ejpam-5113	44	51	well	well	ADV
ejpam-5113	44	52	known	know	VERB
ejpam-5113	44	53	that	that	SCONJ
ejpam-5113	44	54	the	the	DET
ejpam-5113	44	55	composition	composition	NOUN
ejpam-5113	44	56	operator	operator	NOUN
ejpam-5113	44	57	cφf	cφf	NOUN
ejpam-5113	44	58	=	=	SYM
ejpam-5113	44	59	f	f	PROPN
ejpam-5113	44	60	◦	◦	NOUN
ejpam-5113	44	61	φ	φ	PROPN
ejpam-5113	44	62	defines	define	VERB
ejpam-5113	44	63	a	a	DET
ejpam-5113	44	64	linear	linear	ADJ
ejpam-5113	44	65	operator	operator	NOUN
ejpam-5113	44	66	cφ	cφ	NOUN
ejpam-5113	44	67	which	which	PRON
ejpam-5113	44	68	acts	act	VERB
ejpam-5113	44	69	boundedly	boundedly	ADV
ejpam-5113	44	70	on	on	ADP
ejpam-5113	44	71	various	various	ADJ
ejpam-5113	44	72	spaces	space	NOUN
ejpam-5113	44	73	of	of	ADP
ejpam-5113	44	74	analytic	analytic	ADJ
ejpam-5113	44	75	or	or	CCONJ
ejpam-5113	44	76	harmonic	harmonic	ADJ
ejpam-5113	44	77	functions	function	NOUN
ejpam-5113	44	78	on	on	ADP
ejpam-5113	44	79	d.	d.	PROPN
ejpam-5113	44	80	these	these	DET
ejpam-5113	44	81	operators	operator	NOUN
ejpam-5113	44	82	have	have	AUX
ejpam-5113	44	83	been	be	AUX
ejpam-5113	44	84	studied	study	VERB
ejpam-5113	44	85	on	on	ADP
ejpam-5113	44	86	many	many	ADJ
ejpam-5113	44	87	spaces	space	NOUN
ejpam-5113	44	88	of	of	ADP
ejpam-5113	44	89	analytic	analytic	ADJ
ejpam-5113	44	90	functions	function	NOUN
ejpam-5113	44	91	.	.	PUNCT
ejpam-5113	45	1	during	during	ADP
ejpam-5113	45	2	the	the	DET
ejpam-5113	45	3	past	past	ADJ
ejpam-5113	45	4	few	few	ADJ
ejpam-5113	45	5	decades	decade	NOUN
ejpam-5113	45	6	much	much	ADJ
ejpam-5113	45	7	effort	effort	NOUN
ejpam-5113	45	8	has	have	AUX
ejpam-5113	45	9	been	be	AUX
ejpam-5113	45	10	devoted	devote	VERB
ejpam-5113	45	11	to	to	ADP
ejpam-5113	45	12	the	the	DET
ejpam-5113	45	13	study	study	NOUN
ejpam-5113	45	14	of	of	ADP
ejpam-5113	45	15	these	these	DET
ejpam-5113	45	16	operators	operator	NOUN
ejpam-5113	45	17	with	with	ADP
ejpam-5113	45	18	the	the	DET
ejpam-5113	45	19	goal	goal	NOUN
ejpam-5113	45	20	of	of	ADP
ejpam-5113	45	21	explaining	explain	VERB
ejpam-5113	45	22	the	the	DET
ejpam-5113	45	23	operator	operator	NOUN
ejpam-5113	45	24	-	-	PUNCT
ejpam-5113	45	25	theoretic	theoretic	NOUN
ejpam-5113	45	26	properties	property	NOUN
ejpam-5113	45	27	of	of	ADP
ejpam-5113	45	28	cφ	cφ	NOUN
ejpam-5113	45	29	in	in	ADP
ejpam-5113	45	30	terms	term	NOUN
ejpam-5113	45	31	of	of	ADP
ejpam-5113	45	32	the	the	DET
ejpam-5113	45	33	function	function	NOUN
ejpam-5113	45	34	-	-	PUNCT
ejpam-5113	45	35	theoretic	theoretic	NOUN
ejpam-5113	45	36	properties	property	NOUN
ejpam-5113	45	37	of	of	ADP
ejpam-5113	45	38	the	the	DET
ejpam-5113	45	39	induced	induced	ADJ
ejpam-5113	45	40	map	map	NOUN
ejpam-5113	45	41	φ	φ	NOUN
ejpam-5113	45	42	.	.	PUNCT
ejpam-5113	46	1	we	we	PRON
ejpam-5113	46	2	refer	refer	VERB
ejpam-5113	46	3	the	the	DET
ejpam-5113	46	4	reader	reader	NOUN
ejpam-5113	46	5	to	to	ADP
ejpam-5113	46	6	the	the	DET
ejpam-5113	46	7	monographs	monograph	NOUN
ejpam-5113	46	8	(	(	PUNCT
ejpam-5113	46	9	[	[	X
ejpam-5113	46	10	5	5	NUM
ejpam-5113	46	11	]	]	PUNCT
ejpam-5113	46	12	,	,	PUNCT
ejpam-5113	46	13	[	[	X
ejpam-5113	46	14	7	7	NUM
ejpam-5113	46	15	]	]	PUNCT
ejpam-5113	46	16	,	,	PUNCT
ejpam-5113	46	17	[	[	X
ejpam-5113	46	18	9	9	NUM
ejpam-5113	46	19	]	]	PUNCT
ejpam-5113	46	20	,	,	PUNCT
ejpam-5113	46	21	[	[	X
ejpam-5113	46	22	15	15	NUM
ejpam-5113	46	23	]	]	PUNCT
ejpam-5113	46	24	,	,	PUNCT
ejpam-5113	46	25	[	[	X
ejpam-5113	46	26	17	17	NUM
ejpam-5113	46	27	]	]	PUNCT
ejpam-5113	46	28	,	,	PUNCT
ejpam-5113	46	29	[	[	X
ejpam-5113	46	30	22	22	NUM
ejpam-5113	46	31	]	]	PUNCT
ejpam-5113	46	32	,	,	PUNCT
ejpam-5113	46	33	[	[	X
ejpam-5113	46	34	23	23	NUM
ejpam-5113	46	35	]	]	PUNCT
ejpam-5113	46	36	)	)	PUNCT
ejpam-5113	46	37	and	and	CCONJ
ejpam-5113	46	38	the	the	DET
ejpam-5113	46	39	references	reference	NOUN
ejpam-5113	46	40	therein	therein	ADV
ejpam-5113	46	41	.	.	PUNCT
ejpam-5113	47	1	let	let	VERB
ejpam-5113	47	2	g	g	PRON
ejpam-5113	47	3	be	be	AUX
ejpam-5113	47	4	a	a	DET
ejpam-5113	47	5	fixed	fix	VERB
ejpam-5113	47	6	analytic	analytic	ADJ
ejpam-5113	47	7	function	function	NOUN
ejpam-5113	47	8	on	on	ADP
ejpam-5113	47	9	d	d	PROPN
ejpam-5113	47	10	,	,	PUNCT
ejpam-5113	47	11	f	f	PROPN
ejpam-5113	47	12	an	an	DET
ejpam-5113	47	13	analytic	analytic	ADJ
ejpam-5113	47	14	function	function	NOUN
ejpam-5113	47	15	of	of	ADP
ejpam-5113	47	16	d	d	PROPN
ejpam-5113	47	17	and	and	CCONJ
ejpam-5113	47	18	z	z	PROPN
ejpam-5113	47	19	∈	∈	PROPN
ejpam-5113	47	20	d.	d.	PROPN
ejpam-5113	47	21	the	the	DET
ejpam-5113	47	22	volterra	volterra	PROPN
ejpam-5113	47	23	type	type	NOUN
ejpam-5113	47	24	composition	composition	NOUN
ejpam-5113	47	25	operators	operator	NOUN
ejpam-5113	47	26	are	be	AUX
ejpam-5113	47	27	defined	define	VERB
ejpam-5113	47	28	as	as	ADP
ejpam-5113	47	29	(	(	PUNCT
ejpam-5113	47	30	tφ	tφ	PROPN
ejpam-5113	47	31	g	g	PROPN
ejpam-5113	47	32	f	f	PROPN
ejpam-5113	47	33	)	)	PUNCT
ejpam-5113	48	1	(	(	PUNCT
ejpam-5113	48	2	z	z	X
ejpam-5113	48	3	)	)	PUNCT
ejpam-5113	48	4	=	=	SYM
ejpam-5113	48	5	∫	∫	PROPN
ejpam-5113	48	6	z	z	NOUN
ejpam-5113	48	7	0	0	NUM
ejpam-5113	48	8	f(φ(ζ))g′(ζ)dζ	f(φ(ζ))g′(ζ)dζ	NOUN
ejpam-5113	48	9	,	,	PUNCT
ejpam-5113	48	10	(	(	PUNCT
ejpam-5113	48	11	iφg	iφg	NOUN
ejpam-5113	48	12	f	f	PROPN
ejpam-5113	48	13	)	)	PUNCT
ejpam-5113	49	1	(	(	PUNCT
ejpam-5113	49	2	z	z	X
ejpam-5113	49	3	)	)	PUNCT
ejpam-5113	49	4	=	=	SYM
ejpam-5113	50	1	∫	∫	PROPN
ejpam-5113	50	2	z	z	NOUN
ejpam-5113	50	3	0	0	NUM
ejpam-5113	50	4	f	f	PROPN
ejpam-5113	50	5	′(φ(ζ))g(ζ)dζ	′(φ(ζ))g(ζ)dζ	PROPN
ejpam-5113	50	6	.	.	PUNCT
ejpam-5113	51	1	the	the	DET
ejpam-5113	51	2	classical	classical	ADJ
ejpam-5113	51	3	volterra	volterra	NOUN
ejpam-5113	51	4	operators	operator	NOUN
ejpam-5113	51	5	are	be	AUX
ejpam-5113	51	6	obtained	obtain	VERB
ejpam-5113	51	7	in	in	ADP
ejpam-5113	51	8	the	the	DET
ejpam-5113	51	9	case	case	NOUN
ejpam-5113	51	10	when	when	SCONJ
ejpam-5113	51	11	φ(z	φ(z	PROPN
ejpam-5113	51	12	)	)	PUNCT
ejpam-5113	51	13	=	=	PUNCT
ejpam-5113	52	1	z.	z.	NOUN
ejpam-5113	53	1	these	these	DET
ejpam-5113	53	2	operators	operator	NOUN
ejpam-5113	53	3	have	have	AUX
ejpam-5113	53	4	been	be	AUX
ejpam-5113	53	5	studied	study	VERB
ejpam-5113	53	6	by	by	ADP
ejpam-5113	53	7	many	many	ADJ
ejpam-5113	53	8	researchers	researcher	NOUN
ejpam-5113	53	9	,	,	PUNCT
ejpam-5113	53	10	for	for	ADP
ejpam-5113	53	11	example	example	NOUN
ejpam-5113	53	12	see	see	VERB
ejpam-5113	53	13	(	(	PUNCT
ejpam-5113	53	14	[	[	X
ejpam-5113	53	15	3	3	NUM
ejpam-5113	53	16	]	]	PUNCT
ejpam-5113	53	17	,	,	PUNCT
ejpam-5113	54	1	[	[	X
ejpam-5113	54	2	11	11	NUM
ejpam-5113	54	3	]	]	PUNCT
ejpam-5113	54	4	,	,	PUNCT
ejpam-5113	54	5	[	[	X
ejpam-5113	54	6	12	12	NUM
ejpam-5113	54	7	]	]	PUNCT
ejpam-5113	54	8	,	,	PUNCT
ejpam-5113	54	9	[	[	X
ejpam-5113	54	10	19	19	NUM
ejpam-5113	54	11	]	]	PUNCT
ejpam-5113	54	12	,	,	PUNCT
ejpam-5113	55	1	[	[	X
ejpam-5113	55	2	21	21	NUM
ejpam-5113	55	3	]	]	PUNCT
ejpam-5113	55	4	,	,	PUNCT
ejpam-5113	56	1	[	[	X
ejpam-5113	56	2	24	24	NUM
ejpam-5113	56	3	]	]	PUNCT
ejpam-5113	56	4	,	,	PUNCT
ejpam-5113	56	5	[	[	X
ejpam-5113	56	6	25	25	NUM
ejpam-5113	56	7	]	]	PUNCT
ejpam-5113	56	8	)	)	PUNCT
ejpam-5113	56	9	and	and	CCONJ
ejpam-5113	56	10	the	the	DET
ejpam-5113	56	11	references	reference	NOUN
ejpam-5113	56	12	therein	therein	ADV
ejpam-5113	56	13	.	.	PUNCT
ejpam-5113	57	1	in	in	ADP
ejpam-5113	57	2	this	this	DET
ejpam-5113	57	3	paper	paper	NOUN
ejpam-5113	57	4	,	,	PUNCT
ejpam-5113	57	5	we	we	PRON
ejpam-5113	57	6	are	be	AUX
ejpam-5113	57	7	investigating	investigate	VERB
ejpam-5113	57	8	the	the	DET
ejpam-5113	57	9	boundedness	boundedness	NOUN
ejpam-5113	57	10	and	and	CCONJ
ejpam-5113	57	11	compactness	compactness	NOUN
ejpam-5113	57	12	of	of	ADP
ejpam-5113	57	13	the	the	DET
ejpam-5113	57	14	volterra	volterra	NOUN
ejpam-5113	57	15	type	type	NOUN
ejpam-5113	57	16	composition	composition	NOUN
ejpam-5113	57	17	operators	operator	NOUN
ejpam-5113	57	18	tφ	tφ	VERB
ejpam-5113	57	19	g	g	PROPN
ejpam-5113	57	20	and	and	CCONJ
ejpam-5113	57	21	iφg	iφg	NOUN
ejpam-5113	57	22	acting	act	VERB
ejpam-5113	57	23	between	between	ADP
ejpam-5113	57	24	sp(d	sp(d	NOUN
ejpam-5113	57	25	)	)	PUNCT
ejpam-5113	57	26	spaces	space	NOUN
ejpam-5113	57	27	and	and	CCONJ
ejpam-5113	57	28	weighted	weight	VERB
ejpam-5113	57	29	zygmund	zygmund	PROPN
ejpam-5113	57	30	spaces	space	NOUN
ejpam-5113	57	31	zµ.	zµ.	PROPN
ejpam-5113	57	32	2	2	NUM
ejpam-5113	57	33	.	.	PUNCT
ejpam-5113	57	34	preliminaries	preliminary	NOUN
ejpam-5113	57	35	in	in	ADP
ejpam-5113	57	36	this	this	DET
ejpam-5113	57	37	section	section	NOUN
ejpam-5113	57	38	we	we	PRON
ejpam-5113	57	39	present	present	VERB
ejpam-5113	57	40	some	some	PRON
ejpam-5113	57	41	well	well	ADV
ejpam-5113	57	42	known	know	VERB
ejpam-5113	57	43	,	,	PUNCT
ejpam-5113	57	44	but	but	CCONJ
ejpam-5113	57	45	useful	useful	ADJ
ejpam-5113	57	46	,	,	PUNCT
ejpam-5113	57	47	information	information	NOUN
ejpam-5113	57	48	that	that	PRON
ejpam-5113	57	49	are	be	AUX
ejpam-5113	57	50	curial	curial	ADJ
ejpam-5113	57	51	for	for	ADP
ejpam-5113	57	52	the	the	DET
ejpam-5113	57	53	main	main	ADJ
ejpam-5113	57	54	results	result	NOUN
ejpam-5113	57	55	of	of	ADP
ejpam-5113	57	56	this	this	DET
ejpam-5113	57	57	paper	paper	NOUN
ejpam-5113	57	58	.	.	PUNCT
ejpam-5113	58	1	the	the	DET
ejpam-5113	58	2	following	follow	VERB
ejpam-5113	58	3	lemma	lemma	PROPN
ejpam-5113	58	4	is	be	AUX
ejpam-5113	58	5	a	a	DET
ejpam-5113	58	6	well	well	ADV
ejpam-5113	58	7	known	know	VERB
ejpam-5113	58	8	fact	fact	NOUN
ejpam-5113	58	9	that	that	PRON
ejpam-5113	58	10	can	can	AUX
ejpam-5113	58	11	be	be	AUX
ejpam-5113	58	12	proven	prove	VERB
ejpam-5113	58	13	by	by	ADP
ejpam-5113	58	14	using	use	VERB
ejpam-5113	58	15	cauchy	cauchy	ADJ
ejpam-5113	58	16	estimates	estimate	NOUN
ejpam-5113	58	17	,	,	PUNCT
ejpam-5113	58	18	so	so	SCONJ
ejpam-5113	58	19	we	we	PRON
ejpam-5113	58	20	omit	omit	VERB
ejpam-5113	58	21	the	the	DET
ejpam-5113	58	22	proof	proof	NOUN
ejpam-5113	58	23	.	.	PUNCT
ejpam-5113	59	1	lemma	lemma	PROPN
ejpam-5113	59	2	1	1	NUM
ejpam-5113	59	3	.	.	PUNCT
ejpam-5113	60	1	if	if	SCONJ
ejpam-5113	60	2	{	{	PUNCT
ejpam-5113	60	3	fn	fn	NOUN
ejpam-5113	60	4	}	}	PUNCT
ejpam-5113	60	5	is	be	AUX
ejpam-5113	60	6	a	a	DET
ejpam-5113	60	7	sequence	sequence	NOUN
ejpam-5113	60	8	converges	converge	NOUN
ejpam-5113	60	9	to	to	ADP
ejpam-5113	60	10	zero	zero	NUM
ejpam-5113	60	11	on	on	ADP
ejpam-5113	60	12	compact	compact	ADJ
ejpam-5113	60	13	subsets	subset	NOUN
ejpam-5113	60	14	of	of	ADP
ejpam-5113	60	15	d	d	NOUN
ejpam-5113	60	16	,	,	PUNCT
ejpam-5113	60	17	then	then	ADV
ejpam-5113	60	18	{	{	PUNCT
ejpam-5113	60	19	f	f	NOUN
ejpam-5113	60	20	′	′	NUM
ejpam-5113	60	21	n	n	CCONJ
ejpam-5113	60	22	}	}	PUNCT
ejpam-5113	60	23	also	also	ADV
ejpam-5113	60	24	converges	converge	VERB
ejpam-5113	60	25	to	to	ADP
ejpam-5113	60	26	zero	zero	NUM
ejpam-5113	60	27	on	on	ADP
ejpam-5113	60	28	compact	compact	ADJ
ejpam-5113	60	29	subsets	subset	NOUN
ejpam-5113	60	30	of	of	ADP
ejpam-5113	60	31	d	d	PROPN
ejpam-5113	60	32	as	as	ADP
ejpam-5113	60	33	n	n	PROPN
ejpam-5113	60	34	→	→	SYM
ejpam-5113	60	35	∞.	∞.	PROPN
ejpam-5113	60	36	in	in	ADP
ejpam-5113	60	37	particular	particular	ADJ
ejpam-5113	60	38	if	if	SCONJ
ejpam-5113	60	39	k	k	PROPN
ejpam-5113	60	40	is	be	AUX
ejpam-5113	60	41	a	a	DET
ejpam-5113	60	42	compact	compact	ADJ
ejpam-5113	60	43	subset	subset	NOUN
ejpam-5113	60	44	of	of	ADP
ejpam-5113	60	45	d	d	PROPN
ejpam-5113	60	46	,	,	PUNCT
ejpam-5113	60	47	then	then	ADV
ejpam-5113	60	48	lim	lim	PROPN
ejpam-5113	60	49	n→∞	n→∞	NUM
ejpam-5113	60	50	sup	sup	NOUN
ejpam-5113	60	51	w∈k	w∈k	NOUN
ejpam-5113	60	52	|f	|f	PROPN
ejpam-5113	60	53	′(w)|	′(w)|	X
ejpam-5113	61	1	=	=	PUNCT
ejpam-5113	61	2	0	0	X
ejpam-5113	61	3	.	.	PUNCT
ejpam-5113	62	1	the	the	DET
ejpam-5113	62	2	following	follow	VERB
ejpam-5113	62	3	lemma	lemma	PROPN
ejpam-5113	62	4	is	be	AUX
ejpam-5113	62	5	a	a	DET
ejpam-5113	62	6	know	know	ADJ
ejpam-5113	62	7	fact	fact	NOUN
ejpam-5113	62	8	,	,	PUNCT
ejpam-5113	62	9	for	for	ADP
ejpam-5113	62	10	the	the	DET
ejpam-5113	62	11	readers	reader	NOUN
ejpam-5113	62	12	who	who	PRON
ejpam-5113	62	13	are	be	AUX
ejpam-5113	62	14	interested	interested	ADJ
ejpam-5113	62	15	in	in	ADP
ejpam-5113	62	16	its	its	PRON
ejpam-5113	62	17	proof	proof	NOUN
ejpam-5113	62	18	we	we	PRON
ejpam-5113	62	19	refer	refer	VERB
ejpam-5113	62	20	them	they	PRON
ejpam-5113	62	21	to	to	ADP
ejpam-5113	62	22	(	(	PUNCT
ejpam-5113	62	23	theorem	theorem	NOUN
ejpam-5113	62	24	1	1	NUM
ejpam-5113	62	25	,	,	PUNCT
ejpam-5113	62	26	[	[	X
ejpam-5113	62	27	16	16	NUM
ejpam-5113	62	28	]	]	PUNCT
ejpam-5113	62	29	)	)	PUNCT
ejpam-5113	62	30	.	.	PUNCT
ejpam-5113	63	1	w.	w.	PROPN
ejpam-5113	63	2	al	al	PROPN
ejpam-5113	63	3	-	-	PUNCT
ejpam-5113	63	4	rawashdeh	rawashdeh	PROPN
ejpam-5113	63	5	/	/	SYM
ejpam-5113	63	6	eur	eur	PROPN
ejpam-5113	63	7	.	.	PUNCT
ejpam-5113	64	1	j.	j.	PROPN
ejpam-5113	64	2	pure	pure	PROPN
ejpam-5113	64	3	appl	appl	PROPN
ejpam-5113	64	4	.	.	PROPN
ejpam-5113	64	5	math	math	PROPN
ejpam-5113	64	6	,	,	PUNCT
ejpam-5113	64	7	17	17	NUM
ejpam-5113	64	8	(	(	PUNCT
ejpam-5113	64	9	2	2	NUM
ejpam-5113	64	10	)	)	PUNCT
ejpam-5113	64	11	(	(	PUNCT
ejpam-5113	64	12	2024	2024	NUM
ejpam-5113	64	13	)	)	PUNCT
ejpam-5113	64	14	,	,	PUNCT
ejpam-5113	64	15	931	931	NUM
ejpam-5113	64	16	-	-	SYM
ejpam-5113	64	17	944	944	NUM
ejpam-5113	64	18	934	934	NUM
ejpam-5113	64	19	lemma	lemma	PROPN
ejpam-5113	64	20	2	2	NUM
ejpam-5113	64	21	.	.	PUNCT
ejpam-5113	65	1	if	if	SCONJ
ejpam-5113	65	2	1	1	NUM
ejpam-5113	65	3	≤	≤	NOUN
ejpam-5113	65	4	p	p	X
ejpam-5113	65	5	<	<	X
ejpam-5113	65	6	∞	∞	PROPN
ejpam-5113	65	7	,	,	PUNCT
ejpam-5113	65	8	the	the	DET
ejpam-5113	65	9	following	follow	VERB
ejpam-5113	65	10	are	be	AUX
ejpam-5113	65	11	true	true	ADJ
ejpam-5113	65	12	:	:	PUNCT
ejpam-5113	65	13	(	(	PUNCT
ejpam-5113	65	14	i	i	NOUN
ejpam-5113	65	15	)	)	PUNCT
ejpam-5113	65	16	sp(d	sp(d	PUNCT
ejpam-5113	65	17	)	)	PUNCT
ejpam-5113	66	1	⊂	⊂	PROPN
ejpam-5113	66	2	s1(d	s1(d	X
ejpam-5113	66	3	)	)	PUNCT
ejpam-5113	66	4	⊂	⊂	PROPN
ejpam-5113	66	5	h∞	h∞	PROPN
ejpam-5113	66	6	;	;	PUNCT
ejpam-5113	66	7	(	(	PUNCT
ejpam-5113	66	8	ii	ii	NOUN
ejpam-5113	66	9	)	)	PUNCT
ejpam-5113	66	10	∥f∥∞	∥f∥∞	NUM
ejpam-5113	66	11	≤	≤	NUM
ejpam-5113	66	12	π∥f∥s1(d	π∥f∥s1(d	NUM
ejpam-5113	66	13	)	)	PUNCT
ejpam-5113	66	14	≤	≤	NUM
ejpam-5113	66	15	π∥f∥sp(d	π∥f∥sp(d	NOUN
ejpam-5113	66	16	)	)	PUNCT
ejpam-5113	66	17	;	;	PUNCT
ejpam-5113	66	18	(	(	PUNCT
ejpam-5113	66	19	iii	iii	X
ejpam-5113	66	20	)	)	PUNCT
ejpam-5113	66	21	sp(d	sp(d	PUNCT
ejpam-5113	66	22	)	)	PUNCT
ejpam-5113	66	23	is	be	AUX
ejpam-5113	66	24	a	a	DET
ejpam-5113	66	25	banach	banach	NOUN
ejpam-5113	66	26	algebra	algebra	NOUN
ejpam-5113	66	27	;	;	PUNCT
ejpam-5113	66	28	(	(	PUNCT
ejpam-5113	66	29	iv	iv	X
ejpam-5113	66	30	)	)	PUNCT
ejpam-5113	66	31	polynomials	polynomial	NOUN
ejpam-5113	66	32	are	be	AUX
ejpam-5113	66	33	dense	dense	ADJ
ejpam-5113	66	34	in	in	ADP
ejpam-5113	66	35	sp(d	sp(d	NOUN
ejpam-5113	66	36	)	)	PUNCT
ejpam-5113	66	37	.	.	PUNCT
ejpam-5113	67	1	3	3	X
ejpam-5113	67	2	.	.	X
ejpam-5113	67	3	boundedness	boundedness	NOUN
ejpam-5113	67	4	and	and	CCONJ
ejpam-5113	67	5	compactness	compactness	NOUN
ejpam-5113	67	6	of	of	ADP
ejpam-5113	67	7	iφg	iφg	NOUN
ejpam-5113	67	8	in	in	ADP
ejpam-5113	67	9	this	this	DET
ejpam-5113	67	10	section	section	NOUN
ejpam-5113	67	11	,	,	PUNCT
ejpam-5113	67	12	we	we	PRON
ejpam-5113	67	13	characterize	characterize	VERB
ejpam-5113	67	14	the	the	DET
ejpam-5113	67	15	boundedness	boundedness	NOUN
ejpam-5113	67	16	and	and	CCONJ
ejpam-5113	67	17	compactness	compactness	NOUN
ejpam-5113	67	18	of	of	ADP
ejpam-5113	67	19	the	the	DET
ejpam-5113	67	20	operator	operator	NOUN
ejpam-5113	67	21	iφg	iφg	NOUN
ejpam-5113	67	22	acting	act	VERB
ejpam-5113	67	23	between	between	ADP
ejpam-5113	67	24	sp	sp	ADP
ejpam-5113	67	25	spaces	space	NOUN
ejpam-5113	67	26	and	and	CCONJ
ejpam-5113	67	27	weighted	weight	VERB
ejpam-5113	67	28	zygmund	zygmund	PROPN
ejpam-5113	67	29	spaces	spaces	PROPN
ejpam-5113	67	30	zµ.	zµ.	PRON
ejpam-5113	67	31	the	the	DET
ejpam-5113	67	32	results	result	NOUN
ejpam-5113	67	33	will	will	AUX
ejpam-5113	67	34	be	be	AUX
ejpam-5113	67	35	written	write	VERB
ejpam-5113	67	36	in	in	ADP
ejpam-5113	67	37	terms	term	NOUN
ejpam-5113	67	38	of	of	ADP
ejpam-5113	67	39	k1(z	k1(z	PROPN
ejpam-5113	67	40	)	)	PUNCT
ejpam-5113	67	41	=	=	NOUN
ejpam-5113	67	42	µ(z)|g′(z)|	µ(z)|g′(z)|	X
ejpam-5113	67	43	(	(	PUNCT
ejpam-5113	67	44	1−	1−	NUM
ejpam-5113	67	45	|φ(z)|2)1	|φ(z)|2)1	NOUN
ejpam-5113	67	46	/	/	SYM
ejpam-5113	67	47	p	p	NOUN
ejpam-5113	67	48	,	,	PUNCT
ejpam-5113	67	49	and	and	CCONJ
ejpam-5113	67	50	k2(z	k2(z	PROPN
ejpam-5113	67	51	)	)	PUNCT
ejpam-5113	67	52	=	=	PUNCT
ejpam-5113	67	53	µ(z)|g(z)||φ′(z)|	µ(z)|g(z)||φ′(z)|	VERB
ejpam-5113	67	54	(	(	PUNCT
ejpam-5113	67	55	1−	1−	NUM
ejpam-5113	67	56	|φ(z)|2)(1+p)/p	|φ(z)|2)(1+p)/p	NOUN
ejpam-5113	67	57	,	,	PUNCT
ejpam-5113	68	1	where	where	SCONJ
ejpam-5113	68	2	z	z	PROPN
ejpam-5113	68	3	∈	∈	PROPN
ejpam-5113	68	4	d	d	NOUN
ejpam-5113	68	5	,	,	PUNCT
ejpam-5113	68	6	g	g	PROPN
ejpam-5113	68	7	∈	∈	PROPN
ejpam-5113	68	8	h(d	h(d	PROPN
ejpam-5113	68	9	)	)	PUNCT
ejpam-5113	68	10	,	,	PUNCT
ejpam-5113	68	11	and	and	CCONJ
ejpam-5113	68	12	φ	φ	PROPN
ejpam-5113	68	13	is	be	AUX
ejpam-5113	68	14	the	the	DET
ejpam-5113	68	15	analytic	analytic	ADJ
ejpam-5113	68	16	selfmap	selfmap	NOUN
ejpam-5113	68	17	of	of	ADP
ejpam-5113	68	18	d.	d.	PROPN
ejpam-5113	68	19	in	in	ADP
ejpam-5113	68	20	the	the	DET
ejpam-5113	68	21	following	follow	VERB
ejpam-5113	68	22	theorem	theorem	NOUN
ejpam-5113	68	23	1	1	NUM
ejpam-5113	68	24	,	,	PUNCT
ejpam-5113	68	25	we	we	PRON
ejpam-5113	68	26	characterize	characterize	VERB
ejpam-5113	68	27	the	the	DET
ejpam-5113	68	28	boundedness	boundedness	NOUN
ejpam-5113	68	29	of	of	ADP
ejpam-5113	68	30	iφg	iφg	NOUN
ejpam-5113	68	31	that	that	PRON
ejpam-5113	68	32	acts	act	VERB
ejpam-5113	68	33	between	between	ADP
ejpam-5113	68	34	sp	sp	ADP
ejpam-5113	68	35	spaces	space	NOUN
ejpam-5113	68	36	and	and	CCONJ
ejpam-5113	68	37	weighted	weight	VERB
ejpam-5113	68	38	zygmund	zygmund	PROPN
ejpam-5113	68	39	spaces	space	NOUN
ejpam-5113	68	40	.	.	PUNCT
ejpam-5113	69	1	theorem	theorem	NOUN
ejpam-5113	69	2	1	1	X
ejpam-5113	69	3	.	.	PUNCT
ejpam-5113	70	1	let	let	VERB
ejpam-5113	70	2	g	g	NOUN
ejpam-5113	70	3	be	be	AUX
ejpam-5113	70	4	an	an	DET
ejpam-5113	70	5	analytic	analytic	ADJ
ejpam-5113	70	6	function	function	NOUN
ejpam-5113	70	7	on	on	ADP
ejpam-5113	70	8	d	d	PROPN
ejpam-5113	70	9	and	and	CCONJ
ejpam-5113	70	10	φ	φ	PROPN
ejpam-5113	70	11	be	be	VERB
ejpam-5113	70	12	an	an	DET
ejpam-5113	70	13	analytic	analytic	ADJ
ejpam-5113	70	14	selfmap	selfmap	NOUN
ejpam-5113	70	15	of	of	ADP
ejpam-5113	70	16	d.	d.	PROPN
ejpam-5113	70	17	then	then	ADV
ejpam-5113	70	18	iφg	iφg	VERB
ejpam-5113	70	19	:	:	PUNCT
ejpam-5113	70	20	sp	sp	ADP
ejpam-5113	70	21	→	→	PUNCT
ejpam-5113	70	22	zµ	zµ	PROPN
ejpam-5113	70	23	is	be	AUX
ejpam-5113	70	24	bounded	bound	VERB
ejpam-5113	70	25	if	if	SCONJ
ejpam-5113	70	26	and	and	CCONJ
ejpam-5113	70	27	only	only	ADV
ejpam-5113	70	28	if	if	SCONJ
ejpam-5113	70	29	m1	m1	PROPN
ejpam-5113	70	30	=	=	PUNCT
ejpam-5113	70	31	sup	sup	VERB
ejpam-5113	70	32	z∈d	z∈d	NUM
ejpam-5113	70	33	k1(z	k1(z	NOUN
ejpam-5113	70	34	)	)	PUNCT
ejpam-5113	70	35	<	<	X
ejpam-5113	70	36	∞	∞	PROPN
ejpam-5113	70	37	and	and	CCONJ
ejpam-5113	70	38	m2	m2	PROPN
ejpam-5113	70	39	=	=	PROPN
ejpam-5113	71	1	sup	sup	NUM
ejpam-5113	71	2	z∈d	z∈d	NUM
ejpam-5113	71	3	k2(z	k2(z	PROPN
ejpam-5113	71	4	)	)	PUNCT
ejpam-5113	71	5	<	<	X
ejpam-5113	71	6	∞.	∞.	PROPN
ejpam-5113	71	7	proof	proof	NOUN
ejpam-5113	71	8	.	.	PUNCT
ejpam-5113	72	1	suppose	suppose	VERB
ejpam-5113	72	2	that	that	SCONJ
ejpam-5113	72	3	iφg	iφg	NOUN
ejpam-5113	72	4	:	:	PUNCT
ejpam-5113	72	5	sp	sp	ADP
ejpam-5113	72	6	→	→	PUNCT
ejpam-5113	72	7	zµ	zµ	X
ejpam-5113	72	8	is	be	AUX
ejpam-5113	72	9	bounded	bound	VERB
ejpam-5113	72	10	.	.	PUNCT
ejpam-5113	73	1	first	first	ADV
ejpam-5113	73	2	,	,	PUNCT
ejpam-5113	73	3	for	for	ADP
ejpam-5113	73	4	a	a	DET
ejpam-5113	73	5	fixed	fix	VERB
ejpam-5113	73	6	w	w	PROPN
ejpam-5113	73	7	∈	∈	PROPN
ejpam-5113	73	8	d	d	NOUN
ejpam-5113	73	9	we	we	PRON
ejpam-5113	73	10	consider	consider	VERB
ejpam-5113	73	11	the	the	DET
ejpam-5113	73	12	test	test	NOUN
ejpam-5113	73	13	function	function	NOUN
ejpam-5113	73	14	f1,w(z	f1,w(z	NOUN
ejpam-5113	73	15	)	)	PUNCT
ejpam-5113	73	16	=	=	SYM
ejpam-5113	73	17	(	(	PUNCT
ejpam-5113	73	18	1−	1−	NUM
ejpam-5113	73	19	|φ(w)|2	|φ(w)|2	NUM
ejpam-5113	73	20	)	)	PUNCT
ejpam-5113	73	21	(	(	PUNCT
ejpam-5113	73	22	2p−1)/p	2p−1)/p	NUM
ejpam-5113	73	23	φ(w)(1−	φ(w)(1−	NUM
ejpam-5113	73	24	φ(w)z	φ(w)z	NOUN
ejpam-5113	73	25	)	)	PUNCT
ejpam-5113	73	26	.	.	PUNCT
ejpam-5113	74	1	by	by	ADP
ejpam-5113	74	2	direct	direct	ADJ
ejpam-5113	74	3	calculations	calculation	NOUN
ejpam-5113	74	4	,	,	PUNCT
ejpam-5113	74	5	we	we	PRON
ejpam-5113	74	6	get	get	VERB
ejpam-5113	74	7	∥f1,w∥sp	∥f1,w∥sp	ADJ
ejpam-5113	75	1	=	=	SYM
ejpam-5113	75	2	∥f	∥f	ADJ
ejpam-5113	75	3	′	′	NUM
ejpam-5113	75	4	1,w∥hp	1,w∥hp	NUM
ejpam-5113	75	5	≤	≤	NUM
ejpam-5113	75	6	2(2p−2)/p	2(2p−2)/p	NUM
ejpam-5113	75	7	,	,	PUNCT
ejpam-5113	75	8	(	(	PUNCT
ejpam-5113	75	9	1	1	X
ejpam-5113	75	10	)	)	PUNCT
ejpam-5113	75	11	f	f	NOUN
ejpam-5113	75	12	′	′	NUM
ejpam-5113	75	13	1,w(φ(w	1,w(φ(w	NUM
ejpam-5113	75	14	)	)	PUNCT
ejpam-5113	75	15	)	)	PUNCT
ejpam-5113	76	1	=	=	SYM
ejpam-5113	76	2	1	1	NUM
ejpam-5113	76	3	(	(	PUNCT
ejpam-5113	76	4	1−	1−	NUM
ejpam-5113	76	5	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	76	6	/	/	SYM
ejpam-5113	76	7	p	p	NOUN
ejpam-5113	76	8	,	,	PUNCT
ejpam-5113	76	9	(	(	PUNCT
ejpam-5113	76	10	2	2	X
ejpam-5113	76	11	)	)	PUNCT
ejpam-5113	76	12	w.	w.	PROPN
ejpam-5113	76	13	al	al	PROPN
ejpam-5113	76	14	-	-	PUNCT
ejpam-5113	76	15	rawashdeh	rawashdeh	PROPN
ejpam-5113	76	16	/	/	SYM
ejpam-5113	76	17	eur	eur	PROPN
ejpam-5113	76	18	.	.	PUNCT
ejpam-5113	77	1	j.	j.	PROPN
ejpam-5113	77	2	pure	pure	PROPN
ejpam-5113	77	3	appl	appl	PROPN
ejpam-5113	77	4	.	.	PROPN
ejpam-5113	77	5	math	math	PROPN
ejpam-5113	77	6	,	,	PUNCT
ejpam-5113	77	7	17	17	NUM
ejpam-5113	77	8	(	(	PUNCT
ejpam-5113	77	9	2	2	NUM
ejpam-5113	77	10	)	)	PUNCT
ejpam-5113	77	11	(	(	PUNCT
ejpam-5113	77	12	2024	2024	NUM
ejpam-5113	77	13	)	)	PUNCT
ejpam-5113	77	14	,	,	PUNCT
ejpam-5113	77	15	931	931	NUM
ejpam-5113	77	16	-	-	SYM
ejpam-5113	77	17	944	944	NUM
ejpam-5113	77	18	935	935	NUM
ejpam-5113	77	19	and	and	CCONJ
ejpam-5113	77	20	f	f	X
ejpam-5113	77	21	′′	′′	PROPN
ejpam-5113	77	22	1,w(φ(w	1,w(φ(w	NUM
ejpam-5113	77	23	)	)	PUNCT
ejpam-5113	77	24	)	)	PUNCT
ejpam-5113	78	1	=	=	SYM
ejpam-5113	78	2	2φ(w	2φ(w	NUM
ejpam-5113	78	3	)	)	PUNCT
ejpam-5113	78	4	(	(	PUNCT
ejpam-5113	78	5	1−	1−	NUM
ejpam-5113	78	6	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	78	7	.	.	PUNCT
ejpam-5113	79	1	(	(	PUNCT
ejpam-5113	79	2	3	3	X
ejpam-5113	79	3	)	)	PUNCT
ejpam-5113	79	4	therefore	therefore	ADV
ejpam-5113	79	5	,	,	PUNCT
ejpam-5113	79	6	we	we	PRON
ejpam-5113	79	7	obtain	obtain	VERB
ejpam-5113	79	8	the	the	DET
ejpam-5113	79	9	following	follow	VERB
ejpam-5113	79	10	(	(	PUNCT
ejpam-5113	79	11	iφg	iφg	PROPN
ejpam-5113	79	12	f1,w	f1,w	PROPN
ejpam-5113	79	13	)	)	PUNCT
ejpam-5113	80	1	′′	′′	PROPN
ejpam-5113	80	2	(	(	PUNCT
ejpam-5113	80	3	w	w	PROPN
ejpam-5113	80	4	)	)	PUNCT
ejpam-5113	80	5	=	=	PUNCT
ejpam-5113	80	6	(	(	PUNCT
ejpam-5113	80	7	f	f	NOUN
ejpam-5113	80	8	′	′	NUM
ejpam-5113	80	9	1,w(φ(w))g(w	1,w(φ(w))g(w	NUM
ejpam-5113	80	10	)	)	PUNCT
ejpam-5113	80	11	)	)	PUNCT
ejpam-5113	80	12	′	′	NUM
ejpam-5113	81	1	=	=	PUNCT
ejpam-5113	81	2	f	f	X
ejpam-5113	82	1	′′	′′	PROPN
ejpam-5113	82	2	1,w(φ(w))g(w)φ	1,w(φ(w))g(w)φ	NUM
ejpam-5113	82	3	′(w	′(w	NOUN
ejpam-5113	82	4	)	)	PUNCT
ejpam-5113	83	1	+	+	NUM
ejpam-5113	83	2	f	f	NOUN
ejpam-5113	83	3	′	′	NUM
ejpam-5113	83	4	1,w(φ(w))g	1,w(φ(w))g	NUM
ejpam-5113	83	5	′(w	′(w	NOUN
ejpam-5113	83	6	)	)	PUNCT
ejpam-5113	83	7	=	=	SYM
ejpam-5113	83	8	2φ(w)φ′(w)g(w	2φ(w)φ′(w)g(w	NUM
ejpam-5113	83	9	)	)	PUNCT
ejpam-5113	83	10	(	(	PUNCT
ejpam-5113	83	11	1−	1−	NUM
ejpam-5113	83	12	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	83	13	+	+	CCONJ
ejpam-5113	83	14	g′(w	g′(w	NOUN
ejpam-5113	83	15	)	)	PUNCT
ejpam-5113	83	16	(	(	PUNCT
ejpam-5113	83	17	1−	1−	NUM
ejpam-5113	83	18	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	83	19	/	/	SYM
ejpam-5113	83	20	p	p	X
ejpam-5113	83	21	(	(	PUNCT
ejpam-5113	83	22	4	4	NUM
ejpam-5113	83	23	)	)	PUNCT
ejpam-5113	83	24	moreover	moreover	ADV
ejpam-5113	83	25	,	,	PUNCT
ejpam-5113	83	26	we	we	PRON
ejpam-5113	83	27	consider	consider	VERB
ejpam-5113	83	28	another	another	DET
ejpam-5113	83	29	test	test	NOUN
ejpam-5113	83	30	function	function	NOUN
ejpam-5113	83	31	f2,w(z	f2,w(z	PROPN
ejpam-5113	83	32	)	)	PUNCT
ejpam-5113	83	33	=	=	SYM
ejpam-5113	83	34	(	(	PUNCT
ejpam-5113	83	35	1−	1−	NUM
ejpam-5113	83	36	|φ(w)|2	|φ(w)|2	NUM
ejpam-5113	83	37	)	)	PUNCT
ejpam-5113	83	38	(	(	PUNCT
ejpam-5113	83	39	3p−1)/p	3p−1)/p	NUM
ejpam-5113	83	40	2φ(w)(1−	2φ(w)(1−	NUM
ejpam-5113	83	41	φ(w)z)2	φ(w)z)2	NOUN
ejpam-5113	83	42	.	.	PUNCT
ejpam-5113	84	1	by	by	ADP
ejpam-5113	84	2	direct	direct	ADJ
ejpam-5113	84	3	calculations	calculation	NOUN
ejpam-5113	84	4	,	,	PUNCT
ejpam-5113	84	5	we	we	PRON
ejpam-5113	84	6	get	get	VERB
ejpam-5113	84	7	∥f2,w∥sp	∥f2,w∥sp	NOUN
ejpam-5113	85	1	=	=	SYM
ejpam-5113	85	2	∥f	∥f	ADJ
ejpam-5113	86	1	′	′	NUM
ejpam-5113	86	2	2,w∥hp	2,w∥hp	NUM
ejpam-5113	86	3	≤	≤	NUM
ejpam-5113	86	4	2(3p−2)/p	2(3p−2)/p	NUM
ejpam-5113	86	5	,	,	PUNCT
ejpam-5113	86	6	f	f	PROPN
ejpam-5113	86	7	′	′	NUM
ejpam-5113	87	1	2,w(φ(w	2,w(φ(w	NUM
ejpam-5113	87	2	)	)	PUNCT
ejpam-5113	87	3	)	)	PUNCT
ejpam-5113	88	1	=	=	SYM
ejpam-5113	88	2	1	1	NUM
ejpam-5113	88	3	(	(	PUNCT
ejpam-5113	88	4	1−	1−	NUM
ejpam-5113	88	5	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	88	6	/	/	SYM
ejpam-5113	88	7	p	p	NOUN
ejpam-5113	88	8	,	,	PUNCT
ejpam-5113	88	9	and	and	CCONJ
ejpam-5113	88	10	f	f	X
ejpam-5113	88	11	′′	′′	PROPN
ejpam-5113	88	12	2,w(φ(w	2,w(φ(w	NUM
ejpam-5113	88	13	)	)	PUNCT
ejpam-5113	88	14	)	)	PUNCT
ejpam-5113	88	15	=	=	SYM
ejpam-5113	88	16	3φ(w	3φ(w	NUM
ejpam-5113	88	17	)	)	PUNCT
ejpam-5113	88	18	(	(	PUNCT
ejpam-5113	88	19	1−	1−	NUM
ejpam-5113	88	20	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	88	21	.	.	PUNCT
ejpam-5113	89	1	similarly	similarly	ADV
ejpam-5113	89	2	,	,	PUNCT
ejpam-5113	89	3	we	we	PRON
ejpam-5113	89	4	obtain	obtain	VERB
ejpam-5113	89	5	the	the	DET
ejpam-5113	89	6	following	follow	VERB
ejpam-5113	89	7	(	(	PUNCT
ejpam-5113	89	8	iφg	iφg	NOUN
ejpam-5113	89	9	f2,w	f2,w	PROPN
ejpam-5113	89	10	)	)	PUNCT
ejpam-5113	89	11	′′	′′	PROPN
ejpam-5113	89	12	(	(	PUNCT
ejpam-5113	89	13	w	w	PROPN
ejpam-5113	89	14	)	)	PUNCT
ejpam-5113	89	15	=	=	SYM
ejpam-5113	89	16	3φ(w)φ′(w)g(w	3φ(w)φ′(w)g(w	NUM
ejpam-5113	89	17	)	)	PUNCT
ejpam-5113	89	18	(	(	PUNCT
ejpam-5113	89	19	1−	1−	NUM
ejpam-5113	89	20	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	89	21	+	+	CCONJ
ejpam-5113	89	22	g′(w	g′(w	NOUN
ejpam-5113	89	23	)	)	PUNCT
ejpam-5113	89	24	(	(	PUNCT
ejpam-5113	89	25	1−	1−	NUM
ejpam-5113	89	26	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	89	27	/	/	SYM
ejpam-5113	89	28	p	p	X
ejpam-5113	89	29	(	(	PUNCT
ejpam-5113	89	30	5	5	NUM
ejpam-5113	89	31	)	)	PUNCT
ejpam-5113	89	32	now	now	ADV
ejpam-5113	89	33	,	,	PUNCT
ejpam-5113	89	34	using	use	VERB
ejpam-5113	89	35	equations	equation	NOUN
ejpam-5113	89	36	(	(	PUNCT
ejpam-5113	89	37	4	4	NUM
ejpam-5113	89	38	)	)	PUNCT
ejpam-5113	89	39	and	and	CCONJ
ejpam-5113	89	40	(	(	PUNCT
ejpam-5113	89	41	5	5	NUM
ejpam-5113	89	42	)	)	PUNCT
ejpam-5113	89	43	,	,	PUNCT
ejpam-5113	89	44	we	we	PRON
ejpam-5113	89	45	get	get	VERB
ejpam-5113	89	46	(	(	PUNCT
ejpam-5113	89	47	iφg	iφg	NOUN
ejpam-5113	89	48	f2,w	f2,w	PROPN
ejpam-5113	89	49	)	)	PUNCT
ejpam-5113	90	1	′′	′′	PROPN
ejpam-5113	90	2	(	(	PUNCT
ejpam-5113	90	3	w)−	w)−	PROPN
ejpam-5113	90	4	(	(	PUNCT
ejpam-5113	90	5	iφg	iφg	NOUN
ejpam-5113	90	6	f1,w	f1,w	PROPN
ejpam-5113	90	7	)	)	PUNCT
ejpam-5113	90	8	′′	′′	PROPN
ejpam-5113	90	9	(	(	PUNCT
ejpam-5113	90	10	w	w	PROPN
ejpam-5113	90	11	)	)	PUNCT
ejpam-5113	90	12	=	=	SYM
ejpam-5113	90	13	φ(w)φ′(w)g(w	φ(w)φ′(w)g(w	ADJ
ejpam-5113	90	14	)	)	PUNCT
ejpam-5113	90	15	(	(	PUNCT
ejpam-5113	90	16	1−	1−	NUM
ejpam-5113	90	17	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	90	18	.	.	PUNCT
ejpam-5113	91	1	hence	hence	ADV
ejpam-5113	91	2	,	,	PUNCT
ejpam-5113	91	3	by	by	ADP
ejpam-5113	91	4	the	the	DET
ejpam-5113	91	5	boundedness	boundedness	NOUN
ejpam-5113	91	6	of	of	ADP
ejpam-5113	91	7	iφg	iφg	NOUN
ejpam-5113	91	8	:	:	PUNCT
ejpam-5113	91	9	sp	sp	ADP
ejpam-5113	91	10	→	→	PUNCT
ejpam-5113	91	11	zµ	zµ	VERB
ejpam-5113	91	12	we	we	PRON
ejpam-5113	91	13	have	have	VERB
ejpam-5113	91	14	µ(w	µ(w	NOUN
ejpam-5113	91	15	)	)	PUNCT
ejpam-5113	91	16	∣∣∣φ(w)φ′(w)g(w	∣∣∣φ(w)φ′(w)g(w	PROPN
ejpam-5113	91	17	)	)	PUNCT
ejpam-5113	91	18	∣∣∣	∣∣∣	NOUN
ejpam-5113	92	1	(	(	PUNCT
ejpam-5113	92	2	1−	1−	NUM
ejpam-5113	92	3	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	92	4	≤	≤	NOUN
ejpam-5113	92	5	∥iφg	∥iφg	ADV
ejpam-5113	92	6	∥∥f2,w∥sp	∥∥f2,w∥sp	NOUN
ejpam-5113	92	7	+	+	CCONJ
ejpam-5113	92	8	∥iφg	∥iφg	NOUN
ejpam-5113	92	9	∥∥f1,w∥sp	∥∥f1,w∥sp	VERB
ejpam-5113	92	10	≤	≤	NUM
ejpam-5113	92	11	∥iφg	∥iφg	NOUN
ejpam-5113	92	12	∥	∥	NUM
ejpam-5113	93	1	(	(	PUNCT
ejpam-5113	93	2	2(3p−2)/p	2(3p−2)/p	NUM
ejpam-5113	93	3	+	+	CCONJ
ejpam-5113	93	4	2(2p−2)/p	2(2p−2)/p	NUM
ejpam-5113	93	5	)	)	PUNCT
ejpam-5113	93	6	≤	≤	PROPN
ejpam-5113	93	7	c1	c1	NOUN
ejpam-5113	93	8	(	(	PUNCT
ejpam-5113	93	9	6	6	NUM
ejpam-5113	93	10	)	)	PUNCT
ejpam-5113	93	11	w.	w.	PROPN
ejpam-5113	93	12	al	al	PROPN
ejpam-5113	93	13	-	-	PUNCT
ejpam-5113	93	14	rawashdeh	rawashdeh	PROPN
ejpam-5113	93	15	/	/	SYM
ejpam-5113	93	16	eur	eur	PROPN
ejpam-5113	93	17	.	.	PUNCT
ejpam-5113	94	1	j.	j.	PROPN
ejpam-5113	94	2	pure	pure	PROPN
ejpam-5113	94	3	appl	appl	PROPN
ejpam-5113	94	4	.	.	PROPN
ejpam-5113	94	5	math	math	PROPN
ejpam-5113	94	6	,	,	PUNCT
ejpam-5113	94	7	17	17	NUM
ejpam-5113	94	8	(	(	PUNCT
ejpam-5113	94	9	2	2	NUM
ejpam-5113	94	10	)	)	PUNCT
ejpam-5113	94	11	(	(	PUNCT
ejpam-5113	94	12	2024	2024	NUM
ejpam-5113	94	13	)	)	PUNCT
ejpam-5113	94	14	,	,	PUNCT
ejpam-5113	94	15	931	931	NUM
ejpam-5113	94	16	-	-	SYM
ejpam-5113	94	17	944	944	NUM
ejpam-5113	94	18	936	936	NUM
ejpam-5113	94	19	on	on	ADP
ejpam-5113	94	20	the	the	DET
ejpam-5113	94	21	other	other	ADJ
ejpam-5113	94	22	hand	hand	NOUN
ejpam-5113	95	1	,	,	PUNCT
ejpam-5113	95	2	lemma	lemma	PROPN
ejpam-5113	95	3	2	2	NUM
ejpam-5113	95	4	tells	tell	VERB
ejpam-5113	95	5	us	we	PRON
ejpam-5113	95	6	that	that	PRON
ejpam-5113	95	7	polynomials	polynomial	NOUN
ejpam-5113	95	8	are	be	AUX
ejpam-5113	95	9	dense	dense	ADJ
ejpam-5113	95	10	in	in	ADP
ejpam-5113	95	11	sp	sp	ADP
ejpam-5113	95	12	spaces	space	NOUN
ejpam-5113	95	13	.	.	PUNCT
ejpam-5113	96	1	thus	thus	ADV
ejpam-5113	96	2	pn(z	pn(z	PUNCT
ejpam-5113	96	3	)	)	PUNCT
ejpam-5113	96	4	=	=	SYM
ejpam-5113	96	5	zn	zn	X
ejpam-5113	96	6	in	in	ADP
ejpam-5113	96	7	sp	sp	ADP
ejpam-5113	96	8	and	and	CCONJ
ejpam-5113	96	9	we	we	PRON
ejpam-5113	96	10	get	get	VERB
ejpam-5113	96	11	the	the	DET
ejpam-5113	96	12	following	follow	VERB
ejpam-5113	96	13	(	(	PUNCT
ejpam-5113	96	14	iφg	iφg	NOUN
ejpam-5113	96	15	p1	p1	NOUN
ejpam-5113	96	16	)	)	PUNCT
ejpam-5113	97	1	′′	′′	PROPN
ejpam-5113	97	2	(	(	PUNCT
ejpam-5113	97	3	z	z	NOUN
ejpam-5113	97	4	)	)	PUNCT
ejpam-5113	97	5	=	=	SYM
ejpam-5113	97	6	(	(	PUNCT
ejpam-5113	97	7	∫	∫	PROPN
ejpam-5113	97	8	z	z	PROPN
ejpam-5113	97	9	0	0	NUM
ejpam-5113	97	10	p	p	NOUN
ejpam-5113	97	11	′	′	NUM
ejpam-5113	97	12	1(φ(w))g(w)dw	1(φ(w))g(w)dw	NUM
ejpam-5113	97	13	)	)	PUNCT
ejpam-5113	98	1	′′	′′	PROPN
ejpam-5113	98	2	=	=	PRON
ejpam-5113	98	3	(	(	PUNCT
ejpam-5113	98	4	∫	∫	PROPN
ejpam-5113	98	5	z	z	PROPN
ejpam-5113	98	6	0	0	PROPN
ejpam-5113	98	7	g(w)dw	g(w)dw	PROPN
ejpam-5113	98	8	)	)	PUNCT
ejpam-5113	98	9	′′	′′	PROPN
ejpam-5113	98	10	=	=	PUNCT
ejpam-5113	98	11	g′(z	g′(z	PROPN
ejpam-5113	98	12	)	)	PUNCT
ejpam-5113	98	13	.	.	PUNCT
ejpam-5113	99	1	similarly	similarly	ADV
ejpam-5113	99	2	,	,	PUNCT
ejpam-5113	99	3	we	we	PRON
ejpam-5113	99	4	obtain	obtain	VERB
ejpam-5113	99	5	the	the	DET
ejpam-5113	99	6	following	follow	VERB
ejpam-5113	99	7	(	(	PUNCT
ejpam-5113	99	8	iφg	iφg	NOUN
ejpam-5113	99	9	p2	p2	PROPN
ejpam-5113	99	10	)	)	PUNCT
ejpam-5113	100	1	′′	′′	PROPN
ejpam-5113	100	2	(	(	PUNCT
ejpam-5113	100	3	z	z	NOUN
ejpam-5113	100	4	)	)	PUNCT
ejpam-5113	100	5	=	=	SYM
ejpam-5113	100	6	(	(	PUNCT
ejpam-5113	100	7	∫	∫	PROPN
ejpam-5113	100	8	z	z	PROPN
ejpam-5113	100	9	0	0	NUM
ejpam-5113	100	10	p	p	NOUN
ejpam-5113	100	11	′	′	NUM
ejpam-5113	100	12	2(φ(w))g(w)dw	2(φ(w))g(w)dw	NOUN
ejpam-5113	100	13	)	)	PUNCT
ejpam-5113	101	1	′′	′′	PROPN
ejpam-5113	101	2	=	=	PRON
ejpam-5113	101	3	(	(	PUNCT
ejpam-5113	101	4	∫	∫	PROPN
ejpam-5113	101	5	z	z	PROPN
ejpam-5113	101	6	0	0	NUM
ejpam-5113	101	7	2φ(w)g(w)dw	2φ(w)g(w)dw	NUM
ejpam-5113	101	8	)	)	PUNCT
ejpam-5113	102	1	′′	′′	PROPN
ejpam-5113	102	2	=	=	PUNCT
ejpam-5113	102	3	2φ(z)g′(z	2φ(z)g′(z	X
ejpam-5113	102	4	)	)	PUNCT
ejpam-5113	102	5	+	+	CCONJ
ejpam-5113	102	6	2φ′(z)g(z	2φ′(z)g(z	NOUN
ejpam-5113	102	7	)	)	PUNCT
ejpam-5113	102	8	.	.	PUNCT
ejpam-5113	103	1	hence	hence	ADV
ejpam-5113	103	2	,	,	PUNCT
ejpam-5113	103	3	using	use	VERB
ejpam-5113	103	4	the	the	DET
ejpam-5113	103	5	previous	previous	ADJ
ejpam-5113	103	6	equations	equation	NOUN
ejpam-5113	103	7	,	,	PUNCT
ejpam-5113	103	8	we	we	PRON
ejpam-5113	103	9	get	get	VERB
ejpam-5113	103	10	2	2	NUM
ejpam-5113	103	11	(	(	PUNCT
ejpam-5113	103	12	φ′g	φ′g	X
ejpam-5113	103	13	)	)	PUNCT
ejpam-5113	103	14	(	(	PUNCT
ejpam-5113	103	15	z	z	X
ejpam-5113	103	16	)	)	PUNCT
ejpam-5113	103	17	=	=	SYM
ejpam-5113	103	18	(	(	PUNCT
ejpam-5113	103	19	iφg	iφg	NOUN
ejpam-5113	103	20	p2	p2	PROPN
ejpam-5113	103	21	)	)	PUNCT
ejpam-5113	104	1	′′	′′	PROPN
ejpam-5113	104	2	(	(	PUNCT
ejpam-5113	104	3	z)−	z)−	PROPN
ejpam-5113	104	4	2φ(z	2φ(z	PROPN
ejpam-5113	104	5	)	)	PUNCT
ejpam-5113	104	6	(	(	PUNCT
ejpam-5113	104	7	iφg	iφg	NOUN
ejpam-5113	104	8	p1	p1	NOUN
ejpam-5113	104	9	)	)	PUNCT
ejpam-5113	104	10	′′	′′	PROPN
ejpam-5113	104	11	(	(	PUNCT
ejpam-5113	104	12	z	z	NOUN
ejpam-5113	104	13	)	)	PUNCT
ejpam-5113	104	14	.	.	PUNCT
ejpam-5113	105	1	(	(	PUNCT
ejpam-5113	105	2	7	7	NUM
ejpam-5113	105	3	)	)	PUNCT
ejpam-5113	105	4	therefore	therefore	ADV
ejpam-5113	105	5	,	,	PUNCT
ejpam-5113	105	6	using	use	VERB
ejpam-5113	105	7	equation	equation	NOUN
ejpam-5113	105	8	(	(	PUNCT
ejpam-5113	105	9	7	7	X
ejpam-5113	105	10	)	)	PUNCT
ejpam-5113	105	11	we	we	PRON
ejpam-5113	105	12	get	get	VERB
ejpam-5113	105	13	sup	sup	NOUN
ejpam-5113	105	14	w∈d	w∈d	NOUN
ejpam-5113	105	15	µ(w)|φ′(w)g(w)|	µ(w)|φ′(w)g(w)|	NOUN
ejpam-5113	106	1	≤	≤	NUM
ejpam-5113	106	2	1	1	NUM
ejpam-5113	106	3	2	2	NUM
ejpam-5113	106	4	∥iφg	∥iφg	NOUN
ejpam-5113	106	5	p2∥zµ	p2∥zµ	NOUN
ejpam-5113	106	6	+	+	CCONJ
ejpam-5113	106	7	sup	sup	NOUN
ejpam-5113	106	8	w∈d	w∈d	NOUN
ejpam-5113	106	9	(	(	PUNCT
ejpam-5113	106	10	∥iφg	∥iφg	ADJ
ejpam-5113	106	11	p1∥zµ	p1∥zµ	NOUN
ejpam-5113	106	12	sup	sup	NOUN
ejpam-5113	106	13	w∈d	w∈d	NOUN
ejpam-5113	106	14	|φ(w)|	|φ(w)|	ADV
ejpam-5113	106	15	)	)	PUNCT
ejpam-5113	106	16	≤	≤	NOUN
ejpam-5113	106	17	∥iφg	∥iφg	NUM
ejpam-5113	107	1	∥∥p2∥sp	∥∥p2∥sp	PROPN
ejpam-5113	107	2	+	+	CCONJ
ejpam-5113	107	3	∥iφg	∥iφg	PROPN
ejpam-5113	107	4	∥∥p1∥sp	∥∥p1∥sp	PROPN
ejpam-5113	107	5	≤	≤	ADJ
ejpam-5113	107	6	c2	c2	PROPN
ejpam-5113	107	7	now	now	ADV
ejpam-5113	107	8	,	,	PUNCT
ejpam-5113	107	9	for	for	ADP
ejpam-5113	107	10	a	a	DET
ejpam-5113	107	11	fixed	fix	VERB
ejpam-5113	107	12	0	0	NUM
ejpam-5113	107	13	<	<	X
ejpam-5113	107	14	r	r	X
ejpam-5113	107	15	<	<	X
ejpam-5113	107	16	1	1	NUM
ejpam-5113	107	17	,	,	PUNCT
ejpam-5113	107	18	consider	consider	VERB
ejpam-5113	107	19	w	w	NOUN
ejpam-5113	107	20	∈	∈	PROPN
ejpam-5113	107	21	d	d	ADP
ejpam-5113	107	22	such	such	ADJ
ejpam-5113	107	23	that	that	SCONJ
ejpam-5113	107	24	0	0	NUM
ejpam-5113	107	25	≤	≤	NUM
ejpam-5113	107	26	|φ(w)|	|φ(w)|	NOUN
ejpam-5113	107	27	≤	≤	NUM
ejpam-5113	107	28	r	r	NOUN
ejpam-5113	107	29	<	<	X
ejpam-5113	107	30	1	1	NUM
ejpam-5113	107	31	.	.	PUNCT
ejpam-5113	108	1	then	then	ADV
ejpam-5113	108	2	we	we	PRON
ejpam-5113	108	3	get	get	VERB
ejpam-5113	108	4	µ(w)|φ(w)φ′(w)g(w)|	µ(w)|φ(w)φ′(w)g(w)|	VERB
ejpam-5113	108	5	(	(	PUNCT
ejpam-5113	108	6	1−	1−	NUM
ejpam-5113	108	7	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	108	8	≤	≤	PROPN
ejpam-5113	108	9	µ(w)|φ′(w)g(w)|	µ(w)|φ′(w)g(w)|	NOUN
ejpam-5113	108	10	(	(	PUNCT
ejpam-5113	108	11	1−	1−	NUM
ejpam-5113	108	12	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	PROPN
ejpam-5113	108	13	≤	≤	PROPN
ejpam-5113	108	14	c2	c2	PROPN
ejpam-5113	108	15	(	(	PUNCT
ejpam-5113	108	16	1−	1−	NUM
ejpam-5113	108	17	r2)1	r2)1	ADJ
ejpam-5113	108	18	+	+	NOUN
ejpam-5113	108	19	1	1	NUM
ejpam-5113	108	20	/	/	SYM
ejpam-5113	108	21	p	p	X
ejpam-5113	108	22	(	(	PUNCT
ejpam-5113	108	23	8)	8)	NUM
ejpam-5113	108	24	moreover	moreover	ADV
ejpam-5113	108	25	,	,	PUNCT
ejpam-5113	108	26	consider	consider	VERB
ejpam-5113	108	27	w	w	NOUN
ejpam-5113	108	28	∈	∈	PROPN
ejpam-5113	109	1	d	d	ADP
ejpam-5113	109	2	such	such	ADJ
ejpam-5113	109	3	that	that	SCONJ
ejpam-5113	109	4	r	r	NOUN
ejpam-5113	109	5	<	<	X
ejpam-5113	109	6	|φ(w)|	|φ(w)|	X
ejpam-5113	109	7	<	<	X
ejpam-5113	109	8	1	1	NUM
ejpam-5113	109	9	.	.	PUNCT
ejpam-5113	110	1	then	then	ADV
ejpam-5113	110	2	we	we	PRON
ejpam-5113	110	3	get	get	VERB
ejpam-5113	110	4	µ(w)|rφ′(w)g(w)|	µ(w)|rφ′(w)g(w)|	PROPN
ejpam-5113	110	5	(	(	PUNCT
ejpam-5113	110	6	1−	1−	NUM
ejpam-5113	110	7	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	PROPN
ejpam-5113	110	8	≤	≤	PROPN
ejpam-5113	110	9	µ(w)|φ(w)φ′(w)g(w)|	µ(w)|φ(w)φ′(w)g(w)|	PUNCT
ejpam-5113	110	10	(	(	PUNCT
ejpam-5113	110	11	1−	1−	NUM
ejpam-5113	110	12	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	110	13	≤	≤	NOUN
ejpam-5113	110	14	∥iφg	∥iφg	NOUN
ejpam-5113	110	15	∥	∥	NUM
ejpam-5113	110	16	(	(	PUNCT
ejpam-5113	110	17	2(3p−2)/p	2(3p−2)/p	NUM
ejpam-5113	110	18	+	+	CCONJ
ejpam-5113	110	19	2(2p−2)/p	2(2p−2)/p	NUM
ejpam-5113	110	20	)	)	PUNCT
ejpam-5113	110	21	.	.	PUNCT
ejpam-5113	111	1	w.	w.	PROPN
ejpam-5113	111	2	al	al	PROPN
ejpam-5113	111	3	-	-	PUNCT
ejpam-5113	111	4	rawashdeh	rawashdeh	PROPN
ejpam-5113	111	5	/	/	SYM
ejpam-5113	111	6	eur	eur	PROPN
ejpam-5113	111	7	.	.	PUNCT
ejpam-5113	112	1	j.	j.	PROPN
ejpam-5113	112	2	pure	pure	PROPN
ejpam-5113	112	3	appl	appl	PROPN
ejpam-5113	112	4	.	.	PROPN
ejpam-5113	112	5	math	math	PROPN
ejpam-5113	112	6	,	,	PUNCT
ejpam-5113	112	7	17	17	NUM
ejpam-5113	112	8	(	(	PUNCT
ejpam-5113	112	9	2	2	NUM
ejpam-5113	112	10	)	)	PUNCT
ejpam-5113	112	11	(	(	PUNCT
ejpam-5113	112	12	2024	2024	NUM
ejpam-5113	112	13	)	)	PUNCT
ejpam-5113	112	14	,	,	PUNCT
ejpam-5113	112	15	931	931	NUM
ejpam-5113	112	16	-	-	SYM
ejpam-5113	112	17	944	944	NUM
ejpam-5113	112	18	937	937	NUM
ejpam-5113	112	19	hence	hence	ADV
ejpam-5113	112	20	,	,	PUNCT
ejpam-5113	112	21	using	use	VERB
ejpam-5113	112	22	equation	equation	NOUN
ejpam-5113	112	23	(	(	PUNCT
ejpam-5113	112	24	6	6	NUM
ejpam-5113	112	25	)	)	PUNCT
ejpam-5113	112	26	,	,	PUNCT
ejpam-5113	112	27	we	we	PRON
ejpam-5113	112	28	get	get	VERB
ejpam-5113	112	29	µ(w)|φ′(w)g(w)|	µ(w)|φ′(w)g(w)|	NOUN
ejpam-5113	112	30	(	(	PUNCT
ejpam-5113	112	31	1−	1−	NUM
ejpam-5113	112	32	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	PROPN
ejpam-5113	112	33	≤	≤	PROPN
ejpam-5113	112	34	c1	c1	PROPN
ejpam-5113	112	35	r	r	NOUN
ejpam-5113	112	36	.	.	PUNCT
ejpam-5113	113	1	(	(	PUNCT
ejpam-5113	113	2	9	9	NUM
ejpam-5113	113	3	)	)	PUNCT
ejpam-5113	113	4	therefore	therefore	ADV
ejpam-5113	113	5	,	,	PUNCT
ejpam-5113	113	6	using	use	VERB
ejpam-5113	113	7	inequalities	inequality	NOUN
ejpam-5113	113	8	(	(	PUNCT
ejpam-5113	113	9	8)	8)	NUM
ejpam-5113	113	10	and	and	CCONJ
ejpam-5113	113	11	(	(	PUNCT
ejpam-5113	113	12	9	9	NUM
ejpam-5113	113	13	)	)	PUNCT
ejpam-5113	113	14	,	,	PUNCT
ejpam-5113	113	15	we	we	PRON
ejpam-5113	113	16	get	get	VERB
ejpam-5113	113	17	m2	m2	PROPN
ejpam-5113	113	18	=	=	PUNCT
ejpam-5113	113	19	sup	sup	VERB
ejpam-5113	113	20	z∈d	z∈d	NOUN
ejpam-5113	113	21	µ(z)|φ′(z)g(z)|	µ(z)|φ′(z)g(z)|	NOUN
ejpam-5113	113	22	(	(	PUNCT
ejpam-5113	113	23	1−	1−	NUM
ejpam-5113	113	24	|φ(z)|2)(p+1)/p	|φ(z)|2)(p+1)/p	PROPN
ejpam-5113	113	25	≤	≤	PROPN
ejpam-5113	113	26	max	max	PROPN
ejpam-5113	113	27	{	{	PUNCT
ejpam-5113	113	28	c1	c1	NOUN
ejpam-5113	113	29	r	r	PROPN
ejpam-5113	113	30	+	+	PROPN
ejpam-5113	113	31	c2	c2	PROPN
ejpam-5113	113	32	(	(	PUNCT
ejpam-5113	113	33	1−	1−	NUM
ejpam-5113	113	34	r2)1	r2)1	ADJ
ejpam-5113	113	35	+	+	NOUN
ejpam-5113	113	36	1	1	NUM
ejpam-5113	113	37	/	/	SYM
ejpam-5113	113	38	p	p	NOUN
ejpam-5113	113	39	}	}	PUNCT
ejpam-5113	113	40	<	<	X
ejpam-5113	113	41	∞.	∞.	PROPN
ejpam-5113	113	42	second	second	ADJ
ejpam-5113	113	43	,	,	PUNCT
ejpam-5113	113	44	for	for	ADP
ejpam-5113	113	45	a	a	DET
ejpam-5113	113	46	fixed	fix	VERB
ejpam-5113	113	47	w	w	PROPN
ejpam-5113	113	48	∈	∈	PROPN
ejpam-5113	113	49	d	d	PROPN
ejpam-5113	113	50	,	,	PUNCT
ejpam-5113	113	51	using	use	VERB
ejpam-5113	113	52	equations	equation	NOUN
ejpam-5113	113	53	(	(	PUNCT
ejpam-5113	113	54	2	2	NUM
ejpam-5113	113	55	)	)	PUNCT
ejpam-5113	113	56	,	,	PUNCT
ejpam-5113	113	57	(	(	PUNCT
ejpam-5113	113	58	3	3	X
ejpam-5113	113	59	)	)	PUNCT
ejpam-5113	113	60	and	and	CCONJ
ejpam-5113	113	61	(	(	PUNCT
ejpam-5113	113	62	4	4	X
ejpam-5113	113	63	)	)	PUNCT
ejpam-5113	113	64	we	we	PRON
ejpam-5113	113	65	get	get	VERB
ejpam-5113	113	66	µ(w)|g′(w)|	µ(w)|g′(w)|	ADP
ejpam-5113	113	67	(	(	PUNCT
ejpam-5113	113	68	1−	1−	NUM
ejpam-5113	113	69	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	113	70	/	/	SYM
ejpam-5113	113	71	p	p	NOUN
ejpam-5113	113	72	=	=	PUNCT
ejpam-5113	113	73	µ(w	µ(w	PROPN
ejpam-5113	113	74	)	)	PUNCT
ejpam-5113	113	75	∣∣g′(w)f	∣∣g′(w)f	X
ejpam-5113	113	76	′	′	NOUN
ejpam-5113	113	77	1,w(φ(w	1,w(φ(w	NUM
ejpam-5113	113	78	)	)	PUNCT
ejpam-5113	113	79	)	)	PUNCT
ejpam-5113	114	1	+	+	CCONJ
ejpam-5113	114	2	f	f	X
ejpam-5113	114	3	′′	′′	PROPN
ejpam-5113	114	4	1,w(φ(w))g(w)φ	1,w(φ(w))g(w)φ	NUM
ejpam-5113	114	5	′(w)−	′(w)−	VERB
ejpam-5113	114	6	f	f	PROPN
ejpam-5113	114	7	′′	′′	PROPN
ejpam-5113	114	8	1,w(φ(w))g(w)φ	1,w(φ(w))g(w)φ	NUM
ejpam-5113	114	9	′(w	′(w	NOUN
ejpam-5113	114	10	)	)	PUNCT
ejpam-5113	114	11	∣∣	∣∣	NUM
ejpam-5113	114	12	=	=	SYM
ejpam-5113	114	13	µ(w	µ(w	PROPN
ejpam-5113	114	14	)	)	PUNCT
ejpam-5113	114	15	∣∣∣∣∣(iφg	∣∣∣∣∣(iφg	PROPN
ejpam-5113	114	16	f1,w)′′	f1,w)′′	PROPN
ejpam-5113	114	17	(	(	PUNCT
ejpam-5113	114	18	w)−	w)−	PROPN
ejpam-5113	114	19	2φ(w)g(w)φ′(w	2φ(w)g(w)φ′(w	NUM
ejpam-5113	114	20	)	)	PUNCT
ejpam-5113	114	21	(	(	PUNCT
ejpam-5113	114	22	1−	1−	NUM
ejpam-5113	114	23	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NUM
ejpam-5113	115	1	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-5113	115	2	≤	≤	NOUN
ejpam-5113	115	3	∥iφg	∥iφg	ADJ
ejpam-5113	115	4	f1,w∥zµ	f1,w∥zµ	NOUN
ejpam-5113	116	1	+	+	CCONJ
ejpam-5113	116	2	2µ(w)|φ(w)g(w)φ′(w)|	2µ(w)|φ(w)g(w)φ′(w)|	NUM
ejpam-5113	116	3	(	(	PUNCT
ejpam-5113	116	4	1−	1−	NUM
ejpam-5113	116	5	|φ(w)|2)(p+1)/p	|φ(w)|2)(p+1)/p	NOUN
ejpam-5113	116	6	≤	≤	PROPN
ejpam-5113	116	7	∥iφg	∥iφg	ADV
ejpam-5113	116	8	∥∥f1,w∥sp	∥∥f1,w∥sp	NOUN
ejpam-5113	116	9	+	+	CCONJ
ejpam-5113	116	10	2m2	2m2	NUM
ejpam-5113	116	11	.	.	PUNCT
ejpam-5113	117	1	taking	take	VERB
ejpam-5113	117	2	the	the	DET
ejpam-5113	117	3	supremum	supremum	ADJ
ejpam-5113	117	4	over	over	ADP
ejpam-5113	117	5	all	all	PRON
ejpam-5113	117	6	w	w	PROPN
ejpam-5113	117	7	∈	∈	PROPN
ejpam-5113	117	8	d	d	NOUN
ejpam-5113	117	9	,	,	PUNCT
ejpam-5113	117	10	we	we	PRON
ejpam-5113	117	11	get	get	VERB
ejpam-5113	117	12	that	that	DET
ejpam-5113	117	13	m1	m1	PROPN
ejpam-5113	117	14	<	<	X
ejpam-5113	117	15	∞.	∞.	PROPN
ejpam-5113	117	16	conversely	conversely	ADV
ejpam-5113	117	17	,	,	PUNCT
ejpam-5113	117	18	suppose	suppose	VERB
ejpam-5113	117	19	that	that	SCONJ
ejpam-5113	117	20	conditions	condition	NOUN
ejpam-5113	117	21	m1	m1	PROPN
ejpam-5113	117	22	and	and	CCONJ
ejpam-5113	117	23	m2	m2	PROPN
ejpam-5113	117	24	are	be	AUX
ejpam-5113	117	25	finite	finite	ADJ
ejpam-5113	117	26	.	.	PUNCT
ejpam-5113	118	1	let	let	VERB
ejpam-5113	118	2	f	f	PROPN
ejpam-5113	118	3	∈	∈	PROPN
ejpam-5113	118	4	sp	sp	PROPN
ejpam-5113	118	5	,	,	PUNCT
ejpam-5113	118	6	then	then	ADV
ejpam-5113	118	7	it	it	PRON
ejpam-5113	118	8	is	be	AUX
ejpam-5113	118	9	well	well	ADV
ejpam-5113	118	10	known	know	VERB
ejpam-5113	118	11	,	,	PUNCT
ejpam-5113	118	12	see	see	VERB
ejpam-5113	118	13	[	[	X
ejpam-5113	118	14	6	6	NUM
ejpam-5113	118	15	]	]	PUNCT
ejpam-5113	118	16	or	or	CCONJ
ejpam-5113	118	17	[	[	X
ejpam-5113	118	18	23	23	NUM
ejpam-5113	118	19	]	]	PUNCT
ejpam-5113	118	20	,	,	PUNCT
ejpam-5113	118	21	that	that	SCONJ
ejpam-5113	118	22	for	for	ADP
ejpam-5113	118	23	all	all	DET
ejpam-5113	118	24	z	z	NOUN
ejpam-5113	118	25	∈	∈	PROPN
ejpam-5113	118	26	d	d	NOUN
ejpam-5113	118	27	we	we	PRON
ejpam-5113	118	28	have	have	VERB
ejpam-5113	118	29	|f	|f	PROPN
ejpam-5113	118	30	′(z)|	′(z)|	X
ejpam-5113	118	31	≤	≤	PUNCT
ejpam-5113	119	1	∥f	∥f	PROPN
ejpam-5113	119	2	′∥hp	′∥hp	ADP
ejpam-5113	119	3	(	(	PUNCT
ejpam-5113	119	4	1−	1−	NUM
ejpam-5113	119	5	|z|2)1	|z|2)1	NOUN
ejpam-5113	119	6	/	/	SYM
ejpam-5113	119	7	p	p	NOUN
ejpam-5113	119	8	,	,	PUNCT
ejpam-5113	119	9	and	and	CCONJ
ejpam-5113	120	1	|f	|f	PROPN
ejpam-5113	120	2	′′(z)|	′′(z)|	PROPN
ejpam-5113	120	3	≤	≤	PUNCT
ejpam-5113	121	1	∥f	∥f	VERB
ejpam-5113	121	2	′∥hp	′∥hp	ADP
ejpam-5113	121	3	(	(	PUNCT
ejpam-5113	121	4	1−	1−	NUM
ejpam-5113	121	5	|z|2)1	|z|2)1	NOUN
ejpam-5113	121	6	+	+	NOUN
ejpam-5113	121	7	1	1	NUM
ejpam-5113	121	8	/	/	SYM
ejpam-5113	121	9	p	p	NOUN
ejpam-5113	121	10	.	.	PUNCT
ejpam-5113	122	1	therefore	therefore	ADV
ejpam-5113	122	2	,	,	PUNCT
ejpam-5113	122	3	for	for	ADP
ejpam-5113	122	4	z	z	PROPN
ejpam-5113	122	5	∈	∈	PROPN
ejpam-5113	122	6	d	d	X
ejpam-5113	122	7	,	,	PUNCT
ejpam-5113	122	8	we	we	PRON
ejpam-5113	122	9	have	have	VERB
ejpam-5113	122	10	µ(z	µ(z	NOUN
ejpam-5113	122	11	)	)	PUNCT
ejpam-5113	122	12	∣∣∣(iφg	∣∣∣(iφg	PROPN
ejpam-5113	122	13	f)′′	f)′′	PROPN
ejpam-5113	122	14	(	(	PUNCT
ejpam-5113	122	15	z)∣∣∣	z)∣∣∣	NOUN
ejpam-5113	122	16	=	=	SYM
ejpam-5113	122	17	µ(z	µ(z	PROPN
ejpam-5113	122	18	)	)	PUNCT
ejpam-5113	122	19	∣∣∣∣(∫	∣∣∣∣(∫	NOUN
ejpam-5113	122	20	z	z	NOUN
ejpam-5113	122	21	0	0	NUM
ejpam-5113	123	1	f	f	PROPN
ejpam-5113	123	2	′(φ(w))g(w)dw	′(φ(w))g(w)dw	PROPN
ejpam-5113	123	3	)	)	PUNCT
ejpam-5113	123	4	′′∣∣∣∣	′′∣∣∣∣	PROPN
ejpam-5113	123	5	=	=	SYM
ejpam-5113	123	6	(	(	PUNCT
ejpam-5113	123	7	f	f	NOUN
ejpam-5113	123	8	′(φ(z))g(z	′(φ(z))g(z	NOUN
ejpam-5113	123	9	)	)	PUNCT
ejpam-5113	123	10	)	)	PUNCT
ejpam-5113	123	11	′	′	NUM
ejpam-5113	124	1	=	=	PUNCT
ejpam-5113	124	2	µ(z	µ(z	PROPN
ejpam-5113	124	3	)	)	PUNCT
ejpam-5113	124	4	∣∣f	∣∣f	NOUN
ejpam-5113	124	5	′′(φ(z))φ′(z)g(z	′′(φ(z))φ′(z)g(z	NOUN
ejpam-5113	124	6	)	)	PUNCT
ejpam-5113	125	1	+	+	CCONJ
ejpam-5113	125	2	f	f	PROPN
ejpam-5113	125	3	′(φ(z))g′(z	′(φ(z))g′(z	PROPN
ejpam-5113	125	4	)	)	PUNCT
ejpam-5113	125	5	∣∣	∣∣	X
ejpam-5113	125	6	≤	≤	X
ejpam-5113	126	1	µ(z)|φ′(z)g(z)|	µ(z)|φ′(z)g(z)|	X
ejpam-5113	126	2	(	(	PUNCT
ejpam-5113	126	3	1−	1−	NUM
ejpam-5113	126	4	|φ(z)|2)(p+1)/p	|φ(z)|2)(p+1)/p	NOUN
ejpam-5113	126	5	∥f	∥f	VERB
ejpam-5113	126	6	′∥hp	′∥hp	ADV
ejpam-5113	126	7	+	+	X
ejpam-5113	126	8	µ(z)|g′(z)|	µ(z)|g′(z)|	X
ejpam-5113	126	9	(	(	PUNCT
ejpam-5113	126	10	1−	1−	NUM
ejpam-5113	126	11	|φ(z)|2)1	|φ(z)|2)1	NOUN
ejpam-5113	126	12	/	/	SYM
ejpam-5113	126	13	p	p	NOUN
ejpam-5113	126	14	∥f	∥f	PROPN
ejpam-5113	126	15	′∥hp	′∥hp	ADP
ejpam-5113	126	16	w.	w.	PROPN
ejpam-5113	126	17	al	al	PROPN
ejpam-5113	126	18	-	-	PUNCT
ejpam-5113	126	19	rawashdeh	rawashdeh	PROPN
ejpam-5113	126	20	/	/	SYM
ejpam-5113	126	21	eur	eur	PROPN
ejpam-5113	126	22	.	.	PUNCT
ejpam-5113	127	1	j.	j.	PROPN
ejpam-5113	127	2	pure	pure	PROPN
ejpam-5113	127	3	appl	appl	PROPN
ejpam-5113	127	4	.	.	PROPN
ejpam-5113	127	5	math	math	PROPN
ejpam-5113	127	6	,	,	PUNCT
ejpam-5113	127	7	17	17	NUM
ejpam-5113	127	8	(	(	PUNCT
ejpam-5113	127	9	2	2	NUM
ejpam-5113	127	10	)	)	PUNCT
ejpam-5113	127	11	(	(	PUNCT
ejpam-5113	127	12	2024	2024	NUM
ejpam-5113	127	13	)	)	PUNCT
ejpam-5113	127	14	,	,	PUNCT
ejpam-5113	127	15	931	931	NUM
ejpam-5113	127	16	-	-	SYM
ejpam-5113	127	17	944	944	NUM
ejpam-5113	127	18	938	938	NUM
ejpam-5113	127	19	≤	≤	NOUN
ejpam-5113	127	20	(	(	PUNCT
ejpam-5113	127	21	m1	m1	PROPN
ejpam-5113	127	22	+	+	NOUN
ejpam-5113	127	23	m2	m2	PROPN
ejpam-5113	127	24	)	)	PUNCT
ejpam-5113	127	25	(	(	PUNCT
ejpam-5113	127	26	∥f∥sp	∥f∥sp	PROPN
ejpam-5113	127	27	−	−	PROPN
ejpam-5113	127	28	|f(0)|	|f(0)|	NOUN
ejpam-5113	127	29	)	)	PUNCT
ejpam-5113	127	30	≤	≤	NOUN
ejpam-5113	127	31	(	(	PUNCT
ejpam-5113	127	32	m1	m1	PROPN
ejpam-5113	127	33	+	+	NOUN
ejpam-5113	127	34	m2	m2	PROPN
ejpam-5113	127	35	)	)	PUNCT
ejpam-5113	127	36	∥f∥sp	∥f∥sp	INTJ
ejpam-5113	127	37	.	.	PUNCT
ejpam-5113	128	1	taking	take	VERB
ejpam-5113	128	2	the	the	DET
ejpam-5113	128	3	supremum	supremum	ADJ
ejpam-5113	128	4	over	over	ADP
ejpam-5113	128	5	all	all	DET
ejpam-5113	128	6	z	z	NOUN
ejpam-5113	128	7	∈	∈	PROPN
ejpam-5113	129	1	d	d	NOUN
ejpam-5113	129	2	,	,	PUNCT
ejpam-5113	129	3	we	we	PRON
ejpam-5113	129	4	get	get	VERB
ejpam-5113	129	5	∥	∥	NUM
ejpam-5113	130	1	(	(	PUNCT
ejpam-5113	130	2	iφg	iφg	NOUN
ejpam-5113	130	3	f	f	PROPN
ejpam-5113	130	4	)	)	PUNCT
ejpam-5113	131	1	(	(	PUNCT
ejpam-5113	131	2	z)∥zµ	z)∥zµ	NOUN
ejpam-5113	131	3	≤	≤	NUM
ejpam-5113	131	4	(	(	PUNCT
ejpam-5113	131	5	m1	m1	PROPN
ejpam-5113	131	6	+	+	NOUN
ejpam-5113	131	7	m2	m2	PROPN
ejpam-5113	131	8	)	)	PUNCT
ejpam-5113	131	9	∥f∥sp	∥f∥sp	PROPN
ejpam-5113	131	10	.	.	PUNCT
ejpam-5113	132	1	hence	hence	ADV
ejpam-5113	132	2	,	,	PUNCT
ejpam-5113	132	3	iφg	iφg	PROPN
ejpam-5113	132	4	is	be	AUX
ejpam-5113	132	5	bounded	bound	VERB
ejpam-5113	132	6	,	,	PUNCT
ejpam-5113	132	7	as	as	SCONJ
ejpam-5113	132	8	desired	desire	VERB
ejpam-5113	132	9	.	.	PUNCT
ejpam-5113	133	1	in	in	ADP
ejpam-5113	133	2	the	the	DET
ejpam-5113	133	3	following	follow	VERB
ejpam-5113	133	4	theorem	theorem	NOUN
ejpam-5113	133	5	2	2	NUM
ejpam-5113	133	6	,	,	PUNCT
ejpam-5113	133	7	we	we	PRON
ejpam-5113	133	8	characterize	characterize	VERB
ejpam-5113	133	9	the	the	DET
ejpam-5113	133	10	compactness	compactness	NOUN
ejpam-5113	133	11	of	of	ADP
ejpam-5113	133	12	iφg	iφg	NOUN
ejpam-5113	133	13	that	that	PRON
ejpam-5113	133	14	acts	act	VERB
ejpam-5113	133	15	between	between	ADP
ejpam-5113	133	16	sp	sp	ADP
ejpam-5113	133	17	spaces	space	NOUN
ejpam-5113	133	18	and	and	CCONJ
ejpam-5113	133	19	weighted	weight	VERB
ejpam-5113	133	20	zygmund	zygmund	PROPN
ejpam-5113	133	21	spaces	space	NOUN
ejpam-5113	133	22	.	.	PUNCT
ejpam-5113	134	1	theorem	theorem	NOUN
ejpam-5113	134	2	2	2	NUM
ejpam-5113	134	3	.	.	PUNCT
ejpam-5113	135	1	let	let	VERB
ejpam-5113	135	2	g	g	NOUN
ejpam-5113	135	3	be	be	AUX
ejpam-5113	135	4	an	an	DET
ejpam-5113	135	5	analytic	analytic	ADJ
ejpam-5113	135	6	function	function	NOUN
ejpam-5113	135	7	on	on	ADP
ejpam-5113	135	8	d	d	PROPN
ejpam-5113	135	9	,	,	PUNCT
ejpam-5113	135	10	φ	φ	PROPN
ejpam-5113	135	11	be	be	VERB
ejpam-5113	135	12	an	an	DET
ejpam-5113	135	13	analytic	analytic	ADJ
ejpam-5113	135	14	selfmap	selfmap	NOUN
ejpam-5113	135	15	of	of	ADP
ejpam-5113	135	16	d	d	PROPN
ejpam-5113	135	17	and	and	CCONJ
ejpam-5113	135	18	iφg	iφg	NOUN
ejpam-5113	135	19	:	:	PUNCT
ejpam-5113	135	20	sp	sp	ADP
ejpam-5113	135	21	→	→	PUNCT
ejpam-5113	135	22	zµ	zµ	AUX
ejpam-5113	135	23	be	be	AUX
ejpam-5113	135	24	bounded	bound	VERB
ejpam-5113	135	25	.	.	PUNCT
ejpam-5113	136	1	then	then	ADV
ejpam-5113	136	2	iφg	iφg	PROPN
ejpam-5113	136	3	is	be	AUX
ejpam-5113	136	4	compact	compact	ADJ
ejpam-5113	136	5	if	if	SCONJ
ejpam-5113	137	1	and	and	CCONJ
ejpam-5113	137	2	only	only	ADV
ejpam-5113	137	3	if	if	SCONJ
ejpam-5113	137	4	lim	lim	PROPN
ejpam-5113	137	5	|φ(z)|→1	|φ(z)|→1	PROPN
ejpam-5113	137	6	k1(z	k1(z	PROPN
ejpam-5113	137	7	)	)	PUNCT
ejpam-5113	137	8	=	=	SYM
ejpam-5113	137	9	0	0	NUM
ejpam-5113	137	10	and	and	CCONJ
ejpam-5113	137	11	lim	lim	PROPN
ejpam-5113	137	12	|φ(z)|→1	|φ(z)|→1	PROPN
ejpam-5113	137	13	k2(z	k2(z	PROPN
ejpam-5113	137	14	)	)	PUNCT
ejpam-5113	137	15	=	=	NOUN
ejpam-5113	137	16	0	0	X
ejpam-5113	137	17	.	.	PUNCT
ejpam-5113	137	18	(	(	PUNCT
ejpam-5113	137	19	10	10	NUM
ejpam-5113	137	20	)	)	PUNCT
ejpam-5113	137	21	proof	proof	NOUN
ejpam-5113	137	22	.	.	PUNCT
ejpam-5113	138	1	suppose	suppose	VERB
ejpam-5113	138	2	iφg	iφg	NOUN
ejpam-5113	138	3	is	be	AUX
ejpam-5113	138	4	compact	compact	ADJ
ejpam-5113	138	5	.	.	PUNCT
ejpam-5113	139	1	let	let	VERB
ejpam-5113	139	2	{	{	PUNCT
ejpam-5113	139	3	zn}n∈n	zn}n∈n	VERB
ejpam-5113	139	4	be	be	AUX
ejpam-5113	139	5	a	a	DET
ejpam-5113	139	6	sequence	sequence	NOUN
ejpam-5113	139	7	in	in	ADP
ejpam-5113	139	8	the	the	DET
ejpam-5113	139	9	open	open	ADJ
ejpam-5113	139	10	unit	unit	NOUN
ejpam-5113	139	11	disk	disk	NOUN
ejpam-5113	139	12	d	d	NOUN
ejpam-5113	139	13	such	such	ADJ
ejpam-5113	139	14	that	that	SCONJ
ejpam-5113	139	15	|φ(zn)|	|φ(zn)|	NOUN
ejpam-5113	139	16	→	→	SYM
ejpam-5113	139	17	1	1	NUM
ejpam-5113	139	18	as	as	ADP
ejpam-5113	139	19	n	n	NUM
ejpam-5113	139	20	→	→	PUNCT
ejpam-5113	139	21	∞.	∞.	PROPN
ejpam-5113	139	22	for	for	ADP
ejpam-5113	139	23	each	each	DET
ejpam-5113	139	24	n	n	PRON
ejpam-5113	139	25	∈	∈	PROPN
ejpam-5113	139	26	n	n	CCONJ
ejpam-5113	139	27	,	,	PUNCT
ejpam-5113	139	28	consider	consider	VERB
ejpam-5113	139	29	the	the	DET
ejpam-5113	139	30	test	test	NOUN
ejpam-5113	139	31	functions	function	NOUN
ejpam-5113	139	32	f1,w	f1,w	PROPN
ejpam-5113	139	33	and	and	CCONJ
ejpam-5113	139	34	f2,w	f2,w	PROPN
ejpam-5113	139	35	we	we	PRON
ejpam-5113	139	36	used	use	VERB
ejpam-5113	139	37	in	in	ADP
ejpam-5113	139	38	the	the	DET
ejpam-5113	139	39	proof	proof	NOUN
ejpam-5113	139	40	of	of	ADP
ejpam-5113	139	41	theorem	theorem	NOUN
ejpam-5113	139	42	1	1	NUM
ejpam-5113	139	43	with	with	ADP
ejpam-5113	139	44	w	w	PROPN
ejpam-5113	139	45	=	=	SYM
ejpam-5113	139	46	zn	zn	PROPN
ejpam-5113	139	47	.	.	PUNCT
ejpam-5113	140	1	then	then	ADV
ejpam-5113	140	2	,	,	PUNCT
ejpam-5113	140	3	we	we	PRON
ejpam-5113	140	4	get	get	VERB
ejpam-5113	140	5	f1,zn(φ(zn	f1,zn(φ(zn	NOUN
ejpam-5113	140	6	)	)	PUNCT
ejpam-5113	140	7	)	)	PUNCT
ejpam-5113	141	1	=	=	SYM
ejpam-5113	141	2	φ(zn	φ(zn	X
ejpam-5113	141	3	)	)	PUNCT
ejpam-5113	141	4	(	(	PUNCT
ejpam-5113	141	5	1−	1−	NUM
ejpam-5113	141	6	|φ(zn)|2	|φ(zn)|2	NOUN
ejpam-5113	141	7	)	)	PUNCT
ejpam-5113	141	8	1−1	1−1	NUM
ejpam-5113	141	9	/	/	SYM
ejpam-5113	141	10	p	p	NOUN
ejpam-5113	141	11	,	,	PUNCT
ejpam-5113	141	12	and	and	CCONJ
ejpam-5113	141	13	f2,zn(φ(zn	f2,zn(φ(zn	NOUN
ejpam-5113	141	14	)	)	PUNCT
ejpam-5113	141	15	)	)	PUNCT
ejpam-5113	141	16	=	=	PUNCT
ejpam-5113	142	1	φ(zn	φ(zn	NUM
ejpam-5113	142	2	)	)	PUNCT
ejpam-5113	142	3	2	2	NUM
ejpam-5113	142	4	(	(	PUNCT
ejpam-5113	142	5	1−	1−	NUM
ejpam-5113	142	6	|φ(zn)|2	|φ(zn)|2	NOUN
ejpam-5113	142	7	)	)	PUNCT
ejpam-5113	142	8	1−1	1−1	NUM
ejpam-5113	142	9	/	/	SYM
ejpam-5113	142	10	p	p	X
ejpam-5113	142	11	(	(	PUNCT
ejpam-5113	142	12	2−	2−	NUM
ejpam-5113	142	13	|φ(zn)|2	|φ(zn)|2	NOUN
ejpam-5113	142	14	)	)	PUNCT
ejpam-5113	142	15	.	.	PUNCT
ejpam-5113	143	1	hence	hence	ADV
ejpam-5113	143	2	,	,	PUNCT
ejpam-5113	143	3	the	the	DET
ejpam-5113	143	4	sequences	sequence	NOUN
ejpam-5113	143	5	{	{	PUNCT
ejpam-5113	143	6	f1,zn	f1,zn	NOUN
ejpam-5113	143	7	}	}	PUNCT
ejpam-5113	143	8	and	and	CCONJ
ejpam-5113	143	9	{	{	PUNCT
ejpam-5113	143	10	f2,zn	f2,zn	NOUN
ejpam-5113	143	11	}	}	PUNCT
ejpam-5113	143	12	converge	converge	VERB
ejpam-5113	143	13	to	to	ADP
ejpam-5113	143	14	zero	zero	NUM
ejpam-5113	143	15	uniformly	uniformly	ADV
ejpam-5113	143	16	on	on	ADP
ejpam-5113	143	17	d.	d.	PROPN
ejpam-5113	143	18	then	then	ADV
ejpam-5113	143	19	,	,	PUNCT
ejpam-5113	143	20	by	by	ADP
ejpam-5113	143	21	the	the	DET
ejpam-5113	143	22	compactness	compactness	NOUN
ejpam-5113	143	23	of	of	ADP
ejpam-5113	143	24	iφg	iφg	NOUN
ejpam-5113	143	25	,	,	PUNCT
ejpam-5113	143	26	we	we	PRON
ejpam-5113	143	27	get	get	VERB
ejpam-5113	143	28	lim	lim	PROPN
ejpam-5113	143	29	n→∞	n→∞	NUM
ejpam-5113	143	30	∥iφg	∥iφg	ADV
ejpam-5113	143	31	f1,zn∥zµ	f1,zn∥zµ	NOUN
ejpam-5113	143	32	=	=	NOUN
ejpam-5113	143	33	0	0	PUNCT
ejpam-5113	144	1	and	and	CCONJ
ejpam-5113	144	2	lim	lim	PROPN
ejpam-5113	144	3	n→∞	n→∞	NUM
ejpam-5113	145	1	∥iφg	∥iφg	ADV
ejpam-5113	145	2	f2,zn∥zµ	f2,zn∥zµ	ADJ
ejpam-5113	145	3	=	=	NOUN
ejpam-5113	145	4	0	0	PROPN
ejpam-5113	145	5	.	.	PUNCT
ejpam-5113	146	1	(	(	PUNCT
ejpam-5113	146	2	11	11	NUM
ejpam-5113	146	3	)	)	PUNCT
ejpam-5113	146	4	now	now	ADV
ejpam-5113	146	5	,	,	PUNCT
ejpam-5113	146	6	following	follow	VERB
ejpam-5113	146	7	similar	similar	ADJ
ejpam-5113	146	8	argument	argument	NOUN
ejpam-5113	146	9	as	as	ADP
ejpam-5113	146	10	in	in	ADP
ejpam-5113	146	11	the	the	DET
ejpam-5113	146	12	proof	proof	NOUN
ejpam-5113	146	13	of	of	ADP
ejpam-5113	146	14	theorem	theorem	NOUN
ejpam-5113	146	15	1	1	NUM
ejpam-5113	146	16	,	,	PUNCT
ejpam-5113	146	17	we	we	PRON
ejpam-5113	146	18	get	get	VERB
ejpam-5113	146	19	µ(zn	µ(zn	NOUN
ejpam-5113	146	20	)	)	PUNCT
ejpam-5113	146	21	∣∣∣φ(zn)φ′(zn)g(zn	∣∣∣φ(zn)φ′(zn)g(zn	PROPN
ejpam-5113	146	22	)	)	PUNCT
ejpam-5113	146	23	∣∣∣	∣∣∣	NOUN
ejpam-5113	147	1	(	(	PUNCT
ejpam-5113	147	2	1−	1−	NUM
ejpam-5113	147	3	|φ(zn)|2)(p+1)/p	|φ(zn)|2)(p+1)/p	NOUN
ejpam-5113	147	4	≤	≤	NOUN
ejpam-5113	147	5	∥iφg	∥iφg	ADJ
ejpam-5113	147	6	f1,w∥zµ	f1,w∥zµ	NOUN
ejpam-5113	148	1	+	+	CCONJ
ejpam-5113	148	2	∥iφg	∥iφg	PROPN
ejpam-5113	148	3	f2,w∥zµ	f2,w∥zµ	INTJ
ejpam-5113	148	4	.	.	PUNCT
ejpam-5113	149	1	(	(	PUNCT
ejpam-5113	149	2	12	12	NUM
ejpam-5113	149	3	)	)	PUNCT
ejpam-5113	149	4	hence	hence	ADV
ejpam-5113	149	5	,	,	PUNCT
ejpam-5113	149	6	using	use	VERB
ejpam-5113	149	7	equations	equation	NOUN
ejpam-5113	149	8	(	(	PUNCT
ejpam-5113	149	9	11	11	NUM
ejpam-5113	149	10	)	)	PUNCT
ejpam-5113	149	11	and	and	CCONJ
ejpam-5113	149	12	(	(	PUNCT
ejpam-5113	149	13	12	12	NUM
ejpam-5113	149	14	)	)	PUNCT
ejpam-5113	149	15	,	,	PUNCT
ejpam-5113	149	16	we	we	PRON
ejpam-5113	149	17	get	get	VERB
ejpam-5113	149	18	lim	lim	PROPN
ejpam-5113	149	19	n→∞	n→∞	NUM
ejpam-5113	149	20	µ(zn	µ(zn	PROPN
ejpam-5113	149	21	)	)	PUNCT
ejpam-5113	149	22	|φ′(zn)g(zn)|	|φ′(zn)g(zn)|	PROPN
ejpam-5113	149	23	(	(	PUNCT
ejpam-5113	149	24	1−	1−	NUM
ejpam-5113	149	25	|φ(zn)|2)(p+1)/p	|φ(zn)|2)(p+1)/p	NOUN
ejpam-5113	150	1	=	=	NOUN
ejpam-5113	150	2	0	0	X
ejpam-5113	150	3	.	.	PUNCT
ejpam-5113	151	1	(	(	PUNCT
ejpam-5113	151	2	13	13	NUM
ejpam-5113	151	3	)	)	PUNCT
ejpam-5113	151	4	moreover	moreover	ADV
ejpam-5113	151	5	,	,	PUNCT
ejpam-5113	151	6	following	follow	VERB
ejpam-5113	151	7	similar	similar	ADJ
ejpam-5113	151	8	argument	argument	NOUN
ejpam-5113	151	9	as	as	ADP
ejpam-5113	151	10	in	in	ADP
ejpam-5113	151	11	the	the	DET
ejpam-5113	151	12	proof	proof	NOUN
ejpam-5113	151	13	of	of	ADP
ejpam-5113	151	14	theorem	theorem	NOUN
ejpam-5113	151	15	1	1	NUM
ejpam-5113	151	16	,	,	PUNCT
ejpam-5113	151	17	we	we	PRON
ejpam-5113	151	18	get	get	VERB
ejpam-5113	151	19	µ(zn	µ(zn	NOUN
ejpam-5113	151	20	)	)	PUNCT
ejpam-5113	151	21	|g′(zn)|	|g′(zn)|	NOUN
ejpam-5113	151	22	(	(	PUNCT
ejpam-5113	151	23	1−	1−	NUM
ejpam-5113	151	24	|φ(zn)|2)1	|φ(zn)|2)1	VERB
ejpam-5113	151	25	/	/	SYM
ejpam-5113	151	26	p	p	NOUN
ejpam-5113	151	27	≤	≤	NUM
ejpam-5113	151	28	∥iφg	∥iφg	NOUN
ejpam-5113	151	29	f1,w∥zµ∥+	f1,w∥zµ∥+	NOUN
ejpam-5113	151	30	2µ(zn	2µ(zn	NUM
ejpam-5113	151	31	)	)	PUNCT
ejpam-5113	151	32	|φ′(zn)g(zn)|	|φ′(zn)g(zn)|	PROPN
ejpam-5113	152	1	(	(	PUNCT
ejpam-5113	152	2	1−	1−	NUM
ejpam-5113	152	3	|φ(zn)|2)(p+1)/p	|φ(zn)|2)(p+1)/p	NOUN
ejpam-5113	152	4	.	.	PUNCT
ejpam-5113	153	1	(	(	PUNCT
ejpam-5113	153	2	14	14	NUM
ejpam-5113	153	3	)	)	PUNCT
ejpam-5113	153	4	w.	w.	PROPN
ejpam-5113	153	5	al	al	PROPN
ejpam-5113	153	6	-	-	PUNCT
ejpam-5113	153	7	rawashdeh	rawashdeh	PROPN
ejpam-5113	153	8	/	/	SYM
ejpam-5113	153	9	eur	eur	PROPN
ejpam-5113	153	10	.	.	PUNCT
ejpam-5113	154	1	j.	j.	PROPN
ejpam-5113	154	2	pure	pure	PROPN
ejpam-5113	154	3	appl	appl	PROPN
ejpam-5113	154	4	.	.	PROPN
ejpam-5113	154	5	math	math	PROPN
ejpam-5113	154	6	,	,	PUNCT
ejpam-5113	154	7	17	17	NUM
ejpam-5113	154	8	(	(	PUNCT
ejpam-5113	154	9	2	2	NUM
ejpam-5113	154	10	)	)	PUNCT
ejpam-5113	154	11	(	(	PUNCT
ejpam-5113	154	12	2024	2024	NUM
ejpam-5113	154	13	)	)	PUNCT
ejpam-5113	155	1	,	,	PUNCT
ejpam-5113	155	2	931	931	NUM
ejpam-5113	155	3	-	-	SYM
ejpam-5113	155	4	944	944	NUM
ejpam-5113	155	5	939	939	NUM
ejpam-5113	155	6	hence	hence	ADV
ejpam-5113	155	7	,	,	PUNCT
ejpam-5113	155	8	using	use	VERB
ejpam-5113	155	9	equations	equation	NOUN
ejpam-5113	155	10	(	(	PUNCT
ejpam-5113	155	11	11	11	NUM
ejpam-5113	155	12	)	)	PUNCT
ejpam-5113	155	13	and	and	CCONJ
ejpam-5113	155	14	(	(	PUNCT
ejpam-5113	155	15	14	14	NUM
ejpam-5113	155	16	)	)	PUNCT
ejpam-5113	155	17	,	,	PUNCT
ejpam-5113	155	18	we	we	PRON
ejpam-5113	155	19	get	get	VERB
ejpam-5113	155	20	lim	lim	PROPN
ejpam-5113	155	21	n→∞	n→∞	NUM
ejpam-5113	155	22	µ(zn	µ(zn	NOUN
ejpam-5113	155	23	)	)	PUNCT
ejpam-5113	155	24	|g′(zn)|	|g′(zn)|	NOUN
ejpam-5113	155	25	(	(	PUNCT
ejpam-5113	155	26	1−	1−	NUM
ejpam-5113	155	27	|φ(zn)|2)1	|φ(zn)|2)1	VERB
ejpam-5113	155	28	/	/	SYM
ejpam-5113	155	29	p	p	NOUN
ejpam-5113	156	1	=	=	NOUN
ejpam-5113	157	1	0	0	NUM
ejpam-5113	157	2	.	.	PUNCT
ejpam-5113	158	1	(	(	PUNCT
ejpam-5113	158	2	15	15	NUM
ejpam-5113	158	3	)	)	PUNCT
ejpam-5113	158	4	therefore	therefore	ADV
ejpam-5113	158	5	,	,	PUNCT
ejpam-5113	158	6	equations	equation	NOUN
ejpam-5113	158	7	(	(	PUNCT
ejpam-5113	158	8	13	13	NUM
ejpam-5113	158	9	)	)	PUNCT
ejpam-5113	158	10	and	and	CCONJ
ejpam-5113	158	11	(	(	PUNCT
ejpam-5113	158	12	15	15	X
ejpam-5113	158	13	)	)	PUNCT
ejpam-5113	158	14	give	give	VERB
ejpam-5113	158	15	us	we	PRON
ejpam-5113	158	16	the	the	DET
ejpam-5113	158	17	desired	desire	VERB
ejpam-5113	158	18	conditions	condition	NOUN
ejpam-5113	158	19	lim	lim	PROPN
ejpam-5113	158	20	|φ(z)|→1	|φ(z)|→1	PROPN
ejpam-5113	158	21	k1(z	k1(z	PROPN
ejpam-5113	158	22	)	)	PUNCT
ejpam-5113	158	23	=	=	SYM
ejpam-5113	158	24	0	0	NUM
ejpam-5113	159	1	and	and	CCONJ
ejpam-5113	159	2	lim	lim	PROPN
ejpam-5113	159	3	|φ(z)|→1	|φ(z)|→1	PROPN
ejpam-5113	159	4	k2(z	k2(z	PROPN
ejpam-5113	159	5	)	)	PUNCT
ejpam-5113	159	6	=	=	SYM
ejpam-5113	159	7	0	0	X
ejpam-5113	159	8	.	.	PUNCT
ejpam-5113	160	1	conversely	conversely	ADV
ejpam-5113	160	2	,	,	PUNCT
ejpam-5113	160	3	suppose	suppose	VERB
ejpam-5113	160	4	conditions	condition	NOUN
ejpam-5113	160	5	(	(	PUNCT
ejpam-5113	160	6	10	10	NUM
ejpam-5113	160	7	)	)	PUNCT
ejpam-5113	160	8	hold	hold	NOUN
ejpam-5113	160	9	.	.	PUNCT
ejpam-5113	161	1	then	then	ADV
ejpam-5113	161	2	for	for	ADP
ejpam-5113	161	3	ϵ	ϵ	PROPN
ejpam-5113	161	4	>	>	X
ejpam-5113	161	5	0	0	NUM
ejpam-5113	161	6	,	,	PUNCT
ejpam-5113	161	7	there	there	PRON
ejpam-5113	161	8	is	be	VERB
ejpam-5113	161	9	δ	δ	PROPN
ejpam-5113	161	10	∈	∈	PROPN
ejpam-5113	161	11	(	(	PUNCT
ejpam-5113	161	12	0	0	NUM
ejpam-5113	161	13	,	,	PUNCT
ejpam-5113	161	14	1	1	NUM
ejpam-5113	161	15	)	)	PUNCT
ejpam-5113	161	16	such	such	ADJ
ejpam-5113	161	17	that	that	SCONJ
ejpam-5113	161	18	k1(z	k1(z	PROPN
ejpam-5113	161	19	)	)	PUNCT
ejpam-5113	161	20	<	<	X
ejpam-5113	161	21	ϵ	ϵ	PROPN
ejpam-5113	161	22	and	and	CCONJ
ejpam-5113	161	23	k2(z	k2(z	PROPN
ejpam-5113	161	24	)	)	PUNCT
ejpam-5113	161	25	<	<	X
ejpam-5113	162	1	ϵ	ϵ	X
ejpam-5113	162	2	whenever	whenever	SCONJ
ejpam-5113	162	3	δ	δ	X
ejpam-5113	162	4	<	<	X
ejpam-5113	162	5	|φ(z)|	|φ(z)|	X
ejpam-5113	162	6	<	<	X
ejpam-5113	162	7	1	1	NUM
ejpam-5113	162	8	.	.	PUNCT
ejpam-5113	163	1	let	let	AUX
ejpam-5113	163	2	{	{	PUNCT
ejpam-5113	163	3	fn	fn	AUX
ejpam-5113	163	4	}	}	PUNCT
ejpam-5113	163	5	be	be	AUX
ejpam-5113	163	6	a	a	DET
ejpam-5113	163	7	bounded	bounded	ADJ
ejpam-5113	163	8	sequence	sequence	NOUN
ejpam-5113	163	9	in	in	ADP
ejpam-5113	163	10	sp	sp	ADP
ejpam-5113	163	11	such	such	ADJ
ejpam-5113	163	12	that	that	DET
ejpam-5113	163	13	sup	sup	NOUN
ejpam-5113	163	14	n∈n	n∈n	ADV
ejpam-5113	163	15	∥fn∥sp	∥fn∥sp	NOUN
ejpam-5113	163	16	<	<	X
ejpam-5113	163	17	l	l	NOUN
ejpam-5113	163	18	and	and	CCONJ
ejpam-5113	163	19	{	{	PUNCT
ejpam-5113	163	20	fn	fn	NOUN
ejpam-5113	163	21	}	}	PUNCT
ejpam-5113	163	22	converges	converge	NOUN
ejpam-5113	163	23	to	to	ADP
ejpam-5113	163	24	zero	zero	NUM
ejpam-5113	163	25	uniformly	uniformly	ADV
ejpam-5113	163	26	on	on	ADP
ejpam-5113	163	27	compact	compact	ADJ
ejpam-5113	163	28	subsets	subset	NOUN
ejpam-5113	163	29	of	of	ADP
ejpam-5113	163	30	d.	d.	PROPN
ejpam-5113	163	31	let	let	VERB
ejpam-5113	163	32	u	u	PRON
ejpam-5113	163	33	=	=	PUNCT
ejpam-5113	163	34	{	{	PUNCT
ejpam-5113	163	35	z	z	NOUN
ejpam-5113	163	36	∈	∈	PROPN
ejpam-5113	163	37	d	d	NOUN
ejpam-5113	163	38	:	:	PUNCT
ejpam-5113	163	39	|φ(z)|	|φ(z)|	ADP
ejpam-5113	163	40	≤	≤	NUM
ejpam-5113	163	41	δ	δ	PROPN
ejpam-5113	163	42	}	}	PUNCT
ejpam-5113	163	43	.	.	PUNCT
ejpam-5113	164	1	now	now	ADV
ejpam-5113	164	2	,	,	PUNCT
ejpam-5113	164	3	it	it	PRON
ejpam-5113	164	4	is	be	AUX
ejpam-5113	164	5	clear	clear	ADJ
ejpam-5113	164	6	that	that	SCONJ
ejpam-5113	164	7	sup	sup	VERB
ejpam-5113	164	8	z∈d	z∈d	NOUN
ejpam-5113	164	9	µ(z	µ(z	NOUN
ejpam-5113	164	10	)	)	PUNCT
ejpam-5113	164	11	∣∣∣(iφg	∣∣∣(iφg	ADJ
ejpam-5113	164	12	fn)′′	fn)′′	PROPN
ejpam-5113	164	13	(	(	PUNCT
ejpam-5113	164	14	z)∣∣∣	z)∣∣∣	ADJ
ejpam-5113	164	15	≤	≤	NUM
ejpam-5113	164	16	sup	sup	NOUN
ejpam-5113	164	17	z∈d\u	z∈d\u	PROPN
ejpam-5113	164	18	µ(z	µ(z	PROPN
ejpam-5113	164	19	)	)	PUNCT
ejpam-5113	164	20	∣∣∣(iφg	∣∣∣(iφg	ADJ
ejpam-5113	164	21	fn)′′	fn)′′	PROPN
ejpam-5113	164	22	(	(	PUNCT
ejpam-5113	164	23	z)∣∣∣+	z)∣∣∣+	PROPN
ejpam-5113	164	24	sup	sup	NUM
ejpam-5113	164	25	z∈u	z∈u	PROPN
ejpam-5113	164	26	µ(z	µ(z	PROPN
ejpam-5113	164	27	)	)	PUNCT
ejpam-5113	164	28	∣∣∣(iφg	∣∣∣(iφg	ADJ
ejpam-5113	164	29	fn)′′	fn)′′	PROPN
ejpam-5113	164	30	(	(	PUNCT
ejpam-5113	164	31	z)∣∣∣	z)∣∣∣	ADV
ejpam-5113	164	32	first	first	ADV
ejpam-5113	164	33	,	,	PUNCT
ejpam-5113	164	34	we	we	PRON
ejpam-5113	164	35	consider	consider	VERB
ejpam-5113	164	36	the	the	DET
ejpam-5113	164	37	case	case	NOUN
ejpam-5113	164	38	|φ(z)|	|φ(z)|	VERB
ejpam-5113	164	39	>	>	X
ejpam-5113	164	40	δ	δ	PROPN
ejpam-5113	164	41	then	then	ADV
ejpam-5113	164	42	we	we	PRON
ejpam-5113	164	43	have	have	VERB
ejpam-5113	164	44	µ(z	µ(z	NOUN
ejpam-5113	164	45	)	)	PUNCT
ejpam-5113	164	46	∣∣∣(iφg	∣∣∣(iφg	ADJ
ejpam-5113	164	47	fn)′′	fn)′′	NOUN
ejpam-5113	164	48	(	(	PUNCT
ejpam-5113	164	49	z)∣∣∣	z)∣∣∣	NOUN
ejpam-5113	164	50	=	=	SYM
ejpam-5113	164	51	µ(z	µ(z	PROPN
ejpam-5113	164	52	)	)	PUNCT
ejpam-5113	164	53	∣∣f	∣∣f	NOUN
ejpam-5113	164	54	′′	′′	PROPN
ejpam-5113	164	55	n(φ(z))φ	n(φ(z))φ	ADJ
ejpam-5113	164	56	′(z)g(z	′(z)g(z	NOUN
ejpam-5113	164	57	)	)	PUNCT
ejpam-5113	165	1	+	+	NUM
ejpam-5113	165	2	f	f	AUX
ejpam-5113	165	3	′	′	NOUN
ejpam-5113	165	4	n(φ(z))g	n(φ(z))g	NUM
ejpam-5113	165	5	′(z	′(z	NOUN
ejpam-5113	165	6	)	)	PUNCT
ejpam-5113	166	1	∣∣	∣∣	X
ejpam-5113	167	1	≤	≤	X
ejpam-5113	167	2	µ(z)|φ′(z)g(z)|	µ(z)|φ′(z)g(z)|	X
ejpam-5113	167	3	(	(	PUNCT
ejpam-5113	167	4	1−	1−	NUM
ejpam-5113	167	5	|φ(z)|2)(p+1)/p	|φ(z)|2)(p+1)/p	NOUN
ejpam-5113	167	6	∥f	∥f	PROPN
ejpam-5113	167	7	′	′	NUM
ejpam-5113	168	1	n∥hp	n∥hp	NOUN
ejpam-5113	168	2	+	+	CCONJ
ejpam-5113	168	3	µ(z)|g′(z)|	µ(z)|g′(z)|	X
ejpam-5113	168	4	(	(	PUNCT
ejpam-5113	168	5	1−	1−	NUM
ejpam-5113	168	6	|φ(z)|2)1	|φ(z)|2)1	NOUN
ejpam-5113	168	7	/	/	SYM
ejpam-5113	168	8	p	p	NOUN
ejpam-5113	168	9	∥f	∥f	PROPN
ejpam-5113	168	10	′	′	NUM
ejpam-5113	169	1	n∥hp	n∥hp	PROPN
ejpam-5113	169	2	≤	≤	PROPN
ejpam-5113	169	3	(	(	PUNCT
ejpam-5113	169	4	k2(z	k2(z	PROPN
ejpam-5113	169	5	)	)	PUNCT
ejpam-5113	169	6	+	+	NOUN
ejpam-5113	169	7	k1(z	k1(z	PROPN
ejpam-5113	169	8	)	)	PUNCT
ejpam-5113	169	9	)	)	PUNCT
ejpam-5113	170	1	∥fn∥sp	∥fn∥sp	ADP
ejpam-5113	170	2	<	<	X
ejpam-5113	170	3	2lϵ.	2lϵ.	NUM
ejpam-5113	170	4	(	(	PUNCT
ejpam-5113	170	5	16	16	NUM
ejpam-5113	170	6	)	)	PUNCT
ejpam-5113	170	7	second	second	ADJ
ejpam-5113	170	8	,	,	PUNCT
ejpam-5113	170	9	we	we	PRON
ejpam-5113	170	10	consider	consider	VERB
ejpam-5113	170	11	the	the	DET
ejpam-5113	170	12	case	case	NOUN
ejpam-5113	170	13	|φ(z)|	|φ(z)|	VERB
ejpam-5113	170	14	≤	≤	ADJ
ejpam-5113	170	15	δ	δ	PROPN
ejpam-5113	170	16	.	.	PUNCT
ejpam-5113	171	1	since	since	SCONJ
ejpam-5113	171	2	iφg	iφg	NOUN
ejpam-5113	171	3	is	be	AUX
ejpam-5113	171	4	bounded	bound	VERB
ejpam-5113	171	5	and	and	CCONJ
ejpam-5113	171	6	polynomials	polynomial	NOUN
ejpam-5113	171	7	are	be	AUX
ejpam-5113	171	8	dense	dense	ADJ
ejpam-5113	171	9	in	in	ADP
ejpam-5113	171	10	sp(d	sp(d	NOUN
ejpam-5113	171	11	)	)	PUNCT
ejpam-5113	171	12	,	,	PUNCT
ejpam-5113	171	13	by	by	ADP
ejpam-5113	171	14	taking	take	VERB
ejpam-5113	171	15	f(z	f(z	NOUN
ejpam-5113	171	16	)	)	PUNCT
ejpam-5113	172	1	=	=	PUNCT
ejpam-5113	172	2	z	z	NOUN
ejpam-5113	172	3	we	we	PRON
ejpam-5113	172	4	get	get	VERB
ejpam-5113	172	5	sup	sup	NOUN
ejpam-5113	172	6	z∈d	z∈d	NOUN
ejpam-5113	172	7	µ(z	µ(z	NOUN
ejpam-5113	172	8	)	)	PUNCT
ejpam-5113	172	9	∣∣∣(iφg	∣∣∣(iφg	PROPN
ejpam-5113	172	10	f)′′	f)′′	PROPN
ejpam-5113	172	11	(	(	PUNCT
ejpam-5113	172	12	z)∣∣∣	z)∣∣∣	NOUN
ejpam-5113	172	13	=	=	PUNCT
ejpam-5113	172	14	sup	sup	NOUN
ejpam-5113	172	15	z∈d	z∈d	VERB
ejpam-5113	172	16	µ(z)|g′(z)|	µ(z)|g′(z)|	PRON
ejpam-5113	172	17	<	<	X
ejpam-5113	172	18	∞	∞	PROPN
ejpam-5113	172	19	,	,	PUNCT
ejpam-5113	172	20	(	(	PUNCT
ejpam-5113	172	21	17	17	NUM
ejpam-5113	172	22	)	)	PUNCT
ejpam-5113	172	23	and	and	CCONJ
ejpam-5113	172	24	by	by	ADP
ejpam-5113	172	25	taking	take	VERB
ejpam-5113	172	26	f(z	f(z	PROPN
ejpam-5113	172	27	)	)	PUNCT
ejpam-5113	173	1	=	=	SYM
ejpam-5113	173	2	z2	z2	NOUN
ejpam-5113	173	3	we	we	PRON
ejpam-5113	173	4	get	get	VERB
ejpam-5113	173	5	sup	sup	NOUN
ejpam-5113	173	6	z∈d	z∈d	NOUN
ejpam-5113	173	7	µ(z	µ(z	NOUN
ejpam-5113	173	8	)	)	PUNCT
ejpam-5113	173	9	∣∣∣(iφg	∣∣∣(iφg	PROPN
ejpam-5113	173	10	f)′′	f)′′	PROPN
ejpam-5113	173	11	(	(	PUNCT
ejpam-5113	173	12	z)∣∣∣	z)∣∣∣	NOUN
ejpam-5113	173	13	=	=	SYM
ejpam-5113	173	14	2	2	NUM
ejpam-5113	173	15	sup	sup	NOUN
ejpam-5113	173	16	z∈d	z∈d	NUM
ejpam-5113	173	17	µ(z)|φ(z)g′(z	µ(z)|φ(z)g′(z	NOUN
ejpam-5113	173	18	)	)	PUNCT
ejpam-5113	173	19	+	+	CCONJ
ejpam-5113	173	20	φ′(z)g(z)|	φ′(z)g(z)|	ADJ
ejpam-5113	173	21	<	<	X
ejpam-5113	173	22	∞.	∞.	PROPN
ejpam-5113	173	23	(	(	PUNCT
ejpam-5113	173	24	18	18	NUM
ejpam-5113	173	25	)	)	PUNCT
ejpam-5113	173	26	using	use	VERB
ejpam-5113	173	27	equations	equation	NOUN
ejpam-5113	173	28	(	(	PUNCT
ejpam-5113	173	29	17	17	NUM
ejpam-5113	173	30	)	)	PUNCT
ejpam-5113	173	31	and	and	CCONJ
ejpam-5113	173	32	(	(	PUNCT
ejpam-5113	173	33	18	18	NUM
ejpam-5113	173	34	)	)	PUNCT
ejpam-5113	173	35	,	,	PUNCT
ejpam-5113	173	36	and	and	CCONJ
ejpam-5113	173	37	the	the	DET
ejpam-5113	173	38	boundedness	boundedness	NOUN
ejpam-5113	173	39	of	of	ADP
ejpam-5113	173	40	φ(z	φ(z	PROPN
ejpam-5113	173	41	)	)	PUNCT
ejpam-5113	173	42	we	we	PRON
ejpam-5113	173	43	get	get	VERB
ejpam-5113	173	44	w.	w.	PROPN
ejpam-5113	173	45	al	al	PROPN
ejpam-5113	173	46	-	-	PUNCT
ejpam-5113	173	47	rawashdeh	rawashdeh	PROPN
ejpam-5113	173	48	/	/	SYM
ejpam-5113	173	49	eur	eur	PROPN
ejpam-5113	173	50	.	.	PUNCT
ejpam-5113	174	1	j.	j.	PROPN
ejpam-5113	174	2	pure	pure	PROPN
ejpam-5113	174	3	appl	appl	PROPN
ejpam-5113	174	4	.	.	PROPN
ejpam-5113	174	5	math	math	PROPN
ejpam-5113	174	6	,	,	PUNCT
ejpam-5113	174	7	17	17	NUM
ejpam-5113	174	8	(	(	PUNCT
ejpam-5113	174	9	2	2	NUM
ejpam-5113	174	10	)	)	PUNCT
ejpam-5113	174	11	(	(	PUNCT
ejpam-5113	174	12	2024	2024	NUM
ejpam-5113	174	13	)	)	PUNCT
ejpam-5113	174	14	,	,	PUNCT
ejpam-5113	174	15	931	931	NUM
ejpam-5113	174	16	-	-	SYM
ejpam-5113	174	17	944	944	NUM
ejpam-5113	174	18	940	940	NUM
ejpam-5113	174	19	c1	c1	NOUN
ejpam-5113	174	20	=	=	PUNCT
ejpam-5113	175	1	sup	sup	AUX
ejpam-5113	175	2	z∈d	z∈d	NUM
ejpam-5113	175	3	µ(z)|g′(z)|	µ(z)|g′(z)|	PRON
ejpam-5113	175	4	<	<	X
ejpam-5113	175	5	∞	∞	PROPN
ejpam-5113	175	6	,	,	PUNCT
ejpam-5113	175	7	and	and	CCONJ
ejpam-5113	175	8	c2	c2	PROPN
ejpam-5113	175	9	=	=	PUNCT
ejpam-5113	175	10	sup	sup	NUM
ejpam-5113	175	11	z∈d	z∈d	NOUN
ejpam-5113	175	12	µ(z)|φ′(z)g(z)|	µ(z)|φ′(z)g(z)|	NOUN
ejpam-5113	175	13	<	<	X
ejpam-5113	175	14	∞	∞	PROPN
ejpam-5113	175	15	hence	hence	ADV
ejpam-5113	175	16	,	,	PUNCT
ejpam-5113	175	17	for	for	ADP
ejpam-5113	175	18	|φ(z)|	|φ(z)|	PROPN
ejpam-5113	175	19	≤	≤	ADJ
ejpam-5113	175	20	δ	δ	PROPN
ejpam-5113	175	21	,	,	PUNCT
ejpam-5113	175	22	using	use	VERB
ejpam-5113	175	23	these	these	DET
ejpam-5113	175	24	facts	fact	NOUN
ejpam-5113	175	25	we	we	PRON
ejpam-5113	175	26	get	get	VERB
ejpam-5113	175	27	µ(z	µ(z	PROPN
ejpam-5113	175	28	)	)	PUNCT
ejpam-5113	175	29	∣∣∣(iφg	∣∣∣(iφg	ADJ
ejpam-5113	175	30	fn)′′	fn)′′	PROPN
ejpam-5113	175	31	(	(	PUNCT
ejpam-5113	175	32	z)∣∣∣	z)∣∣∣	PROPN
ejpam-5113	175	33	≤	≤	PROPN
ejpam-5113	175	34	c2	c2	PROPN
ejpam-5113	175	35	∣∣f	∣∣f	PROPN
ejpam-5113	175	36	′′	′′	PROPN
ejpam-5113	175	37	n(φ(z	n(φ(z	NOUN
ejpam-5113	175	38	)	)	PUNCT
ejpam-5113	175	39	)	)	PUNCT
ejpam-5113	175	40	∣∣+	∣∣+	PROPN
ejpam-5113	175	41	c1	c1	PROPN
ejpam-5113	175	42	∣∣f	∣∣f	PROPN
ejpam-5113	175	43	′	′	NUM
ejpam-5113	175	44	n(φ(z	n(φ(z	NOUN
ejpam-5113	175	45	)	)	PUNCT
ejpam-5113	175	46	)	)	PUNCT
ejpam-5113	176	1	∣∣	∣∣	X
ejpam-5113	176	2	.	.	PUNCT
ejpam-5113	177	1	(	(	PUNCT
ejpam-5113	177	2	19	19	NUM
ejpam-5113	177	3	)	)	PUNCT
ejpam-5113	177	4	since	since	SCONJ
ejpam-5113	177	5	{	{	PUNCT
ejpam-5113	177	6	fn	fn	AUX
ejpam-5113	177	7	}	}	PUNCT
ejpam-5113	177	8	is	be	AUX
ejpam-5113	177	9	bounded	bound	VERB
ejpam-5113	177	10	in	in	ADP
ejpam-5113	177	11	sp	sp	ADP
ejpam-5113	177	12	and	and	CCONJ
ejpam-5113	177	13	converges	converge	VERB
ejpam-5113	177	14	to	to	ADP
ejpam-5113	177	15	zero	zero	NUM
ejpam-5113	177	16	on	on	ADP
ejpam-5113	177	17	{	{	PUNCT
ejpam-5113	177	18	w	w	PROPN
ejpam-5113	177	19	∈	∈	PROPN
ejpam-5113	178	1	d	d	NOUN
ejpam-5113	178	2	:	:	PUNCT
ejpam-5113	178	3	|w|	|w|	VERB
ejpam-5113	178	4	≤	≤	NUM
ejpam-5113	178	5	δ	δ	PROPN
ejpam-5113	178	6	}	}	PUNCT
ejpam-5113	178	7	,	,	PUNCT
ejpam-5113	178	8	so	so	ADV
ejpam-5113	178	9	do	do	VERB
ejpam-5113	178	10	the	the	DET
ejpam-5113	178	11	sequences	sequence	NOUN
ejpam-5113	178	12	{	{	PUNCT
ejpam-5113	178	13	f	f	NOUN
ejpam-5113	178	14	′	′	NUM
ejpam-5113	178	15	n	n	CCONJ
ejpam-5113	178	16	}	}	PUNCT
ejpam-5113	178	17	and	and	CCONJ
ejpam-5113	178	18	{	{	PUNCT
ejpam-5113	178	19	f	f	X
ejpam-5113	178	20	′′	′′	PROPN
ejpam-5113	178	21	n	n	CCONJ
ejpam-5113	178	22	}	}	PUNCT
ejpam-5113	178	23	by	by	ADP
ejpam-5113	178	24	cauchy	cauchy	PROPN
ejpam-5113	178	25	’s	’s	PART
ejpam-5113	178	26	estimate	estimate	NOUN
ejpam-5113	178	27	.	.	PUNCT
ejpam-5113	179	1	thus	thus	ADV
ejpam-5113	179	2	,	,	PUNCT
ejpam-5113	179	3	there	there	PRON
ejpam-5113	179	4	exists	exist	VERB
ejpam-5113	179	5	n	n	PRON
ejpam-5113	179	6	∈	∈	PROPN
ejpam-5113	179	7	d	d	ADP
ejpam-5113	179	8	such	such	ADJ
ejpam-5113	179	9	that	that	PRON
ejpam-5113	179	10	for	for	ADP
ejpam-5113	179	11	all	all	DET
ejpam-5113	179	12	n	n	DET
ejpam-5113	179	13	≥	≥	NOUN
ejpam-5113	179	14	n	n	NOUN
ejpam-5113	179	15	and	and	CCONJ
ejpam-5113	179	16	w	w	PROPN
ejpam-5113	179	17	∈	∈	PROPN
ejpam-5113	179	18	d	d	NOUN
ejpam-5113	179	19	with	with	ADP
ejpam-5113	179	20	|w|	|w|	ADJ
ejpam-5113	179	21	≤	≤	NUM
ejpam-5113	179	22	δ	δ	NOUN
ejpam-5113	179	23	we	we	PRON
ejpam-5113	179	24	have	have	VERB
ejpam-5113	179	25	|f	|f	PROPN
ejpam-5113	179	26	′	′	NUM
ejpam-5113	179	27	n(w)|	n(w)|	NOUN
ejpam-5113	179	28	<	<	X
ejpam-5113	179	29	ϵ	ϵ	PROPN
ejpam-5113	180	1	and	and	CCONJ
ejpam-5113	180	2	|f	|f	PRON
ejpam-5113	181	1	′′	′′	PROPN
ejpam-5113	181	2	n(w)|	n(w)|	VERB
ejpam-5113	181	3	<	<	X
ejpam-5113	181	4	ϵ	ϵ	X
ejpam-5113	181	5	hence	hence	ADV
ejpam-5113	181	6	,	,	PUNCT
ejpam-5113	181	7	using	use	VERB
ejpam-5113	181	8	inequality	inequality	NOUN
ejpam-5113	181	9	(	(	PUNCT
ejpam-5113	181	10	19	19	NUM
ejpam-5113	181	11	)	)	PUNCT
ejpam-5113	181	12	,	,	PUNCT
ejpam-5113	181	13	we	we	PRON
ejpam-5113	181	14	get	get	VERB
ejpam-5113	181	15	sup	sup	NOUN
ejpam-5113	181	16	z∈d	z∈d	NOUN
ejpam-5113	181	17	µ(z	µ(z	NOUN
ejpam-5113	181	18	)	)	PUNCT
ejpam-5113	181	19	∣∣∣(iφg	∣∣∣(iφg	ADJ
ejpam-5113	181	20	fn)′′	fn)′′	PROPN
ejpam-5113	181	21	(	(	PUNCT
ejpam-5113	181	22	z)∣∣∣	z)∣∣∣	PROPN
ejpam-5113	181	23	≤	≤	PROPN
ejpam-5113	181	24	c2	c2	PROPN
ejpam-5113	181	25	sup	sup	PROPN
ejpam-5113	181	26	|w|<δ	|w|<δ	PROPN
ejpam-5113	181	27	|f	|f	ADP
ejpam-5113	181	28	′′	′′	PROPN
ejpam-5113	181	29	n(w)|+	n(w)|+	PROPN
ejpam-5113	181	30	c1	c1	PROPN
ejpam-5113	181	31	sup	sup	PROPN
ejpam-5113	181	32	|w|<δ	|w|<δ	PROPN
ejpam-5113	181	33	|f	|f	PROPN
ejpam-5113	181	34	′	′	NUM
ejpam-5113	181	35	n(w)|	n(w)|	PROPN
ejpam-5113	181	36	.	.	PUNCT
ejpam-5113	182	1	<	<	X
ejpam-5113	182	2	(	(	PUNCT
ejpam-5113	182	3	c1	c1	NOUN
ejpam-5113	182	4	+	+	CCONJ
ejpam-5113	182	5	c2)ϵ.	c2)ϵ.	NOUN
ejpam-5113	182	6	(	(	PUNCT
ejpam-5113	182	7	20	20	NUM
ejpam-5113	182	8	)	)	PUNCT
ejpam-5113	182	9	now	now	ADV
ejpam-5113	182	10	,	,	PUNCT
ejpam-5113	182	11	using	use	VERB
ejpam-5113	182	12	inequalities	inequality	NOUN
ejpam-5113	182	13	(	(	PUNCT
ejpam-5113	182	14	16	16	NUM
ejpam-5113	182	15	)	)	PUNCT
ejpam-5113	182	16	and	and	CCONJ
ejpam-5113	182	17	(	(	PUNCT
ejpam-5113	182	18	20	20	NUM
ejpam-5113	182	19	)	)	PUNCT
ejpam-5113	182	20	,	,	PUNCT
ejpam-5113	182	21	we	we	PRON
ejpam-5113	182	22	get	get	VERB
ejpam-5113	182	23	∥iφg	∥iφg	NOUN
ejpam-5113	182	24	fn∥zµ	fn∥zµ	ADJ
ejpam-5113	182	25	=	=	PRON
ejpam-5113	182	26	|f	|f	PROPN
ejpam-5113	182	27	′	′	NUM
ejpam-5113	183	1	n(φ(0))g(0)|+	n(φ(0))g(0)|+	INTJ
ejpam-5113	183	2	sup	sup	NOUN
ejpam-5113	183	3	z∈d	z∈d	PROPN
ejpam-5113	183	4	µ	µ	PROPN
ejpam-5113	183	5	∣∣∣(iφg	∣∣∣(iφg	ADJ
ejpam-5113	183	6	fn)′′	fn)′′	NOUN
ejpam-5113	183	7	(	(	PUNCT
ejpam-5113	183	8	z)∣∣∣	z)∣∣∣	PROPN
ejpam-5113	183	9	≤	≤	PROPN
ejpam-5113	183	10	|f	|f	PUNCT
ejpam-5113	183	11	′	′	NUM
ejpam-5113	184	1	n(φ(0))g(0)|+	n(φ(0))g(0)|+	INTJ
ejpam-5113	184	2	2lϵ+	2lϵ+	NUM
ejpam-5113	184	3	(	(	PUNCT
ejpam-5113	184	4	c1	c1	PROPN
ejpam-5113	184	5	+	+	CCONJ
ejpam-5113	184	6	c2)ϵ	c2)ϵ	NOUN
ejpam-5113	184	7	since	since	SCONJ
ejpam-5113	184	8	{	{	PUNCT
ejpam-5113	184	9	f	f	PROPN
ejpam-5113	184	10	′	′	NUM
ejpam-5113	184	11	n	n	CCONJ
ejpam-5113	184	12	}	}	PUNCT
ejpam-5113	184	13	converges	converge	VERB
ejpam-5113	184	14	to	to	ADP
ejpam-5113	184	15	zero	zero	NUM
ejpam-5113	184	16	uniformly	uniformly	ADV
ejpam-5113	184	17	on	on	ADP
ejpam-5113	184	18	compact	compact	ADJ
ejpam-5113	184	19	subsets	subset	NOUN
ejpam-5113	184	20	of	of	ADP
ejpam-5113	184	21	d	d	PROPN
ejpam-5113	184	22	,	,	PUNCT
ejpam-5113	184	23	it	it	PRON
ejpam-5113	184	24	converges	converge	VERB
ejpam-5113	184	25	pointwise	pointwise	PRON
ejpam-5113	184	26	.	.	PUNCT
ejpam-5113	185	1	thus	thus	ADV
ejpam-5113	185	2	,	,	PUNCT
ejpam-5113	185	3	|f	|f	ADP
ejpam-5113	185	4	′	′	NUM
ejpam-5113	185	5	n(φ(0))g(0)|	n(φ(0))g(0)|	ADV
ejpam-5113	185	6	→	→	SYM
ejpam-5113	185	7	0	0	PUNCT
ejpam-5113	185	8	as	as	ADP
ejpam-5113	185	9	n	n	NUM
ejpam-5113	185	10	→	→	SYM
ejpam-5113	185	11	0	0	NUM
ejpam-5113	185	12	.	.	PUNCT
ejpam-5113	186	1	hence	hence	ADV
ejpam-5113	186	2	,	,	PUNCT
ejpam-5113	186	3	for	for	ADP
ejpam-5113	186	4	arbitrary	arbitrary	ADJ
ejpam-5113	186	5	ϵ	ϵ	X
ejpam-5113	186	6	>	>	X
ejpam-5113	186	7	0	0	NUM
ejpam-5113	186	8	,	,	PUNCT
ejpam-5113	186	9	we	we	PRON
ejpam-5113	186	10	get	get	VERB
ejpam-5113	186	11	∥iφg	∥iφg	ADJ
ejpam-5113	186	12	fn∥zµ	fn∥zµ	PROPN
ejpam-5113	186	13	→	→	SYM
ejpam-5113	186	14	0	0	NUM
ejpam-5113	187	1	as	as	ADP
ejpam-5113	187	2	n	n	NUM
ejpam-5113	187	3	→	→	SYM
ejpam-5113	187	4	0	0	NUM
ejpam-5113	187	5	.	.	PUNCT
ejpam-5113	188	1	therefore	therefore	ADV
ejpam-5113	188	2	,	,	PUNCT
ejpam-5113	188	3	iφg	iφg	NOUN
ejpam-5113	188	4	is	be	AUX
ejpam-5113	188	5	compact	compact	ADJ
ejpam-5113	188	6	,	,	PUNCT
ejpam-5113	188	7	which	which	PRON
ejpam-5113	188	8	completes	complete	VERB
ejpam-5113	188	9	the	the	DET
ejpam-5113	188	10	proof	proof	NOUN
ejpam-5113	188	11	.	.	PUNCT
ejpam-5113	189	1	4	4	X
ejpam-5113	189	2	.	.	X
ejpam-5113	189	3	boundedness	boundedness	NOUN
ejpam-5113	189	4	and	and	CCONJ
ejpam-5113	189	5	compactness	compactness	NOUN
ejpam-5113	189	6	of	of	ADP
ejpam-5113	189	7	tφ	tφ	PROPN
ejpam-5113	189	8	g	g	PROPN
ejpam-5113	189	9	in	in	ADP
ejpam-5113	189	10	this	this	DET
ejpam-5113	189	11	section	section	NOUN
ejpam-5113	189	12	,	,	PUNCT
ejpam-5113	189	13	we	we	PRON
ejpam-5113	189	14	characterize	characterize	VERB
ejpam-5113	189	15	the	the	DET
ejpam-5113	189	16	boundedness	boundedness	NOUN
ejpam-5113	189	17	and	and	CCONJ
ejpam-5113	189	18	compactness	compactness	NOUN
ejpam-5113	189	19	of	of	ADP
ejpam-5113	189	20	the	the	DET
ejpam-5113	189	21	operator	operator	NOUN
ejpam-5113	189	22	tφ	tφ	PROPN
ejpam-5113	189	23	g	g	NOUN
ejpam-5113	189	24	acting	act	VERB
ejpam-5113	189	25	between	between	ADP
ejpam-5113	189	26	sp	sp	ADP
ejpam-5113	189	27	spaces	space	NOUN
ejpam-5113	189	28	and	and	CCONJ
ejpam-5113	189	29	weighted	weight	VERB
ejpam-5113	189	30	zygmund	zygmund	PROPN
ejpam-5113	189	31	spaces	spaces	PROPN
ejpam-5113	189	32	zµ.	zµ.	PROPN
ejpam-5113	189	33	in	in	ADP
ejpam-5113	189	34	the	the	DET
ejpam-5113	189	35	following	following	NOUN
ejpam-5113	189	36	theorem	theorem	NOUN
ejpam-5113	189	37	3	3	NUM
ejpam-5113	189	38	,	,	PUNCT
ejpam-5113	189	39	we	we	PRON
ejpam-5113	189	40	characterize	characterize	VERB
ejpam-5113	189	41	the	the	DET
ejpam-5113	189	42	boundedness	boundedness	NOUN
ejpam-5113	189	43	of	of	ADP
ejpam-5113	189	44	tφ	tφ	PROPN
ejpam-5113	189	45	g	g	PROPN
ejpam-5113	189	46	that	that	PRON
ejpam-5113	189	47	acts	act	VERB
ejpam-5113	189	48	between	between	ADP
ejpam-5113	189	49	sp	sp	ADP
ejpam-5113	189	50	spaces	space	NOUN
ejpam-5113	189	51	and	and	CCONJ
ejpam-5113	189	52	weighted	weight	VERB
ejpam-5113	189	53	zygmund	zygmund	PROPN
ejpam-5113	189	54	spaces	space	NOUN
ejpam-5113	189	55	.	.	PUNCT
ejpam-5113	190	1	theorem	theorem	NOUN
ejpam-5113	190	2	3	3	X
ejpam-5113	190	3	.	.	PUNCT
ejpam-5113	191	1	let	let	VERB
ejpam-5113	191	2	g	g	NOUN
ejpam-5113	191	3	be	be	AUX
ejpam-5113	191	4	an	an	DET
ejpam-5113	191	5	analytic	analytic	ADJ
ejpam-5113	191	6	function	function	NOUN
ejpam-5113	191	7	on	on	ADP
ejpam-5113	191	8	d	d	PROPN
ejpam-5113	191	9	and	and	CCONJ
ejpam-5113	191	10	φ	φ	PROPN
ejpam-5113	191	11	be	be	VERB
ejpam-5113	191	12	an	an	DET
ejpam-5113	191	13	analytic	analytic	ADJ
ejpam-5113	191	14	selfmap	selfmap	NOUN
ejpam-5113	191	15	of	of	ADP
ejpam-5113	191	16	d.	d.	PROPN
ejpam-5113	191	17	then	then	ADV
ejpam-5113	191	18	tφ	tφ	VERB
ejpam-5113	191	19	g	g	PROPN
ejpam-5113	191	20	:	:	PUNCT
ejpam-5113	191	21	sp	sp	ADP
ejpam-5113	191	22	→	→	PUNCT
ejpam-5113	191	23	zµ	zµ	PROPN
ejpam-5113	191	24	is	be	AUX
ejpam-5113	191	25	bounded	bound	VERB
ejpam-5113	191	26	if	if	SCONJ
ejpam-5113	191	27	and	and	CCONJ
ejpam-5113	191	28	only	only	ADV
ejpam-5113	191	29	if	if	SCONJ
ejpam-5113	191	30	g	g	PROPN
ejpam-5113	191	31	∈	∈	PROPN
ejpam-5113	191	32	zµ	zµ	PROPN
ejpam-5113	191	33	and	and	CCONJ
ejpam-5113	191	34	m3	m3	PROPN
ejpam-5113	191	35	=	=	PUNCT
ejpam-5113	191	36	sup	sup	NOUN
ejpam-5113	191	37	z∈d	z∈d	NOUN
ejpam-5113	191	38	µ(z)|g′(z)||φ′(z)|	µ(z)|g′(z)||φ′(z)|	PUNCT
ejpam-5113	191	39	(	(	PUNCT
ejpam-5113	191	40	1−	1−	NUM
ejpam-5113	191	41	|φ(z)|2)1	|φ(z)|2)1	NOUN
ejpam-5113	191	42	/	/	SYM
ejpam-5113	191	43	p	p	X
ejpam-5113	191	44	<	<	X
ejpam-5113	191	45	∞.	∞.	PROPN
ejpam-5113	191	46	w.	w.	PROPN
ejpam-5113	191	47	al	al	PROPN
ejpam-5113	191	48	-	-	PUNCT
ejpam-5113	191	49	rawashdeh	rawashdeh	PROPN
ejpam-5113	191	50	/	/	SYM
ejpam-5113	191	51	eur	eur	PROPN
ejpam-5113	191	52	.	.	PUNCT
ejpam-5113	192	1	j.	j.	PROPN
ejpam-5113	192	2	pure	pure	PROPN
ejpam-5113	192	3	appl	appl	PROPN
ejpam-5113	192	4	.	.	PROPN
ejpam-5113	192	5	math	math	PROPN
ejpam-5113	192	6	,	,	PUNCT
ejpam-5113	192	7	17	17	NUM
ejpam-5113	192	8	(	(	PUNCT
ejpam-5113	192	9	2	2	NUM
ejpam-5113	192	10	)	)	PUNCT
ejpam-5113	192	11	(	(	PUNCT
ejpam-5113	192	12	2024	2024	NUM
ejpam-5113	192	13	)	)	PUNCT
ejpam-5113	192	14	,	,	PUNCT
ejpam-5113	192	15	931	931	NUM
ejpam-5113	192	16	-	-	SYM
ejpam-5113	192	17	944	944	NUM
ejpam-5113	192	18	941	941	NUM
ejpam-5113	192	19	proof	proof	NOUN
ejpam-5113	192	20	.	.	PUNCT
ejpam-5113	193	1	suppose	suppose	VERB
ejpam-5113	193	2	tφ	tφ	PROPN
ejpam-5113	193	3	g	g	PROPN
ejpam-5113	193	4	:	:	PUNCT
ejpam-5113	193	5	sp	sp	ADP
ejpam-5113	193	6	→	→	PUNCT
ejpam-5113	193	7	zµ	zµ	X
ejpam-5113	193	8	is	be	AUX
ejpam-5113	193	9	bounded	bound	VERB
ejpam-5113	193	10	.	.	PUNCT
ejpam-5113	194	1	since	since	SCONJ
ejpam-5113	194	2	polynomials	polynomial	NOUN
ejpam-5113	194	3	are	be	AUX
ejpam-5113	194	4	dense	dense	ADJ
ejpam-5113	194	5	in	in	ADP
ejpam-5113	194	6	sp	sp	NOUN
ejpam-5113	194	7	,	,	PUNCT
ejpam-5113	194	8	p1(z	p1(z	NOUN
ejpam-5113	194	9	)	)	PUNCT
ejpam-5113	194	10	=	=	SYM
ejpam-5113	194	11	1	1	NUM
ejpam-5113	194	12	∈	∈	NOUN
ejpam-5113	194	13	sp	sp	NOUN
ejpam-5113	194	14	.	.	NOUN
ejpam-5113	194	15	by	by	ADP
ejpam-5113	194	16	the	the	DET
ejpam-5113	194	17	boundedness	boundedness	NOUN
ejpam-5113	194	18	of	of	ADP
ejpam-5113	194	19	tφ	tφ	PROPN
ejpam-5113	194	20	g	g	PROPN
ejpam-5113	194	21	,	,	PUNCT
ejpam-5113	194	22	we	we	PRON
ejpam-5113	194	23	get	get	VERB
ejpam-5113	194	24	∥tφ	∥tφ	PROPN
ejpam-5113	194	25	g	g	ADP
ejpam-5113	194	26	p1∥zµ	p1∥zµ	NOUN
ejpam-5113	194	27	<	<	X
ejpam-5113	194	28	∞.	∞.	PROPN
ejpam-5113	194	29	therefore	therefore	ADV
ejpam-5113	194	30	,	,	PUNCT
ejpam-5113	194	31	sup	sup	VERB
ejpam-5113	194	32	z∈d	z∈d	NOUN
ejpam-5113	194	33	µ|g′′(z)|	µ|g′′(z)|	NOUN
ejpam-5113	194	34	=	=	SYM
ejpam-5113	194	35	sup	sup	NOUN
ejpam-5113	194	36	z∈d	z∈d	NOUN
ejpam-5113	194	37	µ	µ	PROPN
ejpam-5113	194	38	∣∣∣(tφ	∣∣∣(tφ	NUM
ejpam-5113	194	39	g	g	PROPN
ejpam-5113	194	40	p1	p1	PROPN
ejpam-5113	194	41	)	)	PUNCT
ejpam-5113	194	42	′′∣∣∣	′′∣∣∣	PROPN
ejpam-5113	194	43	≤	≤	PROPN
ejpam-5113	194	44	∥tφ	∥tφ	PART
ejpam-5113	194	45	g	g	ADP
ejpam-5113	194	46	p1∥zµ	p1∥zµ	NOUN
ejpam-5113	194	47	<	<	X
ejpam-5113	194	48	∞	∞	PROPN
ejpam-5113	194	49	,	,	PUNCT
ejpam-5113	194	50	which	which	PRON
ejpam-5113	194	51	gives	give	VERB
ejpam-5113	194	52	us	we	PRON
ejpam-5113	194	53	that	that	SCONJ
ejpam-5113	194	54	g	g	PROPN
ejpam-5113	194	55	∈	∈	PROPN
ejpam-5113	195	1	zµ.	zµ.	X
ejpam-5113	195	2	second	second	ADJ
ejpam-5113	195	3	,	,	PUNCT
ejpam-5113	195	4	consider	consider	VERB
ejpam-5113	195	5	the	the	DET
ejpam-5113	195	6	test	test	NOUN
ejpam-5113	195	7	function	function	NOUN
ejpam-5113	195	8	f1,w	f1,w	PROPN
ejpam-5113	195	9	we	we	PRON
ejpam-5113	195	10	defined	define	VERB
ejpam-5113	195	11	in	in	ADP
ejpam-5113	195	12	the	the	DET
ejpam-5113	195	13	proof	proof	NOUN
ejpam-5113	195	14	of	of	ADP
ejpam-5113	195	15	theorem	theorem	NOUN
ejpam-5113	195	16	1	1	NUM
ejpam-5113	195	17	.	.	PUNCT
ejpam-5113	196	1	then	then	ADV
ejpam-5113	196	2	,	,	PUNCT
ejpam-5113	196	3	(	(	PUNCT
ejpam-5113	196	4	tφ	tφ	PROPN
ejpam-5113	196	5	g	g	PROPN
ejpam-5113	196	6	f1,w	f1,w	PROPN
ejpam-5113	196	7	)	)	PUNCT
ejpam-5113	197	1	′′	′′	PROPN
ejpam-5113	197	2	(	(	PUNCT
ejpam-5113	197	3	w	w	PROPN
ejpam-5113	197	4	)	)	PUNCT
ejpam-5113	197	5	=	=	SYM
ejpam-5113	197	6	(	(	PUNCT
ejpam-5113	197	7	f1,w(φ(w))g	f1,w(φ(w))g	NOUN
ejpam-5113	197	8	′(w	′(w	NOUN
ejpam-5113	197	9	)	)	PUNCT
ejpam-5113	197	10	)	)	PUNCT
ejpam-5113	197	11	′	′	NUM
ejpam-5113	198	1	=	=	PUNCT
ejpam-5113	198	2	f1,w(φ(w))g	f1,w(φ(w))g	NOUN
ejpam-5113	198	3	′′(w	′′(w	NOUN
ejpam-5113	198	4	)	)	PUNCT
ejpam-5113	199	1	+	+	NUM
ejpam-5113	199	2	f	f	NOUN
ejpam-5113	199	3	′	′	NUM
ejpam-5113	199	4	1,w(φ(w))φ	1,w(φ(w))φ	NUM
ejpam-5113	199	5	′(w)g′(w	′(w)g′(w	NOUN
ejpam-5113	199	6	)	)	PUNCT
ejpam-5113	199	7	=	=	SYM
ejpam-5113	199	8	f1,w(φ(w))g	f1,w(φ(w))g	NOUN
ejpam-5113	199	9	′′(w	′′(w	NOUN
ejpam-5113	199	10	)	)	PUNCT
ejpam-5113	199	11	+	+	CCONJ
ejpam-5113	199	12	φ′(w)g′(w	φ′(w)g′(w	X
ejpam-5113	199	13	)	)	PUNCT
ejpam-5113	199	14	(	(	PUNCT
ejpam-5113	199	15	1−	1−	NUM
ejpam-5113	199	16	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	199	17	/	/	SYM
ejpam-5113	199	18	p	p	NOUN
ejpam-5113	199	19	.	.	PUNCT
ejpam-5113	200	1	therefore	therefore	ADV
ejpam-5113	200	2	,	,	PUNCT
ejpam-5113	200	3	by	by	ADP
ejpam-5113	200	4	the	the	DET
ejpam-5113	200	5	boundedness	boundedness	NOUN
ejpam-5113	200	6	of	of	ADP
ejpam-5113	200	7	tφ	tφ	PROPN
ejpam-5113	200	8	g	g	PROPN
ejpam-5113	200	9	and	and	CCONJ
ejpam-5113	200	10	equation	equation	NOUN
ejpam-5113	200	11	(	(	PUNCT
ejpam-5113	200	12	1	1	NUM
ejpam-5113	200	13	)	)	PUNCT
ejpam-5113	200	14	,	,	PUNCT
ejpam-5113	200	15	we	we	PRON
ejpam-5113	200	16	get	get	VERB
ejpam-5113	200	17	µ(w)|φ′(w)g′(w)|	µ(w)|φ′(w)g′(w)|	NUM
ejpam-5113	200	18	(	(	PUNCT
ejpam-5113	200	19	1−	1−	NUM
ejpam-5113	200	20	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	200	21	/	/	SYM
ejpam-5113	200	22	p	p	NOUN
ejpam-5113	200	23	≤	≤	NUM
ejpam-5113	200	24	µ(w	µ(w	PROPN
ejpam-5113	200	25	)	)	PUNCT
ejpam-5113	200	26	∣∣∣(tφ	∣∣∣(tφ	PROPN
ejpam-5113	200	27	g	g	PROPN
ejpam-5113	200	28	f1,w	f1,w	PROPN
ejpam-5113	200	29	)	)	PUNCT
ejpam-5113	201	1	′′	′′	PROPN
ejpam-5113	201	2	(	(	PUNCT
ejpam-5113	201	3	w	w	PROPN
ejpam-5113	201	4	)	)	PUNCT
ejpam-5113	201	5	∣∣∣+	∣∣∣+	PROPN
ejpam-5113	201	6	µ(w)|g′′(w)||f1,w(φ(w))|	µ(w)|g′′(w)||f1,w(φ(w))|	PROPN
ejpam-5113	201	7	≤	≤	PROPN
ejpam-5113	201	8	∥tφ	∥tφ	PART
ejpam-5113	201	9	g	g	PROPN
ejpam-5113	202	1	f1,w∥zµ	f1,w∥zµ	NOUN
ejpam-5113	202	2	+	+	CCONJ
ejpam-5113	202	3	∥g∥zµ∥f1,w∥sp	∥g∥zµ∥f1,w∥sp	ADJ
ejpam-5113	202	4	≤	≤	ADJ
ejpam-5113	203	1	∥tφ	∥tφ	PROPN
ejpam-5113	203	2	g	g	ADP
ejpam-5113	203	3	∥∥f1,w∥sp	∥∥f1,w∥sp	NOUN
ejpam-5113	204	1	+	+	CCONJ
ejpam-5113	204	2	∥g∥zµ∥f1,w∥sp	∥g∥zµ∥f1,w∥sp	ADV
ejpam-5113	204	3	≤	≤	NOUN
ejpam-5113	204	4	(	(	PUNCT
ejpam-5113	204	5	∥tφ	∥tφ	PROPN
ejpam-5113	204	6	g	g	PROPN
ejpam-5113	204	7	∥+	∥+	PROPN
ejpam-5113	204	8	∥g∥zµ	∥g∥zµ	PROPN
ejpam-5113	204	9	)	)	PUNCT
ejpam-5113	205	1	2(2p−2)/p	2(2p−2)/p	X
ejpam-5113	205	2	.	.	PUNCT
ejpam-5113	206	1	taking	take	VERB
ejpam-5113	206	2	the	the	DET
ejpam-5113	206	3	supremum	supremum	ADJ
ejpam-5113	206	4	over	over	ADP
ejpam-5113	206	5	all	all	PRON
ejpam-5113	206	6	w	w	PROPN
ejpam-5113	206	7	∈	∈	PROPN
ejpam-5113	206	8	d	d	NOUN
ejpam-5113	206	9	,	,	PUNCT
ejpam-5113	206	10	we	we	PRON
ejpam-5113	206	11	get	get	VERB
ejpam-5113	206	12	sup	sup	NOUN
ejpam-5113	206	13	w∈d	w∈d	NOUN
ejpam-5113	206	14	µ(w)|φ′(w)g′(w)|	µ(w)|φ′(w)g′(w)|	NUM
ejpam-5113	206	15	(	(	PUNCT
ejpam-5113	206	16	1−	1−	NUM
ejpam-5113	206	17	|φ(w)|2)1	|φ(w)|2)1	NOUN
ejpam-5113	206	18	/	/	SYM
ejpam-5113	206	19	p	p	X
ejpam-5113	206	20	<	<	X
ejpam-5113	206	21	∞.	∞.	PROPN
ejpam-5113	206	22	conversely	conversely	ADV
ejpam-5113	206	23	,	,	PUNCT
ejpam-5113	206	24	suppose	suppose	VERB
ejpam-5113	206	25	g	g	PROPN
ejpam-5113	206	26	∈	∈	PROPN
ejpam-5113	206	27	zµ	zµ	PROPN
ejpam-5113	206	28	and	and	CCONJ
ejpam-5113	206	29	condition	condition	NOUN
ejpam-5113	206	30	m3	m3	PROPN
ejpam-5113	206	31	is	be	AUX
ejpam-5113	206	32	finite	finite	ADJ
ejpam-5113	206	33	.	.	PUNCT
ejpam-5113	207	1	let	let	VERB
ejpam-5113	207	2	f	f	PROPN
ejpam-5113	207	3	∈	∈	PROPN
ejpam-5113	207	4	sp	sp	ADP
ejpam-5113	207	5	and	and	CCONJ
ejpam-5113	207	6	z	z	PROPN
ejpam-5113	207	7	∈	∈	PROPN
ejpam-5113	207	8	d.	d.	NOUN
ejpam-5113	207	9	then	then	ADV
ejpam-5113	207	10	,	,	PUNCT
ejpam-5113	207	11	by	by	ADP
ejpam-5113	207	12	using	use	VERB
ejpam-5113	207	13	lemma	lemma	PROPN
ejpam-5113	207	14	2	2	NUM
ejpam-5113	207	15	,	,	PUNCT
ejpam-5113	207	16	we	we	PRON
ejpam-5113	207	17	get	get	VERB
ejpam-5113	207	18	µ(z	µ(z	PROPN
ejpam-5113	207	19	)	)	PUNCT
ejpam-5113	207	20	∣∣∣(tφ	∣∣∣(tφ	PROPN
ejpam-5113	207	21	g	g	PROPN
ejpam-5113	207	22	f	f	PROPN
ejpam-5113	207	23	)	)	PUNCT
ejpam-5113	208	1	′′	′′	PROPN
ejpam-5113	208	2	(	(	PUNCT
ejpam-5113	208	3	z	z	NOUN
ejpam-5113	208	4	)	)	PUNCT
ejpam-5113	208	5	∣∣∣	∣∣∣	NOUN
ejpam-5113	208	6	=	=	SYM
ejpam-5113	208	7	µ(z	µ(z	PROPN
ejpam-5113	208	8	)	)	PUNCT
ejpam-5113	208	9	∣∣∣(f(φ(z))g′(z))′∣∣∣	∣∣∣(f(φ(z))g′(z))′∣∣∣	NOUN
ejpam-5113	208	10	=	=	SYM
ejpam-5113	208	11	µ(z	µ(z	PROPN
ejpam-5113	208	12	)	)	PUNCT
ejpam-5113	208	13	∣∣f(φ(z))g′′(z	∣∣f(φ(z))g′′(z	PROPN
ejpam-5113	208	14	)	)	PUNCT
ejpam-5113	209	1	+	+	CCONJ
ejpam-5113	209	2	f	f	PROPN
ejpam-5113	209	3	′(φ(z))φ′(z)g′(z	′(φ(z))φ′(z)g′(z	PROPN
ejpam-5113	209	4	)	)	PUNCT
ejpam-5113	209	5	∣∣	∣∣	X
ejpam-5113	209	6	≤	≤	PROPN
ejpam-5113	209	7	∥g∥zµ∥f∥∞	∥g∥zµ∥f∥∞	PUNCT
ejpam-5113	210	1	+	+	CCONJ
ejpam-5113	210	2	µ(z	µ(z	NOUN
ejpam-5113	210	3	)	)	PUNCT
ejpam-5113	210	4	|φ′(z)g′(z)|	|φ′(z)g′(z)|	NOUN
ejpam-5113	210	5	(	(	PUNCT
ejpam-5113	210	6	1−	1−	NUM
ejpam-5113	210	7	|φ(z)|2)1	|φ(z)|2)1	NOUN
ejpam-5113	210	8	/	/	SYM
ejpam-5113	210	9	p	p	NOUN
ejpam-5113	210	10	∥f	∥f	PROPN
ejpam-5113	210	11	′∥hp	′∥hp	ADV
ejpam-5113	210	12	≤	≤	NUM
ejpam-5113	210	13	π∥g∥zµ∥f∥sp	π∥g∥zµ∥f∥sp	PROPN
ejpam-5113	211	1	+	+	NOUN
ejpam-5113	211	2	m3∥f∥sp	m3∥f∥sp	NUM
ejpam-5113	211	3	.	.	PUNCT
ejpam-5113	212	1	references	reference	NOUN
ejpam-5113	212	2	942	942	NUM
ejpam-5113	212	3	since	since	SCONJ
ejpam-5113	212	4	g	g	PROPN
ejpam-5113	212	5	∈	∈	PROPN
ejpam-5113	212	6	zµ	zµ	PROPN
ejpam-5113	212	7	and	and	CCONJ
ejpam-5113	212	8	f	f	PROPN
ejpam-5113	212	9	∈	∈	PROPN
ejpam-5113	212	10	sp	sp	PROPN
ejpam-5113	212	11	,	,	PUNCT
ejpam-5113	212	12	by	by	ADP
ejpam-5113	212	13	taking	take	VERB
ejpam-5113	212	14	supremum	supremum	ADV
ejpam-5113	212	15	over	over	ADP
ejpam-5113	212	16	all	all	DET
ejpam-5113	212	17	z	z	NOUN
ejpam-5113	212	18	∈	∈	PROPN
ejpam-5113	213	1	d	d	NOUN
ejpam-5113	213	2	,	,	PUNCT
ejpam-5113	213	3	we	we	PRON
ejpam-5113	213	4	get	get	VERB
ejpam-5113	213	5	sup	sup	NOUN
ejpam-5113	213	6	z∈d	z∈d	NOUN
ejpam-5113	213	7	µ(z	µ(z	NOUN
ejpam-5113	213	8	)	)	PUNCT
ejpam-5113	213	9	∣∣∣(tφ	∣∣∣(tφ	PROPN
ejpam-5113	213	10	g	g	PROPN
ejpam-5113	213	11	f	f	PROPN
ejpam-5113	213	12	)	)	PUNCT
ejpam-5113	214	1	′′	′′	PROPN
ejpam-5113	214	2	(	(	PUNCT
ejpam-5113	214	3	z	z	NOUN
ejpam-5113	214	4	)	)	PUNCT
ejpam-5113	214	5	∣∣∣	∣∣∣	NOUN
ejpam-5113	214	6	<	<	X
ejpam-5113	214	7	c∥f∥sp	c∥f∥sp	PROPN
ejpam-5113	214	8	,	,	PUNCT
ejpam-5113	214	9	(	(	PUNCT
ejpam-5113	214	10	21	21	NUM
ejpam-5113	214	11	)	)	PUNCT
ejpam-5113	214	12	for	for	ADP
ejpam-5113	214	13	some	some	DET
ejpam-5113	214	14	constant	constant	ADJ
ejpam-5113	214	15	c.	c.	NOUN
ejpam-5113	214	16	finally	finally	ADV
ejpam-5113	214	17	,	,	PUNCT
ejpam-5113	214	18	using	use	VERB
ejpam-5113	214	19	equation	equation	NOUN
ejpam-5113	214	20	(	(	PUNCT
ejpam-5113	214	21	21	21	NUM
ejpam-5113	214	22	)	)	PUNCT
ejpam-5113	214	23	,	,	PUNCT
ejpam-5113	214	24	we	we	PRON
ejpam-5113	214	25	get	get	VERB
ejpam-5113	214	26	∥tφ	∥tφ	PROPN
ejpam-5113	214	27	g	g	ADP
ejpam-5113	214	28	f∥zµ	f∥zµ	PROPN
ejpam-5113	214	29	=	=	PROPN
ejpam-5113	214	30	∣∣(tφ	∣∣(tφ	PROPN
ejpam-5113	214	31	g	g	PROPN
ejpam-5113	214	32	f	f	PROPN
ejpam-5113	214	33	)	)	PUNCT
ejpam-5113	214	34	(	(	PUNCT
ejpam-5113	214	35	0	0	NUM
ejpam-5113	214	36	)	)	PUNCT
ejpam-5113	214	37	∣∣+	∣∣+	PROPN
ejpam-5113	215	1	∣∣∣(tφ	∣∣∣(tφ	PROPN
ejpam-5113	215	2	g	g	PROPN
ejpam-5113	215	3	f	f	PROPN
ejpam-5113	215	4	)	)	PUNCT
ejpam-5113	215	5	′	′	NOUN
ejpam-5113	216	1	(	(	PUNCT
ejpam-5113	216	2	0	0	NUM
ejpam-5113	216	3	)	)	PUNCT
ejpam-5113	216	4	∣∣∣+	∣∣∣+	PROPN
ejpam-5113	216	5	sup	sup	VERB
ejpam-5113	216	6	z∈d	z∈d	NOUN
ejpam-5113	216	7	µ(z	µ(z	NOUN
ejpam-5113	216	8	)	)	PUNCT
ejpam-5113	216	9	∣∣∣(tφ	∣∣∣(tφ	PROPN
ejpam-5113	216	10	g	g	PROPN
ejpam-5113	216	11	f	f	PROPN
ejpam-5113	216	12	)	)	PUNCT
ejpam-5113	217	1	′′	′′	PROPN
ejpam-5113	217	2	(	(	PUNCT
ejpam-5113	217	3	z	z	NOUN
ejpam-5113	217	4	)	)	PUNCT
ejpam-5113	217	5	∣∣∣	∣∣∣	ADJ
ejpam-5113	217	6	≤	≤	NUM
ejpam-5113	217	7	∣∣∣(tφ	∣∣∣(tφ	PROPN
ejpam-5113	217	8	g	g	PROPN
ejpam-5113	217	9	f	f	PROPN
ejpam-5113	217	10	)	)	PUNCT
ejpam-5113	217	11	′	′	NOUN
ejpam-5113	217	12	(	(	PUNCT
ejpam-5113	217	13	0	0	NUM
ejpam-5113	217	14	)	)	PUNCT
ejpam-5113	217	15	∣∣∣+	∣∣∣+	PROPN
ejpam-5113	217	16	c∥f∥sp	c∥f∥sp	PROPN
ejpam-5113	217	17	<	<	X
ejpam-5113	217	18	(	(	PUNCT
ejpam-5113	217	19	c∗	c∗	PROPN
ejpam-5113	217	20	+	+	CCONJ
ejpam-5113	217	21	c)∥f∥sp	c)∥f∥sp	PROPN
ejpam-5113	217	22	,	,	PUNCT
ejpam-5113	217	23	for	for	ADP
ejpam-5113	217	24	some	some	DET
ejpam-5113	217	25	constant	constant	ADJ
ejpam-5113	217	26	c∗.	c∗.	NOUN
ejpam-5113	217	27	hence	hence	ADV
ejpam-5113	217	28	,	,	PUNCT
ejpam-5113	217	29	tφ	tφ	PROPN
ejpam-5113	217	30	g	g	PROPN
ejpam-5113	217	31	is	be	AUX
ejpam-5113	217	32	bounded	bound	VERB
ejpam-5113	217	33	,	,	PUNCT
ejpam-5113	217	34	as	as	SCONJ
ejpam-5113	217	35	desired	desire	VERB
ejpam-5113	217	36	.	.	PUNCT
ejpam-5113	218	1	the	the	DET
ejpam-5113	218	2	following	follow	VERB
ejpam-5113	218	3	theorem	theorem	VERB
ejpam-5113	218	4	4	4	NUM
ejpam-5113	218	5	characterizes	characterize	VERB
ejpam-5113	218	6	the	the	DET
ejpam-5113	218	7	compactness	compactness	NOUN
ejpam-5113	218	8	of	of	ADP
ejpam-5113	218	9	tφ	tφ	PROPN
ejpam-5113	218	10	g	g	PROPN
ejpam-5113	218	11	:	:	PUNCT
ejpam-5113	218	12	sp	sp	ADP
ejpam-5113	218	13	→	→	SYM
ejpam-5113	218	14	zµ	zµ	X
ejpam-5113	218	15	whose	whose	DET
ejpam-5113	218	16	proof	proof	NOUN
ejpam-5113	218	17	is	be	AUX
ejpam-5113	218	18	similar	similar	ADJ
ejpam-5113	218	19	to	to	ADP
ejpam-5113	218	20	that	that	PRON
ejpam-5113	218	21	of	of	ADP
ejpam-5113	218	22	theorem	theorem	ADJ
ejpam-5113	218	23	2	2	NUM
ejpam-5113	218	24	and	and	CCONJ
ejpam-5113	218	25	theorem	theorem	VERB
ejpam-5113	218	26	3	3	NUM
ejpam-5113	218	27	.	.	PUNCT
ejpam-5113	219	1	so	so	ADV
ejpam-5113	219	2	the	the	DET
ejpam-5113	219	3	details	detail	NOUN
ejpam-5113	219	4	are	be	AUX
ejpam-5113	219	5	omitted	omit	VERB
ejpam-5113	219	6	.	.	PUNCT
ejpam-5113	220	1	theorem	theorem	VERB
ejpam-5113	220	2	4	4	NUM
ejpam-5113	220	3	.	.	PUNCT
ejpam-5113	221	1	let	let	VERB
ejpam-5113	221	2	g	g	NOUN
ejpam-5113	221	3	be	be	AUX
ejpam-5113	221	4	an	an	DET
ejpam-5113	221	5	analytic	analytic	ADJ
ejpam-5113	221	6	function	function	NOUN
ejpam-5113	221	7	on	on	ADP
ejpam-5113	221	8	d	d	PROPN
ejpam-5113	221	9	and	and	CCONJ
ejpam-5113	221	10	φ	φ	PROPN
ejpam-5113	221	11	be	be	VERB
ejpam-5113	221	12	an	an	DET
ejpam-5113	221	13	analytic	analytic	ADJ
ejpam-5113	221	14	selfmap	selfmap	NOUN
ejpam-5113	221	15	of	of	ADP
ejpam-5113	221	16	d.	d.	PROPN
ejpam-5113	221	17	then	then	ADV
ejpam-5113	221	18	tφ	tφ	VERB
ejpam-5113	221	19	g	g	PROPN
ejpam-5113	221	20	:	:	PUNCT
ejpam-5113	221	21	sp	sp	ADP
ejpam-5113	221	22	→	→	PUNCT
ejpam-5113	221	23	zµ	zµ	X
ejpam-5113	221	24	is	be	AUX
ejpam-5113	221	25	compact	compact	ADJ
ejpam-5113	221	26	if	if	SCONJ
ejpam-5113	222	1	and	and	CCONJ
ejpam-5113	222	2	only	only	ADV
ejpam-5113	222	3	if	if	SCONJ
ejpam-5113	222	4	g	g	PROPN
ejpam-5113	222	5	∈	∈	PROPN
ejpam-5113	222	6	zµ	zµ	PROPN
ejpam-5113	222	7	and	and	CCONJ
ejpam-5113	222	8	lim	lim	PROPN
ejpam-5113	222	9	|φ(z)|→1	|φ(z)|→1	PROPN
ejpam-5113	222	10	µ(z)|g′(z)||φ′(z)|	µ(z)|g′(z)||φ′(z)|	PROPN
ejpam-5113	222	11	(	(	PUNCT
ejpam-5113	222	12	1−	1−	NUM
ejpam-5113	222	13	|φ(z)|2)1	|φ(z)|2)1	NOUN
ejpam-5113	222	14	/	/	SYM
ejpam-5113	222	15	p	p	NOUN
ejpam-5113	222	16	=	=	NOUN
ejpam-5113	222	17	0	0	X
ejpam-5113	222	18	.	.	PUNCT
ejpam-5113	223	1	acknowledgements	acknowledgement	NOUN
ejpam-5113	223	2	this	this	DET
ejpam-5113	223	3	research	research	NOUN
ejpam-5113	223	4	is	be	AUX
ejpam-5113	223	5	partially	partially	ADV
ejpam-5113	223	6	funded	fund	VERB
ejpam-5113	223	7	by	by	ADP
ejpam-5113	223	8	zarqa	zarqa	PROPN
ejpam-5113	223	9	university	university	PROPN
ejpam-5113	223	10	.	.	PUNCT
ejpam-5113	224	1	the	the	DET
ejpam-5113	224	2	author	author	NOUN
ejpam-5113	224	3	would	would	AUX
ejpam-5113	224	4	like	like	VERB
ejpam-5113	224	5	to	to	PART
ejpam-5113	224	6	express	express	VERB
ejpam-5113	224	7	his	his	PRON
ejpam-5113	224	8	sincerest	sincere	ADJ
ejpam-5113	224	9	thanks	thank	NOUN
ejpam-5113	224	10	to	to	ADP
ejpam-5113	224	11	zarqa	zarqa	PROPN
ejpam-5113	224	12	university	university	PROPN
ejpam-5113	224	13	for	for	ADP
ejpam-5113	224	14	the	the	DET
ejpam-5113	224	15	financial	financial	ADJ
ejpam-5113	224	16	support	support	NOUN
ejpam-5113	224	17	.	.	PUNCT
ejpam-5113	225	1	the	the	DET
ejpam-5113	225	2	author	author	NOUN
ejpam-5113	225	3	would	would	AUX
ejpam-5113	225	4	like	like	VERB
ejpam-5113	225	5	to	to	PART
ejpam-5113	225	6	express	express	VERB
ejpam-5113	225	7	his	his	PRON
ejpam-5113	225	8	sincerest	sincere	ADJ
ejpam-5113	225	9	thanks	thank	NOUN
ejpam-5113	225	10	to	to	ADP
ejpam-5113	225	11	the	the	DET
ejpam-5113	225	12	referees	referee	NOUN
ejpam-5113	225	13	for	for	ADP
ejpam-5113	225	14	their	their	PRON
ejpam-5113	225	15	valuable	valuable	ADJ
ejpam-5113	225	16	comments	comment	NOUN
ejpam-5113	225	17	and	and	CCONJ
ejpam-5113	225	18	various	various	ADJ
ejpam-5113	225	19	useful	useful	ADJ
ejpam-5113	225	20	suggestions	suggestion	NOUN
ejpam-5113	225	21	.	.	PUNCT
ejpam-5113	226	1	references	reference	NOUN
ejpam-5113	226	2	[	[	X
ejpam-5113	226	3	1	1	NUM
ejpam-5113	226	4	]	]	PUNCT
ejpam-5113	226	5	w.	w.	PROPN
ejpam-5113	226	6	al	al	PROPN
ejpam-5113	226	7	-	-	PUNCT
ejpam-5113	226	8	rawashdeh	rawashdeh	PROPN
ejpam-5113	226	9	.	.	PUNCT
ejpam-5113	227	1	weighted	weight	VERB
ejpam-5113	227	2	composition	composition	NOUN
ejpam-5113	227	3	operators	operator	NOUN
ejpam-5113	227	4	between	between	ADP
ejpam-5113	227	5	weighted	weight	VERB
ejpam-5113	227	6	bergman	bergman	PROPN
ejpam-5113	227	7	and	and	CCONJ
ejpam-5113	227	8	sp	sp	ADP
ejpam-5113	227	9	spaces	space	NOUN
ejpam-5113	227	10	.	.	PUNCT
ejpam-5113	228	1	bulletin	bulletin	NOUN
ejpam-5113	228	2	of	of	ADP
ejpam-5113	228	3	math	math	NOUN
ejpam-5113	228	4	.	.	PUNCT
ejpam-5113	229	1	anal	anal	PROPN
ejpam-5113	229	2	.	.	PUNCT
ejpam-5113	229	3	appl	appl	PROPN
ejpam-5113	229	4	.	.	PROPN
ejpam-5113	229	5	,	,	PUNCT
ejpam-5113	229	6	5:54–64	5:54–64	PROPN
ejpam-5113	229	7	,	,	PUNCT
ejpam-5113	229	8	2013	2013	NUM
ejpam-5113	229	9	.	.	PUNCT
ejpam-5113	230	1	[	[	X
ejpam-5113	230	2	2	2	X
ejpam-5113	230	3	]	]	PUNCT
ejpam-5113	230	4	w.	w.	PROPN
ejpam-5113	230	5	al	al	PROPN
ejpam-5113	230	6	-	-	PUNCT
ejpam-5113	230	7	rawashdeh	rawashdeh	PROPN
ejpam-5113	230	8	.	.	PUNCT
ejpam-5113	231	1	composition	composition	NOUN
ejpam-5113	231	2	operators	operator	NOUN
ejpam-5113	231	3	between	between	ADP
ejpam-5113	231	4	weighted	weight	VERB
ejpam-5113	231	5	bergman	bergman	PROPN
ejpam-5113	231	6	and	and	CCONJ
ejpam-5113	231	7	sp	sp	ADP
ejpam-5113	231	8	spaces	space	NOUN
ejpam-5113	231	9	.	.	PUNCT
ejpam-5113	232	1	new	new	PROPN
ejpam-5113	232	2	zealand	zealand	PROPN
ejpam-5113	232	3	j.	j.	PROPN
ejpam-5113	232	4	mathematics	mathematics	PROPN
ejpam-5113	232	5	,	,	PUNCT
ejpam-5113	232	6	47:141–150	47:141–150	PROPN
ejpam-5113	232	7	,	,	PUNCT
ejpam-5113	232	8	2017	2017	NUM
ejpam-5113	232	9	.	.	PUNCT
ejpam-5113	233	1	[	[	X
ejpam-5113	233	2	3	3	X
ejpam-5113	233	3	]	]	PUNCT
ejpam-5113	233	4	w.	w.	PROPN
ejpam-5113	233	5	al	al	PROPN
ejpam-5113	233	6	-	-	PUNCT
ejpam-5113	233	7	rawashdeh	rawashdeh	PROPN
ejpam-5113	233	8	.	.	PUNCT
ejpam-5113	234	1	generalized	generalized	ADJ
ejpam-5113	234	2	composition	composition	NOUN
ejpam-5113	234	3	operators	operator	NOUN
ejpam-5113	234	4	on	on	ADP
ejpam-5113	234	5	weighted	weight	VERB
ejpam-5113	234	6	hilbert	hilbert	NOUN
ejpam-5113	234	7	spaces	space	NOUN
ejpam-5113	234	8	of	of	ADP
ejpam-5113	234	9	analytic	analytic	ADJ
ejpam-5113	234	10	functions	function	NOUN
ejpam-5113	234	11	.	.	PUNCT
ejpam-5113	235	1	int	int	NOUN
ejpam-5113	235	2	.	.	PUNCT
ejpam-5113	236	1	j.	j.	PROPN
ejpam-5113	236	2	adv	adv	PROPN
ejpam-5113	236	3	.	.	PUNCT
ejpam-5113	237	1	res	res	PROPN
ejpam-5113	237	2	.	.	PUNCT
ejpam-5113	238	1	in	in	ADP
ejpam-5113	238	2	math	math	NOUN
ejpam-5113	238	3	.	.	PUNCT
ejpam-5113	238	4	,	,	PUNCT
ejpam-5113	238	5	10:1–13	10:1–13	NUM
ejpam-5113	238	6	,	,	PUNCT
ejpam-5113	238	7	2017	2017	NUM
ejpam-5113	238	8	.	.	PUNCT
ejpam-5113	239	1	[	[	X
ejpam-5113	239	2	4	4	X
ejpam-5113	239	3	]	]	PUNCT
ejpam-5113	239	4	a.	a.	NOUN
ejpam-5113	239	5	aleman	aleman	NOUN
ejpam-5113	239	6	and	and	CCONJ
ejpam-5113	239	7	a.g	a.g	PROPN
ejpam-5113	239	8	.	.	PROPN
ejpam-5113	239	9	siskakkis	siskakkis	PROPN
ejpam-5113	239	10	.	.	PUNCT
ejpam-5113	240	1	an	an	DET
ejpam-5113	240	2	integral	integral	ADJ
ejpam-5113	240	3	operator	operator	NOUN
ejpam-5113	240	4	on	on	ADP
ejpam-5113	240	5	hp	hp	PROPN
ejpam-5113	240	6	.	.	PROPN
ejpam-5113	240	7	complex	complex	ADJ
ejpam-5113	240	8	variables	variable	NOUN
ejpam-5113	240	9	theory	theory	NOUN
ejpam-5113	240	10	and	and	CCONJ
ejpam-5113	240	11	applications	application	NOUN
ejpam-5113	240	12	,	,	PUNCT
ejpam-5113	240	13	28:149–158	28:149–158	NUM
ejpam-5113	240	14	,	,	PUNCT
ejpam-5113	240	15	1995	1995	NUM
ejpam-5113	240	16	.	.	PUNCT
ejpam-5113	241	1	references	reference	NOUN
ejpam-5113	241	2	943	943	NUM
ejpam-5113	241	3	[	[	X
ejpam-5113	241	4	5	5	NUM
ejpam-5113	241	5	]	]	PUNCT
ejpam-5113	241	6	c.	c.	PROPN
ejpam-5113	241	7	cowen	cowen	PROPN
ejpam-5113	241	8	and	and	CCONJ
ejpam-5113	241	9	b.	b.	PROPN
ejpam-5113	241	10	maccluer	maccluer	NOUN
ejpam-5113	241	11	.	.	PUNCT
ejpam-5113	242	1	composition	composition	NOUN
ejpam-5113	242	2	operators	operator	NOUN
ejpam-5113	242	3	on	on	ADP
ejpam-5113	242	4	spaces	space	NOUN
ejpam-5113	242	5	of	of	ADP
ejpam-5113	242	6	analytic	analytic	ADJ
ejpam-5113	242	7	functions	function	NOUN
ejpam-5113	242	8	.	.	PUNCT
ejpam-5113	243	1	crc	crc	PROPN
ejpam-5113	243	2	press	press	PROPN
ejpam-5113	243	3	,	,	PUNCT
ejpam-5113	243	4	boca	boca	PROPN
ejpam-5113	243	5	raton	raton	PROPN
ejpam-5113	243	6	,	,	PUNCT
ejpam-5113	243	7	1995	1995	NUM
ejpam-5113	243	8	.	.	PUNCT
ejpam-5113	244	1	[	[	X
ejpam-5113	244	2	6	6	NUM
ejpam-5113	244	3	]	]	PUNCT
ejpam-5113	244	4	p.	p.	PROPN
ejpam-5113	244	5	duren	duren	PROPN
ejpam-5113	244	6	.	.	PUNCT
ejpam-5113	244	7	theory	theory	NOUN
ejpam-5113	244	8	of	of	ADP
ejpam-5113	244	9	hp	hp	ADJ
ejpam-5113	244	10	spaces	space	NOUN
ejpam-5113	244	11	.	.	PUNCT
ejpam-5113	245	1	academic	academic	ADJ
ejpam-5113	245	2	press	press	NOUN
ejpam-5113	245	3	,	,	PUNCT
ejpam-5113	245	4	new	new	PROPN
ejpam-5113	245	5	york	york	PROPN
ejpam-5113	245	6	,	,	PUNCT
ejpam-5113	245	7	1970	1970	NUM
ejpam-5113	245	8	.	.	PUNCT
ejpam-5113	246	1	[	[	X
ejpam-5113	246	2	7	7	X
ejpam-5113	246	3	]	]	X
ejpam-5113	246	4	p.	p.	NOUN
ejpam-5113	246	5	duren	duren	PROPN
ejpam-5113	246	6	and	and	CCONJ
ejpam-5113	246	7	a.	a.	NOUN
ejpam-5113	246	8	schuster	schuster	PROPN
ejpam-5113	246	9	.	.	PUNCT
ejpam-5113	247	1	bergman	bergman	PROPN
ejpam-5113	247	2	spaces	space	VERB
ejpam-5113	247	3	.	.	PUNCT
ejpam-5113	248	1	american	american	PROPN
ejpam-5113	248	2	mathematical	mathematical	PROPN
ejpam-5113	248	3	society	society	NOUN
ejpam-5113	248	4	,	,	PUNCT
ejpam-5113	248	5	new	new	PROPN
ejpam-5113	248	6	york	york	PROPN
ejpam-5113	248	7	,	,	PUNCT
ejpam-5113	248	8	2004	2004	NUM
ejpam-5113	248	9	.	.	PUNCT
ejpam-5113	249	1	[	[	X
ejpam-5113	249	2	8	8	NUM
ejpam-5113	249	3	]	]	PUNCT
ejpam-5113	249	4	z.	z.	PROPN
ejpam-5113	249	5	guo	guo	PROPN
ejpam-5113	249	6	.	.	PUNCT
ejpam-5113	250	1	riemann	riemann	PROPN
ejpam-5113	250	2	-	-	PUNCT
ejpam-5113	250	3	stieltjes	stieltjes	PROPN
ejpam-5113	250	4	operators	operator	NOUN
ejpam-5113	250	5	between	between	ADP
ejpam-5113	250	6	zygmund	zygmund	NOUN
ejpam-5113	250	7	-	-	PUNCT
ejpam-5113	250	8	type	type	NOUN
ejpam-5113	250	9	spaces	space	NOUN
ejpam-5113	250	10	.	.	PUNCT
ejpam-5113	251	1	j.	j.	PROPN
ejpam-5113	251	2	appl	appl	PROPN
ejpam-5113	251	3	.	.	PROPN
ejpam-5113	251	4	math	math	PROPN
ejpam-5113	251	5	.	.	PUNCT
ejpam-5113	252	1	and	and	CCONJ
ejpam-5113	252	2	comp	comp	PROPN
ejpam-5113	252	3	.	.	PUNCT
ejpam-5113	252	4	,	,	PUNCT
ejpam-5113	252	5	6(3):332–342	6(3):332–342	NOUN
ejpam-5113	252	6	,	,	PUNCT
ejpam-5113	252	7	2022	2022	NUM
ejpam-5113	252	8	.	.	PUNCT
ejpam-5113	253	1	[	[	X
ejpam-5113	253	2	9	9	NUM
ejpam-5113	253	3	]	]	X
ejpam-5113	253	4	b.	b.	PROPN
ejpam-5113	253	5	korenblum	korenblum	PROPN
ejpam-5113	253	6	h.	h.	PROPN
ejpam-5113	253	7	hedenmalm	hedenmalm	PROPN
ejpam-5113	253	8	and	and	CCONJ
ejpam-5113	253	9	k.	k.	PROPN
ejpam-5113	253	10	zhu	zhu	PROPN
ejpam-5113	253	11	.	.	PUNCT
ejpam-5113	254	1	theory	theory	NOUN
ejpam-5113	254	2	of	of	ADP
ejpam-5113	254	3	bergman	bergman	PROPN
ejpam-5113	254	4	spaces	space	VERB
ejpam-5113	254	5	.	.	PUNCT
ejpam-5113	255	1	springerverlag	springerverlag	PROPN
ejpam-5113	255	2	,	,	PUNCT
ejpam-5113	255	3	new	new	PROPN
ejpam-5113	255	4	york	york	PROPN
ejpam-5113	255	5	,	,	PUNCT
ejpam-5113	255	6	2000	2000	NUM
ejpam-5113	255	7	.	.	PUNCT
ejpam-5113	256	1	[	[	X
ejpam-5113	256	2	10	10	NUM
ejpam-5113	256	3	]	]	X
ejpam-5113	256	4	s.	s.	PROPN
ejpam-5113	256	5	li	li	PROPN
ejpam-5113	256	6	and	and	CCONJ
ejpam-5113	256	7	s.	s.	PROPN
ejpam-5113	256	8	stević.	stević.	PROPN
ejpam-5113	256	9	volterra	volterra	NOUN
ejpam-5113	256	10	-	-	PUNCT
ejpam-5113	256	11	type	type	NOUN
ejpam-5113	256	12	operators	operator	NOUN
ejpam-5113	256	13	on	on	ADP
ejpam-5113	256	14	zygmund	zygmund	PROPN
ejpam-5113	256	15	spaces	space	NOUN
ejpam-5113	256	16	.	.	PUNCT
ejpam-5113	257	1	journal	journal	PROPN
ejpam-5113	257	2	of	of	ADP
ejpam-5113	257	3	inequalities	inequality	NOUN
ejpam-5113	257	4	and	and	CCONJ
ejpam-5113	257	5	applications	application	NOUN
ejpam-5113	257	6	,	,	PUNCT
ejpam-5113	257	7	10	10	NUM
ejpam-5113	257	8	:	:	PUNCT
ejpam-5113	257	9	article	article	NOUN
ejpam-5113	257	10	i	i	PROPN
ejpam-5113	257	11	d	d	PROPN
ejpam-5113	257	12	32124	32124	NUM
ejpam-5113	257	13	,	,	PUNCT
ejpam-5113	257	14	10	10	NUM
ejpam-5113	257	15	pages	page	NOUN
ejpam-5113	257	16	,	,	PUNCT
ejpam-5113	257	17	2007	2007	NUM
ejpam-5113	257	18	.	.	PUNCT
ejpam-5113	258	1	[	[	X
ejpam-5113	258	2	11	11	NUM
ejpam-5113	258	3	]	]	PUNCT
ejpam-5113	258	4	s.	s.	PROPN
ejpam-5113	258	5	li	li	PROPN
ejpam-5113	258	6	and	and	CCONJ
ejpam-5113	258	7	s.	s.	PROPN
ejpam-5113	258	8	stević.	stević.	PROPN
ejpam-5113	258	9	generalized	generalized	ADJ
ejpam-5113	258	10	composition	composition	NOUN
ejpam-5113	258	11	operators	operator	NOUN
ejpam-5113	258	12	on	on	ADP
ejpam-5113	258	13	zygmund	zygmund	PROPN
ejpam-5113	258	14	spaces	space	NOUN
ejpam-5113	258	15	and	and	CCONJ
ejpam-5113	258	16	bloch	bloch	NOUN
ejpam-5113	258	17	type	type	NOUN
ejpam-5113	258	18	spaces	space	VERB
ejpam-5113	258	19	.	.	PUNCT
ejpam-5113	259	1	j.	j.	PROPN
ejpam-5113	259	2	math	math	PROPN
ejpam-5113	259	3	.	.	PUNCT
ejpam-5113	260	1	anal	anal	PROPN
ejpam-5113	260	2	.	.	PUNCT
ejpam-5113	261	1	appl	appl	PROPN
ejpam-5113	261	2	.	.	PROPN
ejpam-5113	262	1	,	,	PUNCT
ejpam-5113	262	2	338:1282–1295	338:1282–1295	NUM
ejpam-5113	262	3	,	,	PUNCT
ejpam-5113	262	4	2008	2008	NUM
ejpam-5113	262	5	.	.	PUNCT
ejpam-5113	263	1	[	[	X
ejpam-5113	263	2	12	12	NUM
ejpam-5113	263	3	]	]	X
ejpam-5113	263	4	s.	s.	PROPN
ejpam-5113	263	5	li	li	PROPN
ejpam-5113	263	6	and	and	CCONJ
ejpam-5113	263	7	s.	s.	PROPN
ejpam-5113	263	8	stević.	stević.	PROPN
ejpam-5113	263	9	products	product	NOUN
ejpam-5113	263	10	of	of	ADP
ejpam-5113	263	11	volterra	volterra	NOUN
ejpam-5113	263	12	type	type	NOUN
ejpam-5113	263	13	operator	operator	NOUN
ejpam-5113	263	14	and	and	CCONJ
ejpam-5113	263	15	composition	composition	NOUN
ejpam-5113	263	16	operator	operator	NOUN
ejpam-5113	263	17	from	from	ADP
ejpam-5113	263	18	h∞	h∞	PROPN
ejpam-5113	263	19	and	and	CCONJ
ejpam-5113	263	20	bloch	bloch	PROPN
ejpam-5113	263	21	spaces	space	VERB
ejpam-5113	263	22	to	to	ADP
ejpam-5113	263	23	the	the	DET
ejpam-5113	263	24	zygmund	zygmund	PROPN
ejpam-5113	263	25	space	space	NOUN
ejpam-5113	263	26	.	.	PUNCT
ejpam-5113	264	1	j.	j.	PROPN
ejpam-5113	264	2	math	math	PROPN
ejpam-5113	264	3	.	.	PUNCT
ejpam-5113	265	1	anal	anal	PROPN
ejpam-5113	265	2	.	.	PUNCT
ejpam-5113	266	1	appl	appl	PROPN
ejpam-5113	266	2	.	.	PROPN
ejpam-5113	266	3	,	,	PUNCT
ejpam-5113	267	1	345:40–52	345:40–52	NUM
ejpam-5113	267	2	,	,	PUNCT
ejpam-5113	267	3	2008	2008	NUM
ejpam-5113	267	4	.	.	PUNCT
ejpam-5113	268	1	[	[	X
ejpam-5113	268	2	13	13	NUM
ejpam-5113	268	3	]	]	X
ejpam-5113	268	4	y.	y.	PROPN
ejpam-5113	268	5	liang	liang	PROPN
ejpam-5113	268	6	.	.	PUNCT
ejpam-5113	268	7	volterra	volterra	NOUN
ejpam-5113	268	8	-	-	PUNCT
ejpam-5113	268	9	type	type	NOUN
ejpam-5113	268	10	operators	operator	NOUN
ejpam-5113	268	11	from	from	ADP
ejpam-5113	268	12	weighted	weight	VERB
ejpam-5113	268	13	bergman	bergman	PROPN
ejpam-5113	268	14	-	-	PUNCT
ejpam-5113	268	15	orlicz	orlicz	PROPN
ejpam-5113	268	16	space	space	NOUN
ejpam-5113	268	17	to	to	ADP
ejpam-5113	268	18	βzygmund	βzygmund	NOUN
ejpam-5113	268	19	-	-	PUNCT
ejpam-5113	268	20	orlicz	orlicz	NOUN
ejpam-5113	268	21	and	and	CCONJ
ejpam-5113	268	22	γ	γ	PROPN
ejpam-5113	268	23	-	-	PUNCT
ejpam-5113	268	24	bloch	bloch	NOUN
ejpam-5113	268	25	-	-	PUNCT
ejpam-5113	268	26	orlicz	orlicz	NOUN
ejpam-5113	268	27	spaces	space	NOUN
ejpam-5113	268	28	.	.	PUNCT
ejpam-5113	269	1	monatsheftefür	monatsheftefür	PROPN
ejpam-5113	269	2	mathematik	mathematik	PROPN
ejpam-5113	269	3	,	,	PUNCT
ejpam-5113	269	4	182:877	182:877	NOUN
ejpam-5113	269	5	–	–	PUNCT
ejpam-5113	269	6	897	897	NUM
ejpam-5113	269	7	,	,	PUNCT
ejpam-5113	269	8	2017	2017	NUM
ejpam-5113	269	9	.	.	PUNCT
ejpam-5113	270	1	[	[	X
ejpam-5113	270	2	14	14	NUM
ejpam-5113	270	3	]	]	X
ejpam-5113	270	4	y.	y.	PROPN
ejpam-5113	270	5	liu	liu	PROPN
ejpam-5113	270	6	and	and	CCONJ
ejpam-5113	270	7	y.	y.	PROPN
ejpam-5113	270	8	yu	yu	PROPN
ejpam-5113	270	9	.	.	PUNCT
ejpam-5113	270	10	riemann	riemann	PROPN
ejpam-5113	270	11	-	-	PUNCT
ejpam-5113	270	12	stieltjes	stieltjes	PROPN
ejpam-5113	270	13	operator	operator	NOUN
ejpam-5113	270	14	from	from	ADP
ejpam-5113	270	15	mixed	mixed	ADJ
ejpam-5113	270	16	norm	norm	NOUN
ejpam-5113	270	17	spaces	space	NOUN
ejpam-5113	270	18	to	to	PART
ejpam-5113	270	19	zygmundtype	zygmundtype	NOUN
ejpam-5113	270	20	spaces	space	NOUN
ejpam-5113	270	21	on	on	ADP
ejpam-5113	270	22	the	the	DET
ejpam-5113	270	23	unit	unit	NOUN
ejpam-5113	270	24	ball	ball	NOUN
ejpam-5113	270	25	.	.	PUNCT
ejpam-5113	271	1	taiwanese	taiwanese	ADJ
ejpam-5113	271	2	journal	journal	PROPN
ejpam-5113	271	3	of	of	ADP
ejpam-5113	271	4	mathematics	mathematic	NOUN
ejpam-5113	271	5	,	,	PUNCT
ejpam-5113	271	6	17:1751–1764	17:1751–1764	NUM
ejpam-5113	271	7	,	,	PUNCT
ejpam-5113	271	8	2013	2013	NUM
ejpam-5113	271	9	.	.	PUNCT
ejpam-5113	272	1	[	[	X
ejpam-5113	272	2	15	15	NUM
ejpam-5113	272	3	]	]	X
ejpam-5113	272	4	s.	s.	PROPN
ejpam-5113	272	5	demiriz	demiriz	PROPN
ejpam-5113	272	6	m.	m.	PROPN
ejpam-5113	272	7	başarır	başarır	PROPN
ejpam-5113	272	8	and	and	CCONJ
ejpam-5113	272	9	e.e	e.e	PROPN
ejpam-5113	272	10	.	.	PROPN
ejpam-5113	272	11	kara	kara	PROPN
ejpam-5113	272	12	.	.	PUNCT
ejpam-5113	273	1	composition	composition	NOUN
ejpam-5113	273	2	operators	operator	NOUN
ejpam-5113	273	3	on	on	ADP
ejpam-5113	273	4	second	second	ADJ
ejpam-5113	273	5	-	-	PUNCT
ejpam-5113	273	6	order	order	NOUN
ejpam-5113	273	7	cesàro	cesàro	NOUN
ejpam-5113	273	8	function	function	NOUN
ejpam-5113	273	9	spaces	space	NOUN
ejpam-5113	273	10	.	.	PUNCT
ejpam-5113	274	1	approximation	approximation	NOUN
ejpam-5113	274	2	theory	theory	NOUN
ejpam-5113	274	3	,	,	PUNCT
ejpam-5113	274	4	sequence	sequence	NOUN
ejpam-5113	274	5	spaces	space	NOUN
ejpam-5113	274	6	and	and	CCONJ
ejpam-5113	274	7	applications	application	NOUN
ejpam-5113	274	8	,	,	PUNCT
ejpam-5113	274	9	1:21–33	1:21–33	NUM
ejpam-5113	274	10	,	,	PUNCT
ejpam-5113	274	11	2022	2022	NUM
ejpam-5113	274	12	.	.	PUNCT
ejpam-5113	275	1	[	[	X
ejpam-5113	275	2	16	16	NUM
ejpam-5113	275	3	]	]	PUNCT
ejpam-5113	275	4	j.	j.	PROPN
ejpam-5113	275	5	liu	liu	PROPN
ejpam-5113	275	6	q.	q.	PROPN
ejpam-5113	275	7	lin	lin	PROPN
ejpam-5113	275	8	and	and	CCONJ
ejpam-5113	275	9	y.	y.	PROPN
ejpam-5113	275	10	wu	wu	PROPN
ejpam-5113	275	11	.	.	PUNCT
ejpam-5113	276	1	volterra	volterra	PROPN
ejpam-5113	276	2	type	type	PROPN
ejpam-5113	276	3	operators	operator	NOUN
ejpam-5113	276	4	on	on	ADP
ejpam-5113	276	5	sp(d	sp(d	NOUN
ejpam-5113	276	6	)	)	PUNCT
ejpam-5113	276	7	spaces	space	NOUN
ejpam-5113	276	8	.	.	PUNCT
ejpam-5113	277	1	j.	j.	PROPN
ejpam-5113	277	2	math	math	PROPN
ejpam-5113	277	3	.	.	PUNCT
ejpam-5113	278	1	anal	anal	PROPN
ejpam-5113	278	2	.	.	PUNCT
ejpam-5113	279	1	and	and	CCONJ
ejpam-5113	279	2	appl	appl	PROPN
ejpam-5113	279	3	.	.	PROPN
ejpam-5113	279	4	,	,	PUNCT
ejpam-5113	279	5	461:1100–1114	461:1100–1114	NUM
ejpam-5113	279	6	,	,	PUNCT
ejpam-5113	279	7	2018	2018	NUM
ejpam-5113	279	8	.	.	PUNCT
ejpam-5113	280	1	[	[	X
ejpam-5113	280	2	17	17	NUM
ejpam-5113	280	3	]	]	X
ejpam-5113	280	4	j.h	j.h	PROPN
ejpam-5113	280	5	.	.	PROPN
ejpam-5113	280	6	shapiro	shapiro	PROPN
ejpam-5113	280	7	.	.	PUNCT
ejpam-5113	281	1	composition	composition	NOUN
ejpam-5113	281	2	operators	operator	NOUN
ejpam-5113	281	3	and	and	CCONJ
ejpam-5113	281	4	classical	classical	ADJ
ejpam-5113	281	5	function	function	NOUN
ejpam-5113	281	6	theory	theory	NOUN
ejpam-5113	281	7	.	.	PUNCT
ejpam-5113	282	1	springer	springer	NOUN
ejpam-5113	282	2	-	-	PUNCT
ejpam-5113	282	3	verlag	verlag	PROPN
ejpam-5113	282	4	,	,	PUNCT
ejpam-5113	282	5	new	new	PROPN
ejpam-5113	282	6	york	york	PROPN
ejpam-5113	282	7	,	,	PUNCT
ejpam-5113	282	8	1993	1993	NUM
ejpam-5113	282	9	.	.	PUNCT
ejpam-5113	283	1	[	[	X
ejpam-5113	283	2	18	18	NUM
ejpam-5113	283	3	]	]	PUNCT
ejpam-5113	283	4	a.	a.	NOUN
ejpam-5113	283	5	siskakis	siskakis	PROPN
ejpam-5113	283	6	and	and	CCONJ
ejpam-5113	283	7	r.	r.	PROPN
ejpam-5113	283	8	zhao	zhao	PROPN
ejpam-5113	283	9	.	.	PUNCT
ejpam-5113	284	1	a	a	DET
ejpam-5113	284	2	volterra	volterra	NOUN
ejpam-5113	284	3	type	type	NOUN
ejpam-5113	284	4	operator	operator	NOUN
ejpam-5113	284	5	on	on	ADP
ejpam-5113	284	6	spaces	space	NOUN
ejpam-5113	284	7	of	of	ADP
ejpam-5113	284	8	analytic	analytic	ADJ
ejpam-5113	284	9	functions	function	NOUN
ejpam-5113	284	10	.	.	PUNCT
ejpam-5113	285	1	contemporary	contemporary	ADJ
ejpam-5113	285	2	mathematics	mathematic	NOUN
ejpam-5113	285	3	,	,	PUNCT
ejpam-5113	285	4	232:299–311	232:299–311	NUM
ejpam-5113	285	5	,	,	PUNCT
ejpam-5113	285	6	1999	1999	NUM
ejpam-5113	285	7	.	.	PUNCT
ejpam-5113	286	1	[	[	X
ejpam-5113	286	2	19	19	NUM
ejpam-5113	286	3	]	]	X
ejpam-5113	286	4	e.	e.	PROPN
ejpam-5113	286	5	wolf	wolf	PROPN
ejpam-5113	286	6	.	.	PUNCT
ejpam-5113	287	1	volterra	volterra	PROPN
ejpam-5113	287	2	composition	composition	NOUN
ejpam-5113	287	3	operators	operator	NOUN
ejpam-5113	287	4	between	between	ADP
ejpam-5113	287	5	weighted	weight	VERB
ejpam-5113	287	6	bergman	bergman	PROPN
ejpam-5113	287	7	spaces	space	VERB
ejpam-5113	287	8	and	and	CCONJ
ejpam-5113	287	9	weighted	weight	VERB
ejpam-5113	287	10	bloch	bloch	PROPN
ejpam-5113	287	11	type	type	NOUN
ejpam-5113	287	12	spaces	space	NOUN
ejpam-5113	287	13	.	.	PUNCT
ejpam-5113	288	1	collect	collect	NOUN
ejpam-5113	288	2	.	.	PUNCT
ejpam-5113	289	1	math	math	NOUN
ejpam-5113	289	2	.	.	PUNCT
ejpam-5113	289	3	,	,	PUNCT
ejpam-5113	289	4	61:57–63	61:57–63	NUM
ejpam-5113	289	5	,	,	PUNCT
ejpam-5113	289	6	2010	2010	NUM
ejpam-5113	289	7	.	.	PUNCT
ejpam-5113	290	1	references	reference	NOUN
ejpam-5113	290	2	944	944	NUM
ejpam-5113	291	1	[	[	X
ejpam-5113	291	2	20	20	NUM
ejpam-5113	291	3	]	]	X
ejpam-5113	291	4	y.	y.	PROPN
ejpam-5113	291	5	yu	yu	PROPN
ejpam-5113	291	6	y.	y.	PROPN
ejpam-5113	291	7	liu	liu	PROPN
ejpam-5113	291	8	and	and	CCONJ
ejpam-5113	291	9	x.	x.	PROPN
ejpam-5113	291	10	liu	liu	PROPN
ejpam-5113	291	11	.	.	PUNCT
ejpam-5113	292	1	riemann	riemann	PROPN
ejpam-5113	292	2	-	-	PUNCT
ejpam-5113	292	3	stieltjes	stieltjes	PROPN
ejpam-5113	292	4	operator	operator	NOUN
ejpam-5113	292	5	from	from	ADP
ejpam-5113	292	6	the	the	DET
ejpam-5113	292	7	general	general	ADJ
ejpam-5113	292	8	space	space	NOUN
ejpam-5113	292	9	to	to	ADP
ejpam-5113	292	10	zygmund	zygmund	NOUN
ejpam-5113	292	11	-	-	PUNCT
ejpam-5113	292	12	type	type	NOUN
ejpam-5113	292	13	spaces	space	NOUN
ejpam-5113	292	14	on	on	ADP
ejpam-5113	292	15	the	the	DET
ejpam-5113	292	16	unit	unit	NOUN
ejpam-5113	292	17	ball	ball	NOUN
ejpam-5113	292	18	.	.	PUNCT
ejpam-5113	293	1	complex	complex	ADJ
ejpam-5113	293	2	analysis	analysis	NOUN
ejpam-5113	293	3	and	and	CCONJ
ejpam-5113	293	4	operator	operator	NOUN
ejpam-5113	293	5	theory	theory	NOUN
ejpam-5113	293	6	,	,	PUNCT
ejpam-5113	293	7	9:985	9:985	NUM
ejpam-5113	293	8	–	–	PUNCT
ejpam-5113	293	9	997	997	NUM
ejpam-5113	293	10	,	,	PUNCT
ejpam-5113	293	11	2015	2015	NUM
ejpam-5113	293	12	.	.	PUNCT
ejpam-5113	294	1	[	[	X
ejpam-5113	294	2	21	21	NUM
ejpam-5113	294	3	]	]	X
ejpam-5113	294	4	w.	w.	PROPN
ejpam-5113	294	5	yang	yang	PROPN
ejpam-5113	294	6	and	and	CCONJ
ejpam-5113	294	7	x.	x.	PROPN
ejpam-5113	294	8	meng	meng	PROPN
ejpam-5113	294	9	.	.	PUNCT
ejpam-5113	295	1	generalized	generalized	ADJ
ejpam-5113	295	2	composition	composition	NOUN
ejpam-5113	295	3	operators	operator	NOUN
ejpam-5113	295	4	from	from	ADP
ejpam-5113	295	5	f(p	f(p	PROPN
ejpam-5113	295	6	,	,	PUNCT
ejpam-5113	295	7	q	q	X
ejpam-5113	295	8	,	,	PUNCT
ejpam-5113	295	9	s	s	PART
ejpam-5113	295	10	)	)	PUNCT
ejpam-5113	295	11	spaces	space	NOUN
ejpam-5113	295	12	to	to	ADP
ejpam-5113	295	13	bloch	bloch	NOUN
ejpam-5113	295	14	-	-	PUNCT
ejpam-5113	295	15	type	type	NOUN
ejpam-5113	295	16	spaces	space	NOUN
ejpam-5113	295	17	.	.	PUNCT
ejpam-5113	296	1	appl	appl	PROPN
ejpam-5113	296	2	.	.	PROPN
ejpam-5113	296	3	math	math	PROPN
ejpam-5113	296	4	.	.	PUNCT
ejpam-5113	297	1	comput	comput	NOUN
ejpam-5113	297	2	.	.	PUNCT
ejpam-5113	297	3	,	,	PUNCT
ejpam-5113	297	4	217:2513–2519	217:2513–2519	NUM
ejpam-5113	297	5	,	,	PUNCT
ejpam-5113	297	6	2010	2010	NUM
ejpam-5113	297	7	.	.	PUNCT
ejpam-5113	298	1	[	[	X
ejpam-5113	298	2	22	22	NUM
ejpam-5113	298	3	]	]	PUNCT
ejpam-5113	298	4	k.	k.	PROPN
ejpam-5113	298	5	zhu	zhu	PROPN
ejpam-5113	298	6	.	.	PUNCT
ejpam-5113	299	1	spaces	space	NOUN
ejpam-5113	299	2	of	of	ADP
ejpam-5113	299	3	holomorphic	holomorphic	ADJ
ejpam-5113	299	4	functions	function	NOUN
ejpam-5113	299	5	in	in	ADP
ejpam-5113	299	6	the	the	DET
ejpam-5113	299	7	unit	unit	NOUN
ejpam-5113	299	8	ball	ball	PROPN
ejpam-5113	299	9	.	.	PUNCT
ejpam-5113	300	1	springer	springer	NOUN
ejpam-5113	300	2	-	-	PUNCT
ejpam-5113	300	3	verlag	verlag	PROPN
ejpam-5113	300	4	,	,	PUNCT
ejpam-5113	300	5	new	new	PROPN
ejpam-5113	300	6	york	york	PROPN
ejpam-5113	300	7	,	,	PUNCT
ejpam-5113	300	8	2005	2005	NUM
ejpam-5113	300	9	.	.	PUNCT
ejpam-5113	301	1	[	[	X
ejpam-5113	301	2	23	23	NUM
ejpam-5113	301	3	]	]	PUNCT
ejpam-5113	301	4	k.	k.	PROPN
ejpam-5113	301	5	zhu	zhu	PROPN
ejpam-5113	301	6	.	.	PUNCT
ejpam-5113	302	1	operator	operator	NOUN
ejpam-5113	302	2	theory	theory	NOUN
ejpam-5113	302	3	in	in	ADP
ejpam-5113	302	4	function	function	NOUN
ejpam-5113	302	5	spaces	space	NOUN
ejpam-5113	302	6	.	.	PUNCT
ejpam-5113	303	1	american	american	PROPN
ejpam-5113	303	2	mathematical	mathematical	PROPN
ejpam-5113	303	3	society	society	NOUN
ejpam-5113	303	4	,	,	PUNCT
ejpam-5113	303	5	new	new	PROPN
ejpam-5113	303	6	york	york	PROPN
ejpam-5113	303	7	,	,	PUNCT
ejpam-5113	303	8	2007	2007	NUM
ejpam-5113	303	9	.	.	PUNCT
ejpam-5113	304	1	[	[	X
ejpam-5113	304	2	24	24	NUM
ejpam-5113	304	3	]	]	PUNCT
ejpam-5113	304	4	x.	x.	NOUN
ejpam-5113	304	5	zhu	zhu	PROPN
ejpam-5113	304	6	.	.	PUNCT
ejpam-5113	305	1	generalized	generalize	VERB
ejpam-5113	305	2	weighted	weight	VERB
ejpam-5113	305	3	composition	composition	NOUN
ejpam-5113	305	4	operators	operator	NOUN
ejpam-5113	305	5	from	from	ADP
ejpam-5113	305	6	bloch	bloch	NOUN
ejpam-5113	305	7	-	-	PUNCT
ejpam-5113	305	8	type	type	NOUN
ejpam-5113	305	9	spaces	space	NOUN
ejpam-5113	305	10	to	to	PART
ejpam-5113	305	11	weighted	weight	VERB
ejpam-5113	305	12	bergman	bergman	PROPN
ejpam-5113	305	13	spaces	space	VERB
ejpam-5113	305	14	.	.	PUNCT
ejpam-5113	306	1	indian	indian	PROPN
ejpam-5113	306	2	j.	j.	PROPN
ejpam-5113	306	3	math	math	PROPN
ejpam-5113	306	4	.	.	PUNCT
ejpam-5113	306	5	,	,	PUNCT
ejpam-5113	306	6	49:139–149	49:139–149	PROPN
ejpam-5113	306	7	,	,	PUNCT
ejpam-5113	306	8	2007	2007	NUM
ejpam-5113	306	9	.	.	PUNCT
ejpam-5113	307	1	[	[	X
ejpam-5113	307	2	25	25	NUM
ejpam-5113	307	3	]	]	PUNCT
ejpam-5113	307	4	x.	x.	NOUN
ejpam-5113	307	5	zhu	zhu	PROPN
ejpam-5113	307	6	.	.	PUNCT
ejpam-5113	308	1	generalized	generalize	VERB
ejpam-5113	308	2	composition	composition	NOUN
ejpam-5113	308	3	operators	operator	NOUN
ejpam-5113	308	4	and	and	CCONJ
ejpam-5113	308	5	volterra	volterra	NOUN
ejpam-5113	308	6	composition	composition	NOUN
ejpam-5113	308	7	operators	operator	NOUN
ejpam-5113	308	8	on	on	ADP
ejpam-5113	308	9	bloch	bloch	PROPN
ejpam-5113	308	10	spaces	space	NOUN
ejpam-5113	308	11	in	in	ADP
ejpam-5113	308	12	the	the	DET
ejpam-5113	308	13	unit	unit	NOUN
ejpam-5113	308	14	ball	ball	NOUN
ejpam-5113	308	15	.	.	PUNCT
ejpam-5113	309	1	complex	complex	ADJ
ejpam-5113	309	2	var	var	NOUN
ejpam-5113	309	3	.	.	PUNCT
ejpam-5113	310	1	elliptic	elliptic	PROPN
ejpam-5113	310	2	equ	equ	PROPN
ejpam-5113	310	3	.	.	PROPN
ejpam-5113	310	4	,	,	PUNCT
ejpam-5113	310	5	54:95–102	54:95–102	NUM
ejpam-5113	310	6	,	,	PUNCT
ejpam-5113	310	7	2009	2009	NUM
ejpam-5113	310	8	.	.	PUNCT