id	sid	tid	token	lemma	pos
ejpam-5281	1	1	european	european	PROPN
ejpam-5281	1	2	journal	journal	PROPN
ejpam-5281	1	3	of	of	ADP
ejpam-5281	1	4	pure	pure	ADJ
ejpam-5281	1	5	and	and	CCONJ
ejpam-5281	1	6	applied	apply	VERB
ejpam-5281	1	7	mathematics	mathematic	NOUN
ejpam-5281	1	8	vol	vol	NOUN
ejpam-5281	1	9	.	.	PROPN
ejpam-5281	2	1	17	17	NUM
ejpam-5281	2	2	,	,	PUNCT
ejpam-5281	2	3	no	no	INTJ
ejpam-5281	2	4	.	.	NOUN
ejpam-5281	2	5	3	3	NUM
ejpam-5281	2	6	,	,	PUNCT
ejpam-5281	2	7	2024	2024	NUM
ejpam-5281	2	8	,	,	PUNCT
ejpam-5281	2	9	1490	1490	NUM
ejpam-5281	2	10	-	-	SYM
ejpam-5281	2	11	1496	1496	NUM
ejpam-5281	2	12	issn	issn	PROPN
ejpam-5281	2	13	1307	1307	NUM
ejpam-5281	2	14	-	-	SYM
ejpam-5281	2	15	5543	5543	NUM
ejpam-5281	2	16	–	–	PUNCT
ejpam-5281	2	17	ejpam.com	ejpam.com	X
ejpam-5281	2	18	published	publish	VERB
ejpam-5281	2	19	by	by	ADP
ejpam-5281	2	20	new	new	PROPN
ejpam-5281	2	21	york	york	PROPN
ejpam-5281	2	22	business	business	PROPN
ejpam-5281	2	23	global	global	ADJ
ejpam-5281	2	24	riesz	riesz	PROPN
ejpam-5281	2	25	inequality	inequality	NOUN
ejpam-5281	2	26	for	for	ADP
ejpam-5281	2	27	harmonic	harmonic	ADJ
ejpam-5281	2	28	quasiregular	quasiregular	ADJ
ejpam-5281	2	29	mappings	mapping	NOUN
ejpam-5281	2	30	elver	elver	PROPN
ejpam-5281	2	31	bajrami	bajrami	PROPN
ejpam-5281	2	32	department	department	PROPN
ejpam-5281	2	33	of	of	ADP
ejpam-5281	2	34	mathematics	mathematics	PROPN
ejpam-5281	2	35	,	,	PUNCT
ejpam-5281	2	36	university	university	PROPN
ejpam-5281	2	37	of	of	ADP
ejpam-5281	2	38	prishtina	prishtina	PROPN
ejpam-5281	2	39	,	,	PUNCT
ejpam-5281	2	40	mother	mother	NOUN
ejpam-5281	2	41	teresa	teresa	PROPN
ejpam-5281	2	42	,	,	PUNCT
ejpam-5281	2	43	no	no	INTJ
ejpam-5281	2	44	.	.	NOUN
ejpam-5281	2	45	5	5	NUM
ejpam-5281	2	46	,	,	PUNCT
ejpam-5281	2	47	10000	10000	NUM
ejpam-5281	2	48	,	,	PUNCT
ejpam-5281	2	49	prishtina	prishtina	PROPN
ejpam-5281	2	50	,	,	PUNCT
ejpam-5281	2	51	kosovo	kosovo	PROPN
ejpam-5281	2	52	abstract	abstract	PROPN
ejpam-5281	2	53	.	.	PUNCT
ejpam-5281	3	1	in	in	ADP
ejpam-5281	3	2	this	this	DET
ejpam-5281	3	3	paper	paper	NOUN
ejpam-5281	3	4	,	,	PUNCT
ejpam-5281	3	5	we	we	PRON
ejpam-5281	3	6	generalize	generalize	VERB
ejpam-5281	3	7	the	the	DET
ejpam-5281	3	8	riesz	riesz	NOUN
ejpam-5281	3	9	theorem	theorem	NOUN
ejpam-5281	3	10	for	for	ADP
ejpam-5281	3	11	harmonic	harmonic	ADJ
ejpam-5281	3	12	quasiregular	quasiregular	ADJ
ejpam-5281	3	13	mappings	mapping	NOUN
ejpam-5281	3	14	for	for	ADP
ejpam-5281	3	15	a	a	DET
ejpam-5281	3	16	special	special	ADJ
ejpam-5281	3	17	case	case	NOUN
ejpam-5281	3	18	(	(	PUNCT
ejpam-5281	3	19	when	when	SCONJ
ejpam-5281	3	20	p	p	NOUN
ejpam-5281	3	21	=	=	NOUN
ejpam-5281	3	22	2	2	NUM
ejpam-5281	3	23	)	)	PUNCT
ejpam-5281	3	24	in	in	ADP
ejpam-5281	3	25	the	the	DET
ejpam-5281	3	26	unit	unit	NOUN
ejpam-5281	3	27	disc	disc	NOUN
ejpam-5281	3	28	.	.	PUNCT
ejpam-5281	4	1	our	our	PRON
ejpam-5281	4	2	results	result	NOUN
ejpam-5281	4	3	improve	improve	VERB
ejpam-5281	4	4	similar	similar	ADJ
ejpam-5281	4	5	results	result	NOUN
ejpam-5281	4	6	in	in	ADP
ejpam-5281	4	7	this	this	DET
ejpam-5281	4	8	field	field	NOUN
ejpam-5281	4	9	and	and	CCONJ
ejpam-5281	4	10	are	be	AUX
ejpam-5281	4	11	proved	prove	VERB
ejpam-5281	4	12	with	with	ADP
ejpam-5281	4	13	milder	mild	ADJ
ejpam-5281	4	14	conditions	condition	NOUN
ejpam-5281	4	15	.	.	PUNCT
ejpam-5281	5	1	moreover	moreover	ADV
ejpam-5281	5	2	,	,	PUNCT
ejpam-5281	5	3	we	we	PRON
ejpam-5281	5	4	prove	prove	VERB
ejpam-5281	5	5	another	another	DET
ejpam-5281	5	6	variant	variant	ADJ
ejpam-5281	5	7	forms	form	NOUN
ejpam-5281	5	8	of	of	ADP
ejpam-5281	5	9	riesz	riesz	NOUN
ejpam-5281	5	10	inequality	inequality	NOUN
ejpam-5281	5	11	for	for	ADP
ejpam-5281	5	12	harmonic	harmonic	ADJ
ejpam-5281	5	13	quasiregular	quasiregular	ADJ
ejpam-5281	5	14	functions	function	NOUN
ejpam-5281	5	15	.	.	PUNCT
ejpam-5281	6	1	2020	2020	NUM
ejpam-5281	6	2	mathematics	mathematic	NOUN
ejpam-5281	6	3	subject	subject	NOUN
ejpam-5281	6	4	classifications	classification	NOUN
ejpam-5281	6	5	:	:	PUNCT
ejpam-5281	6	6	30h10	30h10	NUM
ejpam-5281	6	7	,	,	PUNCT
ejpam-5281	6	8	30h05	30h05	NUM
ejpam-5281	6	9	key	key	ADJ
ejpam-5281	6	10	words	word	NOUN
ejpam-5281	6	11	and	and	CCONJ
ejpam-5281	6	12	phrases	phrase	NOUN
ejpam-5281	6	13	:	:	PUNCT
ejpam-5281	6	14	harmonic	harmonic	ADJ
ejpam-5281	6	15	mappings	mapping	NOUN
ejpam-5281	6	16	,	,	PUNCT
ejpam-5281	6	17	quasiregular	quasiregular	ADJ
ejpam-5281	6	18	mappings	mapping	NOUN
ejpam-5281	6	19	,	,	PUNCT
ejpam-5281	6	20	riesz	riesz	PROPN
ejpam-5281	6	21	theorem	theorem	NOUN
ejpam-5281	6	22	1	1	NUM
ejpam-5281	6	23	.	.	PUNCT
ejpam-5281	6	24	introduction	introduction	NOUN
ejpam-5281	6	25	let	let	VERB
ejpam-5281	6	26	u	u	PRON
ejpam-5281	6	27	=	=	PUNCT
ejpam-5281	6	28	{	{	PUNCT
ejpam-5281	6	29	z	z	PROPN
ejpam-5281	6	30	∈	∈	PROPN
ejpam-5281	6	31	c	c	NOUN
ejpam-5281	6	32	:	:	PUNCT
ejpam-5281	6	33	|z|	|z|	NOUN
ejpam-5281	6	34	<	<	X
ejpam-5281	6	35	1	1	NUM
ejpam-5281	6	36	}	}	PUNCT
ejpam-5281	6	37	be	be	AUX
ejpam-5281	6	38	the	the	DET
ejpam-5281	6	39	unit	unit	NOUN
ejpam-5281	6	40	disk	disk	NOUN
ejpam-5281	6	41	and	and	CCONJ
ejpam-5281	6	42	let	let	VERB
ejpam-5281	6	43	t	t	NOUN
ejpam-5281	6	44	=	=	SYM
ejpam-5281	6	45	{	{	PUNCT
ejpam-5281	6	46	z	z	NOUN
ejpam-5281	6	47	∈	∈	PROPN
ejpam-5281	6	48	c	c	NOUN
ejpam-5281	6	49	:	:	PUNCT
ejpam-5281	6	50	|z|	|z|	NOUN
ejpam-5281	6	51	=	=	SYM
ejpam-5281	6	52	1	1	X
ejpam-5281	6	53	}	}	PUNCT
ejpam-5281	6	54	be	be	AUX
ejpam-5281	6	55	the	the	DET
ejpam-5281	6	56	unit	unit	NOUN
ejpam-5281	6	57	circle	circle	NOUN
ejpam-5281	6	58	in	in	ADP
ejpam-5281	6	59	plane	plane	NOUN
ejpam-5281	6	60	.	.	PUNCT
ejpam-5281	7	1	for	for	ADP
ejpam-5281	7	2	p	p	PROPN
ejpam-5281	7	3	>	>	X
ejpam-5281	7	4	1	1	NUM
ejpam-5281	7	5	we	we	PRON
ejpam-5281	7	6	define	define	VERB
ejpam-5281	7	7	the	the	DET
ejpam-5281	7	8	hardy	hardy	ADJ
ejpam-5281	7	9	class	class	NOUN
ejpam-5281	7	10	hp	hp	NOUN
ejpam-5281	7	11	as	as	ADP
ejpam-5281	7	12	the	the	DET
ejpam-5281	7	13	class	class	NOUN
ejpam-5281	7	14	of	of	ADP
ejpam-5281	7	15	harmonic	harmonic	ADJ
ejpam-5281	7	16	mappings	mapping	NOUN
ejpam-5281	8	1	f	f	NOUN
ejpam-5281	8	2	=	=	SYM
ejpam-5281	8	3	g	g	PROPN
ejpam-5281	8	4	+	+	CCONJ
ejpam-5281	8	5	h	h	NOUN
ejpam-5281	8	6	,	,	PUNCT
ejpam-5281	8	7	where	where	SCONJ
ejpam-5281	8	8	h	h	NOUN
ejpam-5281	8	9	and	and	CCONJ
ejpam-5281	8	10	g	g	PROPN
ejpam-5281	8	11	are	be	AUX
ejpam-5281	8	12	holomorphic	holomorphic	ADJ
ejpam-5281	8	13	mappings	mapping	NOUN
ejpam-5281	8	14	defined	define	VERB
ejpam-5281	8	15	on	on	ADP
ejpam-5281	8	16	unit	unit	NOUN
ejpam-5281	8	17	disk	disk	NOUN
ejpam-5281	8	18	u	u	PROPN
ejpam-5281	8	19	⊂	⊂	PROPN
ejpam-5281	8	20	c.	c.	PROPN
ejpam-5281	8	21	norm	norm	NOUN
ejpam-5281	8	22	in	in	ADP
ejpam-5281	8	23	this	this	DET
ejpam-5281	8	24	space	space	NOUN
ejpam-5281	8	25	is	be	AUX
ejpam-5281	8	26	defined	define	VERB
ejpam-5281	8	27	||f	||f	ADJ
ejpam-5281	8	28	||p	||p	NOUN
ejpam-5281	8	29	=	=	SYM
ejpam-5281	8	30	||f	||f	NOUN
ejpam-5281	8	31	||hp	||hp	NUM
ejpam-5281	8	32	=	=	NOUN
ejpam-5281	8	33	sup	sup	NOUN
ejpam-5281	8	34	0	0	NUM
ejpam-5281	8	35	<	<	NOUN
ejpam-5281	8	36	r<1	r<1	NOUN
ejpam-5281	8	37	mp(f	mp(f	NOUN
ejpam-5281	8	38	,	,	PUNCT
ejpam-5281	8	39	r	r	NOUN
ejpam-5281	8	40	)	)	PUNCT
ejpam-5281	8	41	<	<	X
ejpam-5281	8	42	∞	∞	PROPN
ejpam-5281	8	43	,	,	PUNCT
ejpam-5281	8	44	where	where	SCONJ
ejpam-5281	8	45	mp(f	mp(f	NOUN
ejpam-5281	8	46	,	,	PUNCT
ejpam-5281	8	47	r	r	NOUN
ejpam-5281	8	48	)	)	PUNCT
ejpam-5281	8	49	=	=	SYM
ejpam-5281	9	1	(	(	PUNCT
ejpam-5281	9	2	∫	∫	PROPN
ejpam-5281	9	3	t	t	PROPN
ejpam-5281	9	4	|f(rζ)|pdσ(ζ	|f(rζ)|pdσ(ζ	NUM
ejpam-5281	9	5	)	)	PUNCT
ejpam-5281	9	6	)	)	PUNCT
ejpam-5281	9	7	1	1	X
ejpam-5281	9	8	/	/	SYM
ejpam-5281	9	9	p	p	NOUN
ejpam-5281	9	10	.	.	PUNCT
ejpam-5281	10	1	here	here	ADV
ejpam-5281	10	2	σ	σ	PROPN
ejpam-5281	10	3	is	be	AUX
ejpam-5281	10	4	probability	probability	NOUN
ejpam-5281	10	5	measure	measure	NOUN
ejpam-5281	10	6	on	on	ADP
ejpam-5281	10	7	t.	t.	PROPN
ejpam-5281	10	8	with	with	ADP
ejpam-5281	10	9	hp	hp	PROPN
ejpam-5281	10	10	(	(	PUNCT
ejpam-5281	10	11	hp	hp	PROPN
ejpam-5281	10	12	)	)	PUNCT
ejpam-5281	10	13	,	,	PUNCT
ejpam-5281	10	14	we	we	PRON
ejpam-5281	10	15	denote	denote	VERB
ejpam-5281	10	16	the	the	DET
ejpam-5281	10	17	subclass	subclass	NOUN
ejpam-5281	10	18	of	of	ADP
ejpam-5281	10	19	holomorphic	holomorphic	ADJ
ejpam-5281	10	20	(	(	PUNCT
ejpam-5281	10	21	quasiregular	quasiregular	NOUN
ejpam-5281	10	22	)	)	PUNCT
ejpam-5281	10	23	mappings	mapping	NOUN
ejpam-5281	10	24	that	that	PRON
ejpam-5281	10	25	belongs	belong	VERB
ejpam-5281	10	26	to	to	ADP
ejpam-5281	10	27	the	the	DET
ejpam-5281	10	28	class	class	NOUN
ejpam-5281	10	29	hp	hp	PROPN
ejpam-5281	10	30	.	.	PROPN
ejpam-5281	10	31	for	for	ADP
ejpam-5281	10	32	the	the	DET
ejpam-5281	10	33	theory	theory	NOUN
ejpam-5281	10	34	of	of	ADP
ejpam-5281	10	35	hardy	hardy	ADJ
ejpam-5281	10	36	spaces	space	NOUN
ejpam-5281	10	37	in	in	ADP
ejpam-5281	10	38	the	the	DET
ejpam-5281	10	39	unit	unit	NOUN
ejpam-5281	10	40	disk	disk	NOUN
ejpam-5281	10	41	we	we	PRON
ejpam-5281	10	42	refer	refer	VERB
ejpam-5281	10	43	to	to	ADP
ejpam-5281	10	44	[	[	X
ejpam-5281	10	45	12	12	NUM
ejpam-5281	10	46	]	]	PUNCT
ejpam-5281	10	47	,	,	PUNCT
ejpam-5281	10	48	[	[	X
ejpam-5281	10	49	4	4	NUM
ejpam-5281	10	50	]	]	PUNCT
ejpam-5281	10	51	,	,	PUNCT
ejpam-5281	10	52	[	[	X
ejpam-5281	10	53	5	5	NUM
ejpam-5281	10	54	]	]	PUNCT
ejpam-5281	10	55	and	and	CCONJ
ejpam-5281	10	56	[	[	X
ejpam-5281	10	57	6	6	NUM
ejpam-5281	10	58	]	]	PUNCT
ejpam-5281	10	59	.	.	PUNCT
ejpam-5281	11	1	for	for	ADP
ejpam-5281	11	2	a	a	DET
ejpam-5281	11	3	given	give	VERB
ejpam-5281	11	4	real	real	ADV
ejpam-5281	11	5	-	-	PUNCT
ejpam-5281	11	6	valued	value	VERB
ejpam-5281	11	7	function	function	NOUN
ejpam-5281	11	8	u	u	PROPN
ejpam-5281	11	9	harmonic	harmonic	VERB
ejpam-5281	11	10	in	in	ADP
ejpam-5281	11	11	u	u	NOUN
ejpam-5281	11	12	,	,	PUNCT
ejpam-5281	11	13	let	let	VERB
ejpam-5281	11	14	v	v	PART
ejpam-5281	11	15	be	be	AUX
ejpam-5281	11	16	its	its	PRON
ejpam-5281	11	17	harmonic	harmonic	ADJ
ejpam-5281	11	18	conjugate	conjugate	NOUN
ejpam-5281	11	19	,	,	PUNCT
ejpam-5281	11	20	normalized	normalize	VERB
ejpam-5281	11	21	by	by	ADP
ejpam-5281	11	22	v(0	v(0	PROPN
ejpam-5281	11	23	)	)	PUNCT
ejpam-5281	12	1	=	=	PUNCT
ejpam-5281	12	2	0	0	X
ejpam-5281	12	3	.	.	PUNCT
ejpam-5281	13	1	then	then	ADV
ejpam-5281	13	2	f	f	PROPN
ejpam-5281	13	3	=	=	SYM
ejpam-5281	13	4	u	u	PROPN
ejpam-5281	13	5	+	+	NOUN
ejpam-5281	13	6	iv	iv	NUM
ejpam-5281	13	7	is	be	AUX
ejpam-5281	13	8	analytic	analytic	ADJ
ejpam-5281	13	9	in	in	ADP
ejpam-5281	13	10	u.	u.	PROPN
ejpam-5281	13	11	the	the	DET
ejpam-5281	13	12	following	follow	VERB
ejpam-5281	13	13	theorem	theorem	NOUN
ejpam-5281	13	14	was	be	AUX
ejpam-5281	13	15	proved	prove	VERB
ejpam-5281	13	16	by	by	ADP
ejpam-5281	13	17	m.	m.	NOUN
ejpam-5281	13	18	riesz	riesz	PROPN
ejpam-5281	13	19	.	.	PUNCT
ejpam-5281	14	1	doi	doi	NOUN
ejpam-5281	14	2	:	:	PUNCT
ejpam-5281	14	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5281	https://doi.org/10.29020/nybg.ejpam.v17i3.5281	ADJ
ejpam-5281	14	4	email	email	NOUN
ejpam-5281	14	5	address	address	NOUN
ejpam-5281	14	6	:	:	PUNCT
ejpam-5281	14	7	elver.bajrami@uni-pr.edu	elver.bajrami@uni-pr.edu	PROPN
ejpam-5281	14	8	(	(	PUNCT
ejpam-5281	14	9	e.	e.	PROPN
ejpam-5281	14	10	bajrami	bajrami	PROPN
ejpam-5281	14	11	)	)	PUNCT
ejpam-5281	14	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5281	14	13	1490	1490	NUM
ejpam-5281	14	14	©	©	PROPN
ejpam-5281	14	15	2024	2024	NUM
ejpam-5281	14	16	ejpam	ejpam	NOUN
ejpam-5281	14	17	all	all	DET
ejpam-5281	14	18	rights	right	NOUN
ejpam-5281	14	19	reserved	reserve	VERB
ejpam-5281	14	20	.	.	PUNCT
ejpam-5281	15	1	e.	e.	PROPN
ejpam-5281	15	2	bajrami	bajrami	PROPN
ejpam-5281	15	3	/	/	SYM
ejpam-5281	15	4	eur	eur	PROPN
ejpam-5281	15	5	.	.	PUNCT
ejpam-5281	16	1	j.	j.	PROPN
ejpam-5281	16	2	pure	pure	PROPN
ejpam-5281	16	3	appl	appl	PROPN
ejpam-5281	16	4	.	.	PROPN
ejpam-5281	16	5	math	math	PROPN
ejpam-5281	16	6	,	,	PUNCT
ejpam-5281	16	7	17	17	NUM
ejpam-5281	16	8	(	(	PUNCT
ejpam-5281	16	9	3	3	NUM
ejpam-5281	16	10	)	)	PUNCT
ejpam-5281	16	11	(	(	PUNCT
ejpam-5281	16	12	2024	2024	NUM
ejpam-5281	16	13	)	)	PUNCT
ejpam-5281	16	14	,	,	PUNCT
ejpam-5281	16	15	1490	1490	NUM
ejpam-5281	16	16	-	-	SYM
ejpam-5281	16	17	1496	1496	NUM
ejpam-5281	16	18	1491	1491	NUM
ejpam-5281	16	19	theorem	theorem	VERB
ejpam-5281	16	20	a	a	PRON
ejpam-5281	16	21	.	.	PUNCT
ejpam-5281	17	1	(	(	PUNCT
ejpam-5281	17	2	[	[	X
ejpam-5281	17	3	4	4	NUM
ejpam-5281	17	4	,	,	PUNCT
ejpam-5281	17	5	theorem	theorem	VERB
ejpam-5281	17	6	4.1	4.1	NUM
ejpam-5281	17	7	]	]	PUNCT
ejpam-5281	17	8	)	)	PUNCT
ejpam-5281	17	9	if	if	SCONJ
ejpam-5281	17	10	u	u	PROPN
ejpam-5281	17	11	∈	∈	PROPN
ejpam-5281	17	12	hp	hp	VERB
ejpam-5281	17	13	for	for	ADP
ejpam-5281	17	14	some	some	DET
ejpam-5281	17	15	p	p	NOUN
ejpam-5281	17	16	,	,	PUNCT
ejpam-5281	17	17	1	1	NUM
ejpam-5281	17	18	<	<	X
ejpam-5281	17	19	p	p	X
ejpam-5281	17	20	<	<	X
ejpam-5281	17	21	∞	∞	PROPN
ejpam-5281	17	22	,	,	PUNCT
ejpam-5281	17	23	then	then	ADV
ejpam-5281	17	24	its	its	PRON
ejpam-5281	17	25	harmonic	harmonic	ADJ
ejpam-5281	17	26	conjugate	conjugate	NOUN
ejpam-5281	17	27	v	v	NOUN
ejpam-5281	17	28	is	be	AUX
ejpam-5281	17	29	also	also	ADV
ejpam-5281	17	30	of	of	ADP
ejpam-5281	17	31	class	class	NOUN
ejpam-5281	17	32	hp	hp	PROPN
ejpam-5281	17	33	.	.	PUNCT
ejpam-5281	18	1	furthermore	furthermore	ADV
ejpam-5281	18	2	,	,	PUNCT
ejpam-5281	18	3	there	there	PRON
ejpam-5281	18	4	is	be	VERB
ejpam-5281	18	5	a	a	DET
ejpam-5281	18	6	constant	constant	ADJ
ejpam-5281	18	7	ap	ap	PROPN
ejpam-5281	18	8	,	,	PUNCT
ejpam-5281	18	9	depending	depend	VERB
ejpam-5281	18	10	only	only	ADV
ejpam-5281	18	11	on	on	ADP
ejpam-5281	18	12	p	p	X
ejpam-5281	18	13	,	,	PUNCT
ejpam-5281	18	14	such	such	ADJ
ejpam-5281	18	15	that	that	SCONJ
ejpam-5281	18	16	mp(r	mp(r	NOUN
ejpam-5281	18	17	,	,	PUNCT
ejpam-5281	18	18	v	v	NOUN
ejpam-5281	18	19	)	)	PUNCT
ejpam-5281	18	20	≤	≤	NOUN
ejpam-5281	18	21	apmp(r	apmp(r	PROPN
ejpam-5281	18	22	,	,	PUNCT
ejpam-5281	18	23	u	u	NOUN
ejpam-5281	18	24	)	)	PUNCT
ejpam-5281	18	25	,	,	PUNCT
ejpam-5281	18	26	0	0	NUM
ejpam-5281	18	27	≤	≤	NUM
ejpam-5281	18	28	r	r	NOUN
ejpam-5281	18	29	<	<	X
ejpam-5281	18	30	1	1	NUM
ejpam-5281	18	31	,	,	PUNCT
ejpam-5281	18	32	for	for	ADP
ejpam-5281	18	33	all	all	DET
ejpam-5281	18	34	u	u	PROPN
ejpam-5281	18	35	∈	∈	PROPN
ejpam-5281	18	36	hp	hp	PROPN
ejpam-5281	18	37	.	.	PROPN
ejpam-5281	18	38	problem	problem	NOUN
ejpam-5281	18	39	of	of	ADP
ejpam-5281	18	40	finding	find	VERB
ejpam-5281	18	41	the	the	DET
ejpam-5281	18	42	sharp	sharp	ADJ
ejpam-5281	18	43	constant	constant	ADJ
ejpam-5281	18	44	ap	ap	PROPN
ejpam-5281	18	45	is	be	AUX
ejpam-5281	18	46	very	very	ADV
ejpam-5281	18	47	old	old	ADJ
ejpam-5281	18	48	and	and	CCONJ
ejpam-5281	18	49	has	have	AUX
ejpam-5281	18	50	been	be	AUX
ejpam-5281	18	51	calculated	calculate	VERB
ejpam-5281	18	52	for	for	ADP
ejpam-5281	18	53	several	several	ADJ
ejpam-5281	18	54	classes	class	NOUN
ejpam-5281	18	55	of	of	ADP
ejpam-5281	18	56	functions	function	NOUN
ejpam-5281	18	57	.	.	PUNCT
ejpam-5281	19	1	pichorides	pichoride	NOUN
ejpam-5281	19	2	in	in	ADP
ejpam-5281	19	3	[	[	X
ejpam-5281	19	4	10	10	NUM
ejpam-5281	19	5	]	]	PUNCT
ejpam-5281	19	6	,	,	PUNCT
ejpam-5281	19	7	prove	prove	VERB
ejpam-5281	19	8	that	that	SCONJ
ejpam-5281	19	9	this	this	DET
ejpam-5281	19	10	constant	constant	ADJ
ejpam-5281	19	11	is	be	AUX
ejpam-5281	19	12	ap	ap	NOUN
ejpam-5281	19	13	=	=	PUNCT
ejpam-5281	19	14	cot	cot	NOUN
ejpam-5281	20	1	π	π	X
ejpam-5281	20	2	2p	2p	NOUN
ejpam-5281	20	3	,	,	PUNCT
ejpam-5281	20	4	where	where	SCONJ
ejpam-5281	20	5	p	p	NOUN
ejpam-5281	20	6	=	=	X
ejpam-5281	20	7	max	max	X
ejpam-5281	20	8	{	{	PUNCT
ejpam-5281	20	9	p	p	X
ejpam-5281	20	10	,	,	PUNCT
ejpam-5281	20	11	p	p	PROPN
ejpam-5281	20	12	p−1	p−1	PROPN
ejpam-5281	20	13	}	}	PUNCT
ejpam-5281	20	14	.	.	PUNCT
ejpam-5281	21	1	later	later	ADV
ejpam-5281	21	2	,	,	PUNCT
ejpam-5281	21	3	verbitsky	verbitsky	PROPN
ejpam-5281	21	4	improved	improve	VERB
ejpam-5281	21	5	the	the	DET
ejpam-5281	21	6	above	above	ADJ
ejpam-5281	21	7	inequality	inequality	NOUN
ejpam-5281	21	8	in	in	ADP
ejpam-5281	21	9	[	[	X
ejpam-5281	21	10	13	13	NUM
ejpam-5281	21	11	]	]	PUNCT
ejpam-5281	21	12	with	with	ADP
ejpam-5281	21	13	the	the	DET
ejpam-5281	21	14	following	follow	VERB
ejpam-5281	21	15	sharp	sharp	ADJ
ejpam-5281	21	16	result	result	NOUN
ejpam-5281	21	17	:	:	PUNCT
ejpam-5281	21	18	if	if	SCONJ
ejpam-5281	21	19	f	f	PROPN
ejpam-5281	21	20	=	=	PUNCT
ejpam-5281	21	21	u+	u+	NUM
ejpam-5281	21	22	iv	iv	NUM
ejpam-5281	21	23	∈	∈	PROPN
ejpam-5281	21	24	hp	hp	NOUN
ejpam-5281	21	25	and	and	CCONJ
ejpam-5281	21	26	v(0	v(0	NOUN
ejpam-5281	21	27	)	)	PUNCT
ejpam-5281	21	28	=	=	SYM
ejpam-5281	22	1	0	0	NUM
ejpam-5281	22	2	,	,	PUNCT
ejpam-5281	22	3	then	then	ADV
ejpam-5281	22	4	1	1	NUM
ejpam-5281	22	5	cos	cos	ADP
ejpam-5281	22	6	π	π	PROPN
ejpam-5281	22	7	2p	2p	NUM
ejpam-5281	22	8	||v||p	||v||p	PROPN
ejpam-5281	22	9	≤	≤	PUNCT
ejpam-5281	22	10	||f	||f	NOUN
ejpam-5281	22	11	||p	||p	NOUN
ejpam-5281	22	12	≤	≤	NOUN
ejpam-5281	22	13	1	1	NUM
ejpam-5281	22	14	sin	sin	NOUN
ejpam-5281	22	15	π	π	NOUN
ejpam-5281	22	16	2p	2p	NOUN
ejpam-5281	22	17	||u||p	||u||p	PROPN
ejpam-5281	22	18	.	.	PUNCT
ejpam-5281	23	1	some	some	DET
ejpam-5281	23	2	other	other	ADJ
ejpam-5281	23	3	results	result	NOUN
ejpam-5281	23	4	for	for	ADP
ejpam-5281	23	5	this	this	DET
ejpam-5281	23	6	constant	constant	ADJ
ejpam-5281	23	7	are	be	AUX
ejpam-5281	23	8	obtained	obtain	VERB
ejpam-5281	23	9	by	by	ADP
ejpam-5281	23	10	kalaj	kalaj	NOUN
ejpam-5281	23	11	in	in	ADP
ejpam-5281	23	12	[	[	X
ejpam-5281	23	13	9	9	NUM
ejpam-5281	23	14	]	]	PUNCT
ejpam-5281	23	15	,	,	PUNCT
ejpam-5281	23	16	for	for	ADP
ejpam-5281	23	17	harmonic	harmonic	ADJ
ejpam-5281	23	18	functions	function	NOUN
ejpam-5281	23	19	with	with	ADP
ejpam-5281	23	20	constant	constant	ADJ
ejpam-5281	23	21	ap	ap	NOUN
ejpam-5281	23	22	=	=	PUNCT
ejpam-5281	23	23	(	(	PUNCT
ejpam-5281	23	24	1−	1−	NUM
ejpam-5281	23	25	|	|	ADV
ejpam-5281	23	26	cos	cos	PROPN
ejpam-5281	23	27	π	π	PROPN
ejpam-5281	23	28	2p	2p	NUM
ejpam-5281	24	1	|	|	ADV
ejpam-5281	24	2	)	)	PUNCT
ejpam-5281	24	3	−	−	PROPN
ejpam-5281	25	1	1	1	NUM
ejpam-5281	25	2	2	2	NUM
ejpam-5281	25	3	.	.	PUNCT
ejpam-5281	26	1	also	also	ADV
ejpam-5281	26	2	,	,	PUNCT
ejpam-5281	26	3	this	this	DET
ejpam-5281	26	4	inequality	inequality	NOUN
ejpam-5281	26	5	was	be	AUX
ejpam-5281	26	6	generalized	generalize	VERB
ejpam-5281	26	7	in	in	ADP
ejpam-5281	26	8	several	several	ADJ
ejpam-5281	26	9	directions	direction	NOUN
ejpam-5281	26	10	.	.	PUNCT
ejpam-5281	27	1	let	let	VERB
ejpam-5281	27	2	us	we	PRON
ejpam-5281	27	3	mention	mention	VERB
ejpam-5281	27	4	beckenbach	beckenbach	NOUN
ejpam-5281	27	5	’s	’s	PART
ejpam-5281	27	6	results	result	NOUN
ejpam-5281	27	7	:	:	PUNCT
ejpam-5281	27	8	the	the	DET
ejpam-5281	27	9	same	same	ADJ
ejpam-5281	27	10	inequality	inequality	NOUN
ejpam-5281	27	11	holds	hold	VERB
ejpam-5281	27	12	where	where	SCONJ
ejpam-5281	27	13	in	in	ADP
ejpam-5281	27	14	place	place	NOUN
ejpam-5281	27	15	of	of	ADP
ejpam-5281	27	16	|f	|f	PROPN
ejpam-5281	27	17	|p	|p	X
ejpam-5281	27	18	we	we	PRON
ejpam-5281	27	19	have	have	VERB
ejpam-5281	27	20	a	a	DET
ejpam-5281	27	21	positive	positive	ADJ
ejpam-5281	27	22	logarithmically	logarithmically	ADV
ejpam-5281	27	23	subharmonic	subharmonic	ADJ
ejpam-5281	27	24	function	function	NOUN
ejpam-5281	27	25	.	.	PUNCT
ejpam-5281	28	1	this	this	DET
ejpam-5281	28	2	kind	kind	NOUN
ejpam-5281	28	3	of	of	ADP
ejpam-5281	28	4	generalizations	generalization	NOUN
ejpam-5281	28	5	can	can	AUX
ejpam-5281	28	6	be	be	AUX
ejpam-5281	28	7	found	find	VERB
ejpam-5281	28	8	in	in	ADP
ejpam-5281	28	9	[	[	X
ejpam-5281	28	10	1	1	NUM
ejpam-5281	28	11	]	]	PUNCT
ejpam-5281	28	12	.	.	PUNCT
ejpam-5281	29	1	we	we	PRON
ejpam-5281	29	2	refer	refer	VERB
ejpam-5281	29	3	interested	interested	ADJ
ejpam-5281	29	4	readers	reader	NOUN
ejpam-5281	29	5	to	to	ADP
ejpam-5281	29	6	[	[	X
ejpam-5281	29	7	2	2	NUM
ejpam-5281	29	8	]	]	PUNCT
ejpam-5281	29	9	,	,	PUNCT
ejpam-5281	29	10	[	[	X
ejpam-5281	29	11	3	3	NUM
ejpam-5281	29	12	]	]	PUNCT
ejpam-5281	29	13	and	and	CCONJ
ejpam-5281	29	14	[	[	X
ejpam-5281	29	15	9	9	NUM
ejpam-5281	29	16	]	]	PUNCT
ejpam-5281	29	17	.	.	PUNCT
ejpam-5281	30	1	our	our	PRON
ejpam-5281	30	2	aim	aim	NOUN
ejpam-5281	30	3	in	in	ADP
ejpam-5281	30	4	this	this	DET
ejpam-5281	30	5	paper	paper	NOUN
ejpam-5281	30	6	is	be	AUX
ejpam-5281	30	7	to	to	PART
ejpam-5281	30	8	find	find	VERB
ejpam-5281	30	9	similar	similar	ADJ
ejpam-5281	30	10	sharp	sharp	ADJ
ejpam-5281	30	11	constant	constant	ADJ
ejpam-5281	30	12	but	but	CCONJ
ejpam-5281	30	13	for	for	ADP
ejpam-5281	30	14	specific	specific	ADJ
ejpam-5281	30	15	class	class	NOUN
ejpam-5281	30	16	of	of	ADP
ejpam-5281	30	17	function	function	NOUN
ejpam-5281	30	18	quasiregular	quasiregular	ADJ
ejpam-5281	30	19	mapping	mapping	NOUN
ejpam-5281	30	20	.	.	PUNCT
ejpam-5281	31	1	in	in	ADP
ejpam-5281	31	2	case	case	NOUN
ejpam-5281	31	3	of	of	ADP
ejpam-5281	31	4	planar	planar	ADJ
ejpam-5281	31	5	harmonic	harmonic	ADJ
ejpam-5281	31	6	k	k	ADJ
ejpam-5281	31	7	-	-	ADJ
ejpam-5281	31	8	quasiregular	quasiregular	ADJ
ejpam-5281	31	9	mappings	mapping	NOUN
ejpam-5281	31	10	it	it	PRON
ejpam-5281	31	11	is	be	AUX
ejpam-5281	31	12	defined	define	VERB
ejpam-5281	31	13	as	as	ADP
ejpam-5281	31	14	below	below	ADV
ejpam-5281	31	15	.	.	PUNCT
ejpam-5281	32	1	given	give	VERB
ejpam-5281	32	2	k	k	PROPN
ejpam-5281	32	3	≥	≥	PROPN
ejpam-5281	32	4	0	0	NUM
ejpam-5281	32	5	,	,	PUNCT
ejpam-5281	32	6	a	a	DET
ejpam-5281	32	7	sense	sense	NOUN
ejpam-5281	32	8	-	-	PUNCT
ejpam-5281	32	9	preserving	preserve	VERB
ejpam-5281	32	10	harmonic	harmonic	ADJ
ejpam-5281	32	11	function	function	NOUN
ejpam-5281	32	12	f	f	NOUN
ejpam-5281	32	13	=	=	SYM
ejpam-5281	32	14	h	h	PROPN
ejpam-5281	33	1	+	+	CCONJ
ejpam-5281	33	2	g	g	NOUN
ejpam-5281	33	3	in	in	ADP
ejpam-5281	33	4	u	u	NOUN
ejpam-5281	33	5	is	be	AUX
ejpam-5281	33	6	said	say	VERB
ejpam-5281	33	7	to	to	PART
ejpam-5281	33	8	be	be	AUX
ejpam-5281	33	9	k	k	NOUN
ejpam-5281	33	10	-	-	ADJ
ejpam-5281	33	11	quasiregular	quasiregular	ADJ
ejpam-5281	33	12	if	if	SCONJ
ejpam-5281	33	13	and	and	CCONJ
ejpam-5281	33	14	only	only	ADV
ejpam-5281	33	15	if	if	SCONJ
ejpam-5281	33	16	||µ||∞	||µ||∞	NOUN
ejpam-5281	33	17	=	=	SYM
ejpam-5281	33	18	sup	sup	NOUN
ejpam-5281	33	19	|g′(z)|	|g′(z)|	NOUN
ejpam-5281	33	20	|h′(z)|	|h′(z)|	PRON
ejpam-5281	33	21	≤	≤	NOUN
ejpam-5281	33	22	k	k	X
ejpam-5281	33	23	<	<	X
ejpam-5281	33	24	1	1	NUM
ejpam-5281	33	25	,	,	PUNCT
ejpam-5281	33	26	where	where	SCONJ
ejpam-5281	33	27	k	k	PROPN
ejpam-5281	33	28	=	=	PROPN
ejpam-5281	33	29	k−1	k−1	PROPN
ejpam-5281	33	30	k+1	k+1	X
ejpam-5281	33	31	.	.	PUNCT
ejpam-5281	34	1	another	another	DET
ejpam-5281	34	2	definition	definition	NOUN
ejpam-5281	34	3	of	of	ADP
ejpam-5281	34	4	quasiregular	quasiregular	ADJ
ejpam-5281	34	5	mappings	mapping	NOUN
ejpam-5281	34	6	in	in	ADP
ejpam-5281	34	7	domain	domain	NOUN
ejpam-5281	34	8	of	of	ADP
ejpam-5281	34	9	rn	rn	PROPN
ejpam-5281	34	10	is	be	AUX
ejpam-5281	34	11	given	give	VERB
ejpam-5281	34	12	in	in	ADP
ejpam-5281	34	13	[	[	NOUN
ejpam-5281	34	14	14	14	NUM
ejpam-5281	34	15	]	]	PUNCT
ejpam-5281	34	16	as	as	SCONJ
ejpam-5281	34	17	follows	follow	VERB
ejpam-5281	34	18	:	:	PUNCT
ejpam-5281	34	19	let	let	VERB
ejpam-5281	34	20	a	a	PRON
ejpam-5281	34	21	⊂	⊂	X
ejpam-5281	34	22	rn	rn	PROPN
ejpam-5281	34	23	be	be	AUX
ejpam-5281	34	24	a	a	DET
ejpam-5281	34	25	domain	domain	NOUN
ejpam-5281	34	26	,	,	PUNCT
ejpam-5281	34	27	and	and	CCONJ
ejpam-5281	34	28	let	let	VERB
ejpam-5281	34	29	n	n	PRON
ejpam-5281	34	30	≥	≥	NOUN
ejpam-5281	34	31	2	2	NUM
ejpam-5281	34	32	.	.	PUNCT
ejpam-5281	35	1	a	a	DET
ejpam-5281	35	2	mapping	mapping	NOUN
ejpam-5281	35	3	f	f	NOUN
ejpam-5281	35	4	:	:	PUNCT
ejpam-5281	35	5	a	a	DET
ejpam-5281	35	6	→	→	SYM
ejpam-5281	35	7	rn	rn	PROPN
ejpam-5281	35	8	is	be	AUX
ejpam-5281	35	9	said	say	VERB
ejpam-5281	35	10	to	to	PART
ejpam-5281	35	11	be	be	AUX
ejpam-5281	35	12	quasiregular	quasiregular	ADJ
ejpam-5281	35	13	,	,	PUNCT
ejpam-5281	35	14	if	if	SCONJ
ejpam-5281	35	15	satisfy	satisfy	VERB
ejpam-5281	35	16	next	next	ADJ
ejpam-5281	35	17	two	two	NUM
ejpam-5281	35	18	conditions	condition	NOUN
ejpam-5281	35	19	:	:	PUNCT
ejpam-5281	35	20	(	(	PUNCT
ejpam-5281	35	21	a	a	X
ejpam-5281	35	22	)	)	PUNCT
ejpam-5281	35	23	f	f	NOUN
ejpam-5281	35	24	is	be	AUX
ejpam-5281	35	25	an	an	DET
ejpam-5281	35	26	absolutely	absolutely	ADV
ejpam-5281	35	27	continuous	continuous	ADJ
ejpam-5281	35	28	functions	function	NOUN
ejpam-5281	35	29	in	in	ADP
ejpam-5281	35	30	every	every	DET
ejpam-5281	35	31	line	line	NOUN
ejpam-5281	35	32	segment	segment	NOUN
ejpam-5281	35	33	parallel	parallel	NOUN
ejpam-5281	35	34	to	to	ADP
ejpam-5281	35	35	the	the	DET
ejpam-5281	35	36	coordinate	coordinate	NOUN
ejpam-5281	35	37	axis	axis	NOUN
ejpam-5281	35	38	and	and	CCONJ
ejpam-5281	35	39	there	there	PRON
ejpam-5281	35	40	exists	exist	VERB
ejpam-5281	35	41	partial	partial	ADJ
ejpam-5281	35	42	derivatives	derivative	NOUN
ejpam-5281	35	43	which	which	PRON
ejpam-5281	35	44	are	be	AUX
ejpam-5281	35	45	locally	locally	ADV
ejpam-5281	35	46	ln	ln	ADJ
ejpam-5281	35	47	integrable	integrable	ADJ
ejpam-5281	35	48	functions	function	NOUN
ejpam-5281	35	49	on	on	ADP
ejpam-5281	35	50	a.	a.	NOUN
ejpam-5281	35	51	(	(	PUNCT
ejpam-5281	35	52	b	b	X
ejpam-5281	35	53	)	)	PUNCT
ejpam-5281	35	54	there	there	PRON
ejpam-5281	35	55	exists	exist	VERB
ejpam-5281	35	56	a	a	DET
ejpam-5281	35	57	constant	constant	ADJ
ejpam-5281	35	58	k	k	X
ejpam-5281	35	59	≥	≥	NUM
ejpam-5281	35	60	1	1	NUM
ejpam-5281	35	61	such	such	ADJ
ejpam-5281	35	62	that	that	SCONJ
ejpam-5281	35	63	,	,	PUNCT
ejpam-5281	35	64	a.e	a.e	PROPN
ejpam-5281	35	65	.	.	PROPN
ejpam-5281	35	66	in	in	ADP
ejpam-5281	35	67	a	a	DET
ejpam-5281	35	68	,	,	PUNCT
ejpam-5281	35	69	lf	lf	INTJ
ejpam-5281	35	70	(	(	PUNCT
ejpam-5281	35	71	x	x	NOUN
ejpam-5281	35	72	)	)	PUNCT
ejpam-5281	35	73	n	n	PRON
ejpam-5281	35	74	≤	≤	NOUN
ejpam-5281	35	75	kjf	kjf	NOUN
ejpam-5281	35	76	(	(	PUNCT
ejpam-5281	35	77	x	x	NOUN
ejpam-5281	35	78	)	)	PUNCT
ejpam-5281	35	79	,	,	PUNCT
ejpam-5281	35	80	e.	e.	PROPN
ejpam-5281	35	81	bajrami	bajrami	PROPN
ejpam-5281	35	82	/	/	SYM
ejpam-5281	35	83	eur	eur	PROPN
ejpam-5281	35	84	.	.	PUNCT
ejpam-5281	36	1	j.	j.	PROPN
ejpam-5281	36	2	pure	pure	PROPN
ejpam-5281	36	3	appl	appl	PROPN
ejpam-5281	36	4	.	.	PROPN
ejpam-5281	36	5	math	math	PROPN
ejpam-5281	36	6	,	,	PUNCT
ejpam-5281	36	7	17	17	NUM
ejpam-5281	36	8	(	(	PUNCT
ejpam-5281	36	9	3	3	NUM
ejpam-5281	36	10	)	)	PUNCT
ejpam-5281	36	11	(	(	PUNCT
ejpam-5281	36	12	2024	2024	NUM
ejpam-5281	36	13	)	)	PUNCT
ejpam-5281	36	14	,	,	PUNCT
ejpam-5281	36	15	1490	1490	NUM
ejpam-5281	36	16	-	-	SYM
ejpam-5281	36	17	1496	1496	NUM
ejpam-5281	36	18	1492	1492	NUM
ejpam-5281	36	19	where	where	SCONJ
ejpam-5281	36	20	lf	lf	ADP
ejpam-5281	36	21	(	(	PUNCT
ejpam-5281	36	22	x	x	X
ejpam-5281	36	23	)	)	PUNCT
ejpam-5281	36	24	is	be	AUX
ejpam-5281	36	25	the	the	DET
ejpam-5281	36	26	maximum	maximum	ADJ
ejpam-5281	36	27	stretching	stretching	NOUN
ejpam-5281	36	28	for	for	ADP
ejpam-5281	36	29	f	f	PROPN
ejpam-5281	36	30	at	at	ADP
ejpam-5281	36	31	the	the	DET
ejpam-5281	36	32	point	point	NOUN
ejpam-5281	37	1	x	x	SYM
ejpam-5281	37	2	,	,	PUNCT
ejpam-5281	37	3	i.e.	i.e.	X
ejpam-5281	37	4	,	,	PUNCT
ejpam-5281	37	5	lf	lf	ADP
ejpam-5281	37	6	(	(	PUNCT
ejpam-5281	37	7	x	x	NOUN
ejpam-5281	37	8	)	)	PUNCT
ejpam-5281	37	9	=	=	SYM
ejpam-5281	38	1	lim	lim	PROPN
ejpam-5281	38	2	y→x	y→x	PROPN
ejpam-5281	38	3	sup	sup	PROPN
ejpam-5281	38	4	|f(y)−	|f(y)−	NOUN
ejpam-5281	38	5	f(x)|	f(x)|	VERB
ejpam-5281	38	6	|y	|y	NOUN
ejpam-5281	38	7	−	−	PROPN
ejpam-5281	38	8	x|	x|	NOUN
ejpam-5281	38	9	,	,	PUNCT
ejpam-5281	38	10	and	and	CCONJ
ejpam-5281	38	11	jf	jf	PROPN
ejpam-5281	38	12	denotes	denote	VERB
ejpam-5281	38	13	the	the	DET
ejpam-5281	38	14	jacobian	jacobian	ADJ
ejpam-5281	38	15	determinant	determinant	ADJ
ejpam-5281	38	16	.	.	PUNCT
ejpam-5281	39	1	the	the	DET
ejpam-5281	39	2	smallest	small	ADJ
ejpam-5281	39	3	constant	constant	ADJ
ejpam-5281	39	4	k	k	PROPN
ejpam-5281	39	5	≤	≤	ADJ
ejpam-5281	39	6	1	1	NUM
ejpam-5281	39	7	in	in	ADP
ejpam-5281	39	8	above	above	ADP
ejpam-5281	39	9	definition	definition	NOUN
ejpam-5281	39	10	is	be	AUX
ejpam-5281	39	11	called	call	VERB
ejpam-5281	39	12	the	the	DET
ejpam-5281	39	13	outer	outer	ADJ
ejpam-5281	39	14	dilatation	dilatation	NOUN
ejpam-5281	39	15	of	of	ADP
ejpam-5281	39	16	f	f	PROPN
ejpam-5281	39	17	and	and	CCONJ
ejpam-5281	39	18	denote	denote	VERB
ejpam-5281	39	19	by	by	ADP
ejpam-5281	39	20	ko(f	ko(f	NOUN
ejpam-5281	39	21	)	)	PUNCT
ejpam-5281	39	22	.	.	PUNCT
ejpam-5281	40	1	also	also	ADV
ejpam-5281	40	2	for	for	ADP
ejpam-5281	40	3	quasiregular	quasiregular	ADJ
ejpam-5281	40	4	function	function	NOUN
ejpam-5281	40	5	f	f	PROPN
ejpam-5281	40	6	,	,	PUNCT
ejpam-5281	40	7	the	the	DET
ejpam-5281	40	8	smallest	small	ADJ
ejpam-5281	40	9	constant	constant	ADJ
ejpam-5281	40	10	k	k	PROPN
ejpam-5281	40	11	≤	≤	NUM
ejpam-5281	40	12	1	1	NUM
ejpam-5281	40	13	,	,	PUNCT
ejpam-5281	40	14	for	for	ADP
ejpam-5281	40	15	which	which	PRON
ejpam-5281	40	16	the	the	DET
ejpam-5281	40	17	inequality	inequality	NOUN
ejpam-5281	40	18	jf	jf	PROPN
ejpam-5281	40	19	(	(	PUNCT
ejpam-5281	40	20	x	x	NOUN
ejpam-5281	40	21	)	)	PUNCT
ejpam-5281	40	22	≤	≤	ADJ
ejpam-5281	40	23	klf	klf	NOUN
ejpam-5281	40	24	(	(	PUNCT
ejpam-5281	40	25	x	x	NOUN
ejpam-5281	40	26	)	)	PUNCT
ejpam-5281	40	27	n	n	CCONJ
ejpam-5281	40	28	,	,	PUNCT
ejpam-5281	40	29	where	where	SCONJ
ejpam-5281	40	30	lf	lf	INTJ
ejpam-5281	40	31	(	(	PUNCT
ejpam-5281	40	32	x	x	NOUN
ejpam-5281	40	33	)	)	PUNCT
ejpam-5281	40	34	=	=	SYM
ejpam-5281	40	35	min{|f	min{|f	PROPN
ejpam-5281	40	36	′(x)h|	′(x)h|	NOUN
ejpam-5281	40	37	:	:	PUNCT
ejpam-5281	40	38	|h|	|h|	NOUN
ejpam-5281	40	39	=	=	SYM
ejpam-5281	40	40	1	1	NUM
ejpam-5281	40	41	}	}	PUNCT
ejpam-5281	40	42	,	,	PUNCT
ejpam-5281	40	43	holds	hold	VERB
ejpam-5281	40	44	(	(	PUNCT
ejpam-5281	40	45	in	in	ADP
ejpam-5281	40	46	a	a	PRON
ejpam-5281	40	47	)	)	PUNCT
ejpam-5281	40	48	,	,	PUNCT
ejpam-5281	40	49	is	be	AUX
ejpam-5281	40	50	called	call	VERB
ejpam-5281	40	51	the	the	DET
ejpam-5281	40	52	inner	inner	ADJ
ejpam-5281	40	53	dilation	dilation	NOUN
ejpam-5281	40	54	of	of	ADP
ejpam-5281	40	55	f	f	PROPN
ejpam-5281	40	56	and	and	CCONJ
ejpam-5281	40	57	denoted	denote	VERB
ejpam-5281	40	58	by	by	ADP
ejpam-5281	40	59	ki(f	ki(f	NOUN
ejpam-5281	40	60	)	)	PUNCT
ejpam-5281	40	61	.	.	PUNCT
ejpam-5281	41	1	the	the	DET
ejpam-5281	41	2	maximal	maximal	ADJ
ejpam-5281	41	3	dilation	dilation	NOUN
ejpam-5281	41	4	of	of	ADP
ejpam-5281	41	5	f	f	PROPN
ejpam-5281	41	6	is	be	AUX
ejpam-5281	41	7	the	the	DET
ejpam-5281	41	8	number	number	NOUN
ejpam-5281	41	9	k(f	k(f	PROPN
ejpam-5281	41	10	)	)	PUNCT
ejpam-5281	42	1	=	=	SYM
ejpam-5281	42	2	max{ki(f),ko(f	max{ki(f),ko(f	NOUN
ejpam-5281	42	3	)	)	PUNCT
ejpam-5281	42	4	}	}	PUNCT
ejpam-5281	42	5	.	.	PUNCT
ejpam-5281	43	1	if	if	SCONJ
ejpam-5281	43	2	k(f	k(f	PROPN
ejpam-5281	43	3	)	)	PUNCT
ejpam-5281	43	4	≤	≤	PUNCT
ejpam-5281	44	1	k	k	PROPN
ejpam-5281	44	2	,	,	PUNCT
ejpam-5281	44	3	then	then	ADV
ejpam-5281	44	4	f	f	PROPN
ejpam-5281	44	5	is	be	AUX
ejpam-5281	44	6	said	say	VERB
ejpam-5281	44	7	to	to	PART
ejpam-5281	44	8	be	be	AUX
ejpam-5281	44	9	k	k	NOUN
ejpam-5281	44	10	-	-	NOUN
ejpam-5281	44	11	quasiregular	quasiregular	NOUN
ejpam-5281	44	12	.	.	PUNCT
ejpam-5281	45	1	if	if	SCONJ
ejpam-5281	45	2	f	f	PROPN
ejpam-5281	45	3	is	be	AUX
ejpam-5281	45	4	not	not	PART
ejpam-5281	45	5	quasiregular	quasiregular	ADJ
ejpam-5281	45	6	,	,	PUNCT
ejpam-5281	45	7	we	we	PRON
ejpam-5281	45	8	set	set	VERB
ejpam-5281	45	9	k(f	k(f	PROPN
ejpam-5281	45	10	)	)	PUNCT
ejpam-5281	45	11	=	=	SYM
ejpam-5281	45	12	ki(f	ki(f	X
ejpam-5281	45	13	)	)	PUNCT
ejpam-5281	45	14	=	=	SYM
ejpam-5281	45	15	ko(f	ko(f	NOUN
ejpam-5281	45	16	)	)	PUNCT
ejpam-5281	45	17	=	=	SYM
ejpam-5281	45	18	∞.	∞.	PROPN
ejpam-5281	45	19	for	for	ADP
ejpam-5281	45	20	a	a	DET
ejpam-5281	45	21	function	function	NOUN
ejpam-5281	45	22	f	f	PROPN
ejpam-5281	45	23	∈	∈	PROPN
ejpam-5281	45	24	u	u	PROPN
ejpam-5281	45	25	,	,	PUNCT
ejpam-5281	45	26	the	the	DET
ejpam-5281	45	27	norm	norm	NOUN
ejpam-5281	45	28	in	in	ADP
ejpam-5281	45	29	class	class	NOUN
ejpam-5281	45	30	hp	hp	NOUN
ejpam-5281	45	31	is	be	AUX
ejpam-5281	45	32	provided	provide	VERB
ejpam-5281	45	33	by	by	ADP
ejpam-5281	45	34	:	:	PUNCT
ejpam-5281	45	35	||f	||f	NOUN
ejpam-5281	45	36	||p	||p	NOUN
ejpam-5281	45	37	=	=	SYM
ejpam-5281	45	38	||f	||f	NOUN
ejpam-5281	45	39	||hp	||hp	NUM
ejpam-5281	45	40	=	=	NOUN
ejpam-5281	45	41	sup	sup	NOUN
ejpam-5281	45	42	0	0	NUM
ejpam-5281	45	43	<	<	NOUN
ejpam-5281	45	44	r<1	r<1	NOUN
ejpam-5281	45	45	mp(r	mp(r	NOUN
ejpam-5281	45	46	,	,	PUNCT
ejpam-5281	45	47	f	f	NOUN
ejpam-5281	45	48	)	)	PUNCT
ejpam-5281	45	49	.	.	PUNCT
ejpam-5281	46	1	for	for	ADP
ejpam-5281	46	2	a	a	DET
ejpam-5281	46	3	more	more	ADV
ejpam-5281	46	4	detailed	detailed	ADJ
ejpam-5281	46	5	observation	observation	NOUN
ejpam-5281	46	6	of	of	ADP
ejpam-5281	46	7	quasiregular	quasiregular	ADJ
ejpam-5281	46	8	mappings	mapping	NOUN
ejpam-5281	46	9	we	we	PRON
ejpam-5281	46	10	refer	refer	VERB
ejpam-5281	46	11	to	to	ADP
ejpam-5281	46	12	[	[	X
ejpam-5281	46	13	8	8	NUM
ejpam-5281	46	14	]	]	PUNCT
ejpam-5281	46	15	,	,	PUNCT
ejpam-5281	46	16	[	[	X
ejpam-5281	46	17	11	11	NUM
ejpam-5281	46	18	]	]	PUNCT
ejpam-5281	46	19	and	and	CCONJ
ejpam-5281	46	20	[	[	X
ejpam-5281	46	21	14	14	NUM
ejpam-5281	46	22	]	]	PUNCT
ejpam-5281	46	23	.	.	PUNCT
ejpam-5281	47	1	similar	similar	ADJ
ejpam-5281	47	2	results	result	NOUN
ejpam-5281	47	3	about	about	ADP
ejpam-5281	47	4	riesz	riesz	NOUN
ejpam-5281	47	5	theorem	theorem	VERB
ejpam-5281	47	6	in	in	ADP
ejpam-5281	47	7	class	class	NOUN
ejpam-5281	47	8	of	of	ADP
ejpam-5281	47	9	quasiregular	quasiregular	ADJ
ejpam-5281	47	10	functions	function	NOUN
ejpam-5281	47	11	,	,	PUNCT
ejpam-5281	47	12	also	also	ADV
ejpam-5281	47	13	are	be	AUX
ejpam-5281	47	14	proved	prove	VERB
ejpam-5281	47	15	by	by	ADP
ejpam-5281	47	16	j.	j.	PROPN
ejpam-5281	47	17	li	li	PROPN
ejpam-5281	47	18	and	and	CCONJ
ejpam-5281	47	19	j.	j.	PROPN
ejpam-5281	47	20	zhu	zhu	PROPN
ejpam-5281	47	21	,	,	PUNCT
ejpam-5281	47	22	in	in	ADP
ejpam-5281	47	23	[	[	X
ejpam-5281	47	24	7	7	NUM
ejpam-5281	47	25	]	]	PUNCT
ejpam-5281	47	26	,	,	PUNCT
ejpam-5281	47	27	but	but	CCONJ
ejpam-5281	47	28	there	there	PRON
ejpam-5281	47	29	are	be	VERB
ejpam-5281	47	30	used	use	VERB
ejpam-5281	47	31	additional	additional	ADJ
ejpam-5281	47	32	conditions	condition	NOUN
ejpam-5281	47	33	about	about	ADP
ejpam-5281	47	34	functions	function	NOUN
ejpam-5281	47	35	u	u	NOUN
ejpam-5281	47	36	and	and	CCONJ
ejpam-5281	47	37	v.	v.	CCONJ
ejpam-5281	47	38	they	they	PRON
ejpam-5281	47	39	generalize	generalize	VERB
ejpam-5281	47	40	this	this	DET
ejpam-5281	47	41	theorem	theorem	NOUN
ejpam-5281	47	42	for	for	ADP
ejpam-5281	47	43	planar	planar	ADJ
ejpam-5281	47	44	harmonic	harmonic	ADJ
ejpam-5281	47	45	k	k	ADJ
ejpam-5281	47	46	-	-	ADJ
ejpam-5281	47	47	quasiregular	quasiregular	ADJ
ejpam-5281	47	48	mappings	mapping	NOUN
ejpam-5281	47	49	(	(	PUNCT
ejpam-5281	47	50	1	1	NUM
ejpam-5281	47	51	<	<	X
ejpam-5281	47	52	p	p	X
ejpam-5281	47	53	≤	≤	NUM
ejpam-5281	47	54	2	2	NUM
ejpam-5281	47	55	)	)	PUNCT
ejpam-5281	47	56	provided	provide	VERB
ejpam-5281	47	57	that	that	SCONJ
ejpam-5281	47	58	the	the	DET
ejpam-5281	47	59	real	real	ADJ
ejpam-5281	47	60	part	part	NOUN
ejpam-5281	47	61	does	do	AUX
ejpam-5281	47	62	not	not	PART
ejpam-5281	47	63	vanish	vanish	VERB
ejpam-5281	47	64	at	at	ADP
ejpam-5281	47	65	the	the	DET
ejpam-5281	47	66	unit	unit	NOUN
ejpam-5281	47	67	disk	disk	NOUN
ejpam-5281	47	68	.	.	PUNCT
ejpam-5281	48	1	moreover	moreover	ADV
ejpam-5281	48	2	,	,	PUNCT
ejpam-5281	48	3	they	they	PRON
ejpam-5281	48	4	extended	extend	VERB
ejpam-5281	48	5	this	this	DET
ejpam-5281	48	6	results	result	NOUN
ejpam-5281	48	7	for	for	ADP
ejpam-5281	48	8	invariant	invariant	ADJ
ejpam-5281	48	9	harmonic	harmonic	ADJ
ejpam-5281	48	10	quasiconformal	quasiconformal	ADJ
ejpam-5281	48	11	mappings	mapping	NOUN
ejpam-5281	48	12	in	in	ADP
ejpam-5281	48	13	the	the	DET
ejpam-5281	48	14	unit	unit	NOUN
ejpam-5281	48	15	ball	ball	NOUN
ejpam-5281	48	16	assuming	assume	VERB
ejpam-5281	48	17	that	that	SCONJ
ejpam-5281	48	18	the	the	DET
ejpam-5281	48	19	first	first	ADJ
ejpam-5281	48	20	coordinate	coordinate	NOUN
ejpam-5281	48	21	in	in	ADP
ejpam-5281	48	22	non	non	ADJ
ejpam-5281	48	23	-	-	ADJ
ejpam-5281	48	24	vanishing	vanishing	ADJ
ejpam-5281	48	25	.	.	PUNCT
ejpam-5281	49	1	in	in	ADP
ejpam-5281	49	2	this	this	DET
ejpam-5281	49	3	paper	paper	NOUN
ejpam-5281	49	4	,	,	PUNCT
ejpam-5281	49	5	using	use	VERB
ejpam-5281	49	6	different	different	ADJ
ejpam-5281	49	7	methods	method	NOUN
ejpam-5281	49	8	,	,	PUNCT
ejpam-5281	49	9	we	we	PRON
ejpam-5281	49	10	find	find	VERB
ejpam-5281	49	11	similar	similar	ADJ
ejpam-5281	49	12	constant	constant	ADJ
ejpam-5281	49	13	as	as	ADP
ejpam-5281	49	14	in	in	ADP
ejpam-5281	49	15	[	[	X
ejpam-5281	49	16	7	7	NUM
ejpam-5281	49	17	]	]	PUNCT
ejpam-5281	49	18	,	,	PUNCT
ejpam-5281	49	19	but	but	CCONJ
ejpam-5281	49	20	without	without	ADP
ejpam-5281	49	21	restriction	restriction	NOUN
ejpam-5281	49	22	about	about	ADP
ejpam-5281	49	23	conditions	condition	NOUN
ejpam-5281	49	24	of	of	ADP
ejpam-5281	49	25	functions	function	NOUN
ejpam-5281	49	26	u	u	NOUN
ejpam-5281	49	27	and	and	CCONJ
ejpam-5281	49	28	v.	v.	ADP
ejpam-5281	49	29	these	these	DET
ejpam-5281	49	30	results	result	NOUN
ejpam-5281	49	31	are	be	AUX
ejpam-5281	49	32	given	give	VERB
ejpam-5281	49	33	with	with	ADP
ejpam-5281	49	34	next	next	ADJ
ejpam-5281	49	35	theorem	theorem	PROPN
ejpam-5281	49	36	.	.	PUNCT
ejpam-5281	50	1	theorem	theorem	NOUN
ejpam-5281	50	2	1	1	NUM
ejpam-5281	50	3	.	.	PUNCT
ejpam-5281	51	1	if	if	SCONJ
ejpam-5281	51	2	f	f	PROPN
ejpam-5281	51	3	=	=	PRON
ejpam-5281	51	4	u+	u+	NUM
ejpam-5281	51	5	iv	iv	NUM
ejpam-5281	51	6	is	be	AUX
ejpam-5281	51	7	harmonic	harmonic	ADJ
ejpam-5281	51	8	k	k	NOUN
ejpam-5281	51	9	-	-	NOUN
ejpam-5281	51	10	quasiregular	quasiregular	ADJ
ejpam-5281	51	11	,	,	PUNCT
ejpam-5281	51	12	with	with	ADP
ejpam-5281	51	13	ℜf(0	ℜf(0	NOUN
ejpam-5281	51	14	)	)	PUNCT
ejpam-5281	52	1	=	=	SYM
ejpam-5281	52	2	0	0	NUM
ejpam-5281	52	3	,	,	PUNCT
ejpam-5281	52	4	then	then	ADV
ejpam-5281	52	5	∥u∥2	∥u∥2	VERB
ejpam-5281	52	6	≤	≤	PROPN
ejpam-5281	52	7	k∥v∥2	k∥v∥2	PROPN
ejpam-5281	52	8	,	,	PUNCT
ejpam-5281	52	9	and	and	CCONJ
ejpam-5281	52	10	the	the	DET
ejpam-5281	52	11	constant	constant	ADJ
ejpam-5281	52	12	k	k	PROPN
ejpam-5281	52	13	is	be	AUX
ejpam-5281	52	14	sharp	sharp	ADJ
ejpam-5281	52	15	.	.	PUNCT
ejpam-5281	53	1	the	the	DET
ejpam-5281	53	2	following	follow	VERB
ejpam-5281	53	3	results	result	NOUN
ejpam-5281	53	4	easily	easily	ADV
ejpam-5281	53	5	follows	follow	VERB
ejpam-5281	53	6	from	from	ADP
ejpam-5281	53	7	theorem	theorem	ADJ
ejpam-5281	53	8	1	1	NUM
ejpam-5281	53	9	.	.	PUNCT
ejpam-5281	53	10	corollary	corollary	ADJ
ejpam-5281	53	11	1	1	NUM
ejpam-5281	53	12	.	.	PUNCT
ejpam-5281	54	1	let	let	VERB
ejpam-5281	54	2	f	f	NOUN
ejpam-5281	54	3	=	=	PUNCT
ejpam-5281	54	4	h	h	PROPN
ejpam-5281	55	1	+	+	CCONJ
ejpam-5281	55	2	g	g	PROPN
ejpam-5281	55	3	be	be	VERB
ejpam-5281	55	4	k	k	NOUN
ejpam-5281	55	5	-	-	NOUN
ejpam-5281	55	6	quasiregular	quasiregular	ADJ
ejpam-5281	55	7	in	in	ADP
ejpam-5281	55	8	u.	u.	PROPN
ejpam-5281	55	9	if	if	SCONJ
ejpam-5281	55	10	u	u	PROPN
ejpam-5281	55	11	∈	∈	PROPN
ejpam-5281	55	12	h2	h2	NOUN
ejpam-5281	55	13	,	,	PUNCT
ejpam-5281	55	14	then	then	ADV
ejpam-5281	55	15	its	its	PRON
ejpam-5281	55	16	harmonic	harmonic	ADJ
ejpam-5281	55	17	conjugate	conjugate	NOUN
ejpam-5281	55	18	v	v	NOUN
ejpam-5281	55	19	is	be	AUX
ejpam-5281	55	20	also	also	ADV
ejpam-5281	55	21	of	of	ADP
ejpam-5281	55	22	class	class	NOUN
ejpam-5281	55	23	h2	h2	PROPN
ejpam-5281	55	24	.	.	PUNCT
ejpam-5281	56	1	based	base	VERB
ejpam-5281	56	2	on	on	ADP
ejpam-5281	56	3	theorem	theorem	ADJ
ejpam-5281	56	4	1	1	NUM
ejpam-5281	56	5	and	and	CCONJ
ejpam-5281	56	6	corollary	corollary	ADJ
ejpam-5281	56	7	1	1	NUM
ejpam-5281	56	8	,	,	PUNCT
ejpam-5281	56	9	we	we	PRON
ejpam-5281	56	10	can	can	AUX
ejpam-5281	56	11	prove	prove	VERB
ejpam-5281	56	12	next	next	ADJ
ejpam-5281	56	13	theorem	theorem	VERB
ejpam-5281	56	14	.	.	PUNCT
ejpam-5281	56	15	theorem	theorem	NOUN
ejpam-5281	56	16	2	2	NUM
ejpam-5281	56	17	.	.	PUNCT
ejpam-5281	57	1	let	let	VERB
ejpam-5281	57	2	f(z	f(z	NUM
ejpam-5281	57	3	)	)	PUNCT
ejpam-5281	57	4	=	=	SYM
ejpam-5281	57	5	h(z)+g(z	h(z)+g(z	NOUN
ejpam-5281	57	6	)	)	PUNCT
ejpam-5281	57	7	=	=	NOUN
ejpam-5281	58	1	∑∞	∑∞	NOUN
ejpam-5281	58	2	k=0	k=0	PUNCT
ejpam-5281	58	3	akz	akz	PROPN
ejpam-5281	58	4	k+	k+	NOUN
ejpam-5281	58	5	∑∞	∑∞	NOUN
ejpam-5281	58	6	k=1	k=1	X
ejpam-5281	58	7	bkz	bkz	AUX
ejpam-5281	58	8	k	k	PROPN
ejpam-5281	58	9	be	be	AUX
ejpam-5281	58	10	harmonic	harmonic	ADJ
ejpam-5281	58	11	k	k	NOUN
ejpam-5281	58	12	-	-	NOUN
ejpam-5281	58	13	quasiregular	quasiregular	ADJ
ejpam-5281	58	14	,	,	PUNCT
ejpam-5281	58	15	with	with	ADP
ejpam-5281	58	16	g(0	g(0	NOUN
ejpam-5281	58	17	)	)	PUNCT
ejpam-5281	58	18	=	=	SYM
ejpam-5281	58	19	0	0	X
ejpam-5281	58	20	.	.	PUNCT
ejpam-5281	59	1	if	if	SCONJ
ejpam-5281	59	2	f	f	PROPN
ejpam-5281	59	3	∈	∈	PROPN
ejpam-5281	59	4	h2	h2	NOUN
ejpam-5281	59	5	,	,	PUNCT
ejpam-5281	59	6	then	then	ADV
ejpam-5281	59	7	following	follow	VERB
ejpam-5281	59	8	sharp	sharp	ADJ
ejpam-5281	59	9	inequality	inequality	NOUN
ejpam-5281	59	10	holds	hold	VERB
ejpam-5281	59	11	||f	||f	NOUN
ejpam-5281	59	12	||2	||2	NOUN
ejpam-5281	59	13	≤	≤	NOUN
ejpam-5281	59	14	ck||h||2	ck||h||2	ADV
ejpam-5281	59	15	,	,	PUNCT
ejpam-5281	59	16	where	where	SCONJ
ejpam-5281	59	17	ck	ck	ADJ
ejpam-5281	59	18	=	=	SYM
ejpam-5281	59	19	1	1	NUM
ejpam-5281	59	20	+	+	CCONJ
ejpam-5281	59	21	k2	k2	PROPN
ejpam-5281	59	22	.	.	PUNCT
ejpam-5281	60	1	e.	e.	PROPN
ejpam-5281	60	2	bajrami	bajrami	PROPN
ejpam-5281	60	3	/	/	SYM
ejpam-5281	60	4	eur	eur	PROPN
ejpam-5281	60	5	.	.	PUNCT
ejpam-5281	61	1	j.	j.	PROPN
ejpam-5281	61	2	pure	pure	PROPN
ejpam-5281	61	3	appl	appl	PROPN
ejpam-5281	61	4	.	.	PROPN
ejpam-5281	61	5	math	math	PROPN
ejpam-5281	61	6	,	,	PUNCT
ejpam-5281	61	7	17	17	NUM
ejpam-5281	61	8	(	(	PUNCT
ejpam-5281	61	9	3	3	NUM
ejpam-5281	61	10	)	)	PUNCT
ejpam-5281	61	11	(	(	PUNCT
ejpam-5281	61	12	2024	2024	NUM
ejpam-5281	61	13	)	)	PUNCT
ejpam-5281	61	14	,	,	PUNCT
ejpam-5281	61	15	1490	1490	NUM
ejpam-5281	61	16	-	-	SYM
ejpam-5281	61	17	1496	1496	NUM
ejpam-5281	61	18	1493	1493	NUM
ejpam-5281	61	19	let	let	VERB
ejpam-5281	61	20	we	we	PRON
ejpam-5281	61	21	say	say	VERB
ejpam-5281	61	22	that	that	SCONJ
ejpam-5281	61	23	this	this	DET
ejpam-5281	61	24	results	result	NOUN
ejpam-5281	61	25	coincide	coincide	VERB
ejpam-5281	61	26	with	with	ADP
ejpam-5281	61	27	results	result	NOUN
ejpam-5281	61	28	in	in	ADP
ejpam-5281	61	29	theorem	theorem	NOUN
ejpam-5281	61	30	2	2	NUM
ejpam-5281	61	31	on	on	ADP
ejpam-5281	61	32	[	[	X
ejpam-5281	61	33	7	7	NUM
ejpam-5281	61	34	]	]	PUNCT
ejpam-5281	61	35	,	,	PUNCT
ejpam-5281	61	36	in	in	ADP
ejpam-5281	61	37	case	case	NOUN
ejpam-5281	61	38	of	of	ADP
ejpam-5281	61	39	n	n	NOUN
ejpam-5281	61	40	=	=	SYM
ejpam-5281	61	41	2	2	NUM
ejpam-5281	61	42	.	.	PUNCT
ejpam-5281	62	1	next	next	ADJ
ejpam-5281	62	2	theorem	theorem	NOUN
ejpam-5281	62	3	generalize	generalize	VERB
ejpam-5281	62	4	previous	previous	ADJ
ejpam-5281	62	5	theorem	theorem	PROPN
ejpam-5281	62	6	.	.	PUNCT
ejpam-5281	62	7	theorem	theorem	NOUN
ejpam-5281	62	8	3	3	X
ejpam-5281	62	9	.	.	PUNCT
ejpam-5281	63	1	let	let	VERB
ejpam-5281	63	2	f(z	f(z	NUM
ejpam-5281	63	3	)	)	PUNCT
ejpam-5281	63	4	=	=	SYM
ejpam-5281	63	5	h(z)+g(z	h(z)+g(z	NOUN
ejpam-5281	63	6	)	)	PUNCT
ejpam-5281	63	7	=	=	NOUN
ejpam-5281	64	1	∑∞	∑∞	NOUN
ejpam-5281	64	2	k=0	k=0	PUNCT
ejpam-5281	64	3	akz	akz	PROPN
ejpam-5281	64	4	k+	k+	NOUN
ejpam-5281	64	5	∑∞	∑∞	NOUN
ejpam-5281	64	6	k=1	k=1	X
ejpam-5281	64	7	bkz	bkz	AUX
ejpam-5281	64	8	k	k	PROPN
ejpam-5281	64	9	be	be	AUX
ejpam-5281	64	10	harmonic	harmonic	ADJ
ejpam-5281	64	11	k	k	NOUN
ejpam-5281	64	12	-	-	NOUN
ejpam-5281	64	13	quasiregular	quasiregular	ADJ
ejpam-5281	64	14	,	,	PUNCT
ejpam-5281	64	15	with	with	ADP
ejpam-5281	64	16	g(0	g(0	NOUN
ejpam-5281	64	17	)	)	PUNCT
ejpam-5281	64	18	=	=	SYM
ejpam-5281	64	19	0	0	X
ejpam-5281	64	20	.	.	PUNCT
ejpam-5281	65	1	if	if	SCONJ
ejpam-5281	65	2	f	f	PROPN
ejpam-5281	65	3	∈	∈	PROPN
ejpam-5281	65	4	hn	hn	PROPN
ejpam-5281	65	5	and	and	CCONJ
ejpam-5281	65	6	n	n	PROPN
ejpam-5281	65	7	>	>	X
ejpam-5281	65	8	2	2	NUM
ejpam-5281	65	9	,	,	PUNCT
ejpam-5281	65	10	then	then	ADV
ejpam-5281	65	11	following	follow	VERB
ejpam-5281	65	12	inequality	inequality	NOUN
ejpam-5281	65	13	holds	hold	VERB
ejpam-5281	65	14	||f	||f	NOUN
ejpam-5281	65	15	||n	||n	PROPN
ejpam-5281	65	16	≤	≤	ADJ
ejpam-5281	65	17	c(k	c(k	NOUN
ejpam-5281	65	18	,	,	PUNCT
ejpam-5281	65	19	n)||h||n	n)||h||n	PROPN
ejpam-5281	65	20	,	,	PUNCT
ejpam-5281	65	21	where	where	SCONJ
ejpam-5281	65	22	c(k	c(k	NOUN
ejpam-5281	65	23	,	,	PUNCT
ejpam-5281	65	24	n	n	CCONJ
ejpam-5281	65	25	)	)	PUNCT
ejpam-5281	65	26	=	=	SYM
ejpam-5281	65	27	(	(	PUNCT
ejpam-5281	65	28	2(1	2(1	NUM
ejpam-5281	66	1	+	+	NUM
ejpam-5281	66	2	k2))n/2	k2))n/2	NOUN
ejpam-5281	66	3	.	.	PUNCT
ejpam-5281	67	1	2	2	X
ejpam-5281	67	2	.	.	X
ejpam-5281	67	3	proof	proof	NOUN
ejpam-5281	67	4	of	of	ADP
ejpam-5281	67	5	main	main	ADJ
ejpam-5281	67	6	results	result	NOUN
ejpam-5281	67	7	proof	proof	NOUN
ejpam-5281	67	8	.	.	PUNCT
ejpam-5281	68	1	[	[	X
ejpam-5281	68	2	proof	proof	NOUN
ejpam-5281	68	3	of	of	ADP
ejpam-5281	68	4	theorem	theorem	NOUN
ejpam-5281	68	5	1	1	NUM
ejpam-5281	68	6	]	]	PUNCT
ejpam-5281	68	7	let	let	VERB
ejpam-5281	68	8	f	f	PROPN
ejpam-5281	68	9	=	=	PRON
ejpam-5281	68	10	h+	h+	AUX
ejpam-5281	68	11	ḡ	ḡ	VERB
ejpam-5281	68	12	=	=	SYM
ejpam-5281	68	13	∞∑	∞∑	NUM
ejpam-5281	68	14	j=0	j=0	PROPN
ejpam-5281	68	15	ajz	ajz	PROPN
ejpam-5281	68	16	j	j	PROPN
ejpam-5281	68	17	+	+	CCONJ
ejpam-5281	68	18	∞∑	∞∑	NUM
ejpam-5281	68	19	j=1	j=1	NOUN
ejpam-5281	68	20	bj	bj	VERB
ejpam-5281	68	21	z̄	z̄	PROPN
ejpam-5281	68	22	j	j	PROPN
ejpam-5281	68	23	.	.	PUNCT
ejpam-5281	69	1	we	we	PRON
ejpam-5281	69	2	can	can	AUX
ejpam-5281	69	3	assume	assume	VERB
ejpam-5281	69	4	that	that	SCONJ
ejpam-5281	69	5	both	both	PRON
ejpam-5281	69	6	of	of	ADP
ejpam-5281	69	7	following	follow	VERB
ejpam-5281	69	8	integrals	integral	NOUN
ejpam-5281	69	9	converge	converge	VERB
ejpam-5281	69	10	.	.	PUNCT
ejpam-5281	70	1	if	if	SCONJ
ejpam-5281	70	2	no	no	INTJ
ejpam-5281	70	3	,	,	PUNCT
ejpam-5281	70	4	then	then	ADV
ejpam-5281	70	5	we	we	PRON
ejpam-5281	70	6	take	take	VERB
ejpam-5281	70	7	the	the	DET
ejpam-5281	70	8	dilatation	dilatation	NOUN
ejpam-5281	70	9	f(rz	f(rz	PROPN
ejpam-5281	70	10	)	)	PUNCT
ejpam-5281	70	11	for	for	ADP
ejpam-5281	70	12	r	r	NOUN
ejpam-5281	70	13	<	<	X
ejpam-5281	70	14	1	1	NUM
ejpam-5281	70	15	.	.	PUNCT
ejpam-5281	71	1	if	if	SCONJ
ejpam-5281	71	2	we	we	PRON
ejpam-5281	71	3	integrate	integrate	VERB
ejpam-5281	71	4	in	in	ADP
ejpam-5281	71	5	the	the	DET
ejpam-5281	71	6	unit	unit	NOUN
ejpam-5281	71	7	circle∫	circle∫	VERB
ejpam-5281	71	8	t	t	PROPN
ejpam-5281	71	9	|g′(z)|2|dz|	|g′(z)|2|dz|	PROPN
ejpam-5281	71	10	≤	≤	PROPN
ejpam-5281	71	11	k2	k2	PROPN
ejpam-5281	71	12	∫	∫	PROPN
ejpam-5281	71	13	u	u	NOUN
ejpam-5281	71	14	|h′(z)|2|dz|	|h′(z)|2|dz|	ADV
ejpam-5281	71	15	we	we	PRON
ejpam-5281	71	16	get	get	VERB
ejpam-5281	71	17	∑	∑	PUNCT
ejpam-5281	71	18	j=1	j=1	PROPN
ejpam-5281	71	19	j2|bj	j2|bj	PROPN
ejpam-5281	71	20	|2	|2	NUM
ejpam-5281	72	1	≤	≤	PROPN
ejpam-5281	72	2	k2	k2	X
ejpam-5281	72	3	∑	∑	PROPN
ejpam-5281	72	4	j=1	j=1	PROPN
ejpam-5281	72	5	j2|aj	j2|aj	PROPN
ejpam-5281	72	6	|2	|2	NUM
ejpam-5281	72	7	.	.	PUNCT
ejpam-5281	73	1	here	here	ADV
ejpam-5281	73	2	k	k	X
ejpam-5281	73	3	=	=	PUNCT
ejpam-5281	73	4	k−1	k−1	PROPN
ejpam-5281	73	5	k+1	k+1	X
ejpam-5281	73	6	.	.	PUNCT
ejpam-5281	74	1	let	let	VERB
ejpam-5281	74	2	u	u	PRON
ejpam-5281	74	3	=	=	PUNCT
ejpam-5281	74	4	ℜ(g	ℜ(g	X
ejpam-5281	75	1	+	+	NUM
ejpam-5281	75	2	h	h	NOUN
ejpam-5281	75	3	)	)	PUNCT
ejpam-5281	75	4	and	and	CCONJ
ejpam-5281	75	5	v	v	X
ejpam-5281	75	6	=	=	SYM
ejpam-5281	75	7	ℜ(i(h−	ℜ(i(h−	PROPN
ejpam-5281	75	8	g	g	NOUN
ejpam-5281	75	9	)	)	PUNCT
ejpam-5281	75	10	)	)	PUNCT
ejpam-5281	75	11	.	.	PUNCT
ejpam-5281	76	1	then	then	ADV
ejpam-5281	76	2	4	4	NUM
ejpam-5281	76	3	1	1	NUM
ejpam-5281	76	4	π	π	NOUN
ejpam-5281	76	5	∫	∫	PROPN
ejpam-5281	76	6	u	u	X
ejpam-5281	76	7	|u|2dxdy	|u|2dxdy	PROPN
ejpam-5281	76	8	=	=	PUNCT
ejpam-5281	76	9	4(ℜa0)2	4(ℜa0)2	NOUN
ejpam-5281	77	1	+	+	CCONJ
ejpam-5281	77	2	∞∑	∞∑	NUM
ejpam-5281	77	3	j=1	j=1	NOUN
ejpam-5281	77	4	(	(	PUNCT
ejpam-5281	77	5	|aj	|aj	X
ejpam-5281	77	6	|2	|2	NUM
ejpam-5281	77	7	+	+	CCONJ
ejpam-5281	77	8	|bj	|bj	PROPN
ejpam-5281	77	9	|2	|2	NUM
ejpam-5281	77	10	+	+	CCONJ
ejpam-5281	77	11	2ℜ(akbj	2ℜ(akbj	NUM
ejpam-5281	77	12	)	)	PUNCT
ejpam-5281	77	13	)	)	PUNCT
ejpam-5281	77	14	and	and	CCONJ
ejpam-5281	77	15	4	4	NUM
ejpam-5281	77	16	1	1	NUM
ejpam-5281	77	17	π	π	NOUN
ejpam-5281	77	18	∫	∫	PROPN
ejpam-5281	77	19	u	u	PROPN
ejpam-5281	77	20	|v|2dxdy	|v|2dxdy	PROPN
ejpam-5281	77	21	=	=	PUNCT
ejpam-5281	77	22	4(ℑa0)2	4(ℑa0)2	PROPN
ejpam-5281	78	1	+	+	CCONJ
ejpam-5281	78	2	∞∑	∞∑	NUM
ejpam-5281	78	3	j=1	j=1	NOUN
ejpam-5281	78	4	(	(	PUNCT
ejpam-5281	78	5	|aj	|aj	X
ejpam-5281	78	6	|2	|2	NUM
ejpam-5281	78	7	+	+	CCONJ
ejpam-5281	78	8	|bj	|bj	PROPN
ejpam-5281	78	9	|2	|2	NUM
ejpam-5281	79	1	−	−	NOUN
ejpam-5281	79	2	2ℜ(akbj	2ℜ(akbj	NUM
ejpam-5281	79	3	)	)	PUNCT
ejpam-5281	79	4	)	)	PUNCT
ejpam-5281	79	5	.	.	PUNCT
ejpam-5281	80	1	without	without	ADP
ejpam-5281	80	2	loss	loss	NOUN
ejpam-5281	80	3	of	of	ADP
ejpam-5281	80	4	generality	generality	NOUN
ejpam-5281	80	5	we	we	PRON
ejpam-5281	80	6	assume	assume	VERB
ejpam-5281	80	7	that	that	SCONJ
ejpam-5281	80	8	a0	a0	PROPN
ejpam-5281	80	9	=	=	SYM
ejpam-5281	80	10	0	0	PROPN
ejpam-5281	80	11	,	,	PUNCT
ejpam-5281	80	12	because	because	SCONJ
ejpam-5281	80	13	ℜ(a0	ℜ(a0	VERB
ejpam-5281	80	14	)	)	PUNCT
ejpam-5281	80	15	=	=	SYM
ejpam-5281	80	16	0	0	NUM
ejpam-5281	80	17	by	by	ADP
ejpam-5281	80	18	assumption	assumption	NOUN
ejpam-5281	80	19	.	.	PUNCT
ejpam-5281	81	1	we	we	PRON
ejpam-5281	81	2	will	will	AUX
ejpam-5281	81	3	find	find	VERB
ejpam-5281	81	4	the	the	DET
ejpam-5281	81	5	best	good	ADJ
ejpam-5281	81	6	constant	constant	ADJ
ejpam-5281	81	7	ck	ck	NOUN
ejpam-5281	81	8	in	in	ADP
ejpam-5281	81	9	the	the	DET
ejpam-5281	81	10	inequality	inequality	NOUN
ejpam-5281	81	11	1	1	NUM
ejpam-5281	81	12	π	π	NOUN
ejpam-5281	81	13	∫	∫	PROPN
ejpam-5281	81	14	u	u	NOUN
ejpam-5281	81	15	|u|2dxdy	|u|2dxdy	PROPN
ejpam-5281	81	16	=	=	PUNCT
ejpam-5281	81	17	∞∑	∞∑	NUM
ejpam-5281	81	18	j=0	j=0	PROPN
ejpam-5281	81	19	(	(	PUNCT
ejpam-5281	81	20	|aj	|aj	NOUN
ejpam-5281	81	21	|2	|2	NUM
ejpam-5281	81	22	+	+	CCONJ
ejpam-5281	81	23	|bj	|bj	PROPN
ejpam-5281	81	24	|2	|2	NUM
ejpam-5281	82	1	+	+	CCONJ
ejpam-5281	82	2	2|aj	2|aj	NUM
ejpam-5281	82	3	||bj	||bj	NOUN
ejpam-5281	82	4	|	|	NOUN
ejpam-5281	82	5	)	)	PUNCT
ejpam-5281	82	6	≤	≤	NOUN
ejpam-5281	83	1	ck	ck	INTJ
ejpam-5281	83	2	1	1	NUM
ejpam-5281	83	3	π	π	NOUN
ejpam-5281	83	4	∫	∫	PROPN
ejpam-5281	83	5	u	u	NOUN
ejpam-5281	83	6	|u|2dxdy	|u|2dxdy	PROPN
ejpam-5281	83	7	=	=	PUNCT
ejpam-5281	83	8	∞∑	∞∑	NUM
ejpam-5281	83	9	j=0	j=0	PROPN
ejpam-5281	83	10	(	(	PUNCT
ejpam-5281	83	11	|aj	|aj	NOUN
ejpam-5281	83	12	|2	|2	NUM
ejpam-5281	84	1	+	+	CCONJ
ejpam-5281	84	2	|bj	|bj	PROPN
ejpam-5281	84	3	|2	|2	NUM
ejpam-5281	85	1	−	−	NUM
ejpam-5281	85	2	2|aj	2|aj	PROPN
ejpam-5281	85	3	||bj	||bj	NOUN
ejpam-5281	85	4	|	|	NOUN
ejpam-5281	85	5	)	)	PUNCT
ejpam-5281	85	6	e.	e.	PROPN
ejpam-5281	85	7	bajrami	bajrami	PROPN
ejpam-5281	85	8	/	/	SYM
ejpam-5281	85	9	eur	eur	PROPN
ejpam-5281	85	10	.	.	PUNCT
ejpam-5281	86	1	j.	j.	PROPN
ejpam-5281	86	2	pure	pure	PROPN
ejpam-5281	86	3	appl	appl	PROPN
ejpam-5281	86	4	.	.	PROPN
ejpam-5281	86	5	math	math	PROPN
ejpam-5281	86	6	,	,	PUNCT
ejpam-5281	86	7	17	17	NUM
ejpam-5281	86	8	(	(	PUNCT
ejpam-5281	86	9	3	3	NUM
ejpam-5281	86	10	)	)	PUNCT
ejpam-5281	86	11	(	(	PUNCT
ejpam-5281	86	12	2024	2024	NUM
ejpam-5281	86	13	)	)	PUNCT
ejpam-5281	86	14	,	,	PUNCT
ejpam-5281	86	15	1490	1490	NUM
ejpam-5281	86	16	-	-	SYM
ejpam-5281	86	17	1496	1496	NUM
ejpam-5281	86	18	1494	1494	NUM
ejpam-5281	86	19	under	under	ADP
ejpam-5281	86	20	the	the	DET
ejpam-5281	86	21	condition	condition	NOUN
ejpam-5281	86	22	∑	∑	PUNCT
ejpam-5281	86	23	j=1	j=1	PROPN
ejpam-5281	86	24	j2|bj	j2|bj	PROPN
ejpam-5281	86	25	|2	|2	NUM
ejpam-5281	86	26	≤	≤	PROPN
ejpam-5281	86	27	k2	k2	X
ejpam-5281	86	28	∑	∑	PROPN
ejpam-5281	86	29	j=1	j=1	PROPN
ejpam-5281	86	30	j2|aj	j2|aj	PROPN
ejpam-5281	86	31	|2	|2	NUM
ejpam-5281	86	32	.	.	PUNCT
ejpam-5281	87	1	let	let	VERB
ejpam-5281	87	2	w	w	X
ejpam-5281	87	3	(	(	PUNCT
ejpam-5281	87	4	a	a	DET
ejpam-5281	87	5	,	,	PUNCT
ejpam-5281	87	6	b	b	NOUN
ejpam-5281	87	7	)	)	PUNCT
ejpam-5281	87	8	=	=	NOUN
ejpam-5281	87	9	∑∞	∑∞	NOUN
ejpam-5281	87	10	j=0(|aj	j=0(|aj	NOUN
ejpam-5281	87	11	|2	|2	NUM
ejpam-5281	88	1	+	+	CCONJ
ejpam-5281	88	2	|bj	|bj	PROPN
ejpam-5281	88	3	|2	|2	NUM
ejpam-5281	89	1	+	+	CCONJ
ejpam-5281	89	2	2|aj	2|aj	NUM
ejpam-5281	89	3	||bj	||bj	NOUN
ejpam-5281	89	4	|)∑∞	|)∑∞	PRON
ejpam-5281	89	5	j=0(|aj	j=0(|aj	PROPN
ejpam-5281	89	6	|2	|2	NUM
ejpam-5281	90	1	+	+	CCONJ
ejpam-5281	90	2	|bj	|bj	PROPN
ejpam-5281	90	3	|2	|2	NUM
ejpam-5281	90	4	−	−	NUM
ejpam-5281	90	5	2|aj	2|aj	PROPN
ejpam-5281	90	6	||bj	||bj	NOUN
ejpam-5281	90	7	|	|	NOUN
ejpam-5281	90	8	)	)	PUNCT
ejpam-5281	90	9	.	.	PUNCT
ejpam-5281	91	1	we	we	PRON
ejpam-5281	91	2	need	need	VERB
ejpam-5281	91	3	to	to	PART
ejpam-5281	91	4	find	find	VERB
ejpam-5281	91	5	the	the	DET
ejpam-5281	91	6	maximum	maximum	NOUN
ejpam-5281	91	7	of	of	ADP
ejpam-5281	91	8	expression	expression	NOUN
ejpam-5281	91	9	w	w	NOUN
ejpam-5281	91	10	under	under	ADP
ejpam-5281	91	11	the	the	DET
ejpam-5281	91	12	condition	condition	NOUN
ejpam-5281	91	13	h(a	h(a	PROPN
ejpam-5281	91	14	,	,	PUNCT
ejpam-5281	91	15	b	b	NOUN
ejpam-5281	91	16	)	)	PUNCT
ejpam-5281	91	17	=	=	PUNCT
ejpam-5281	92	1	∑	∑	PUNCT
ejpam-5281	92	2	j=1	j=1	PROPN
ejpam-5281	92	3	j2|bj	j2|bj	PROPN
ejpam-5281	92	4	|2	|2	NUM
ejpam-5281	93	1	−	−	PROPN
ejpam-5281	93	2	k2	k2	PROPN
ejpam-5281	93	3	∑	∑	PROPN
ejpam-5281	93	4	j=1	j=1	PROPN
ejpam-5281	93	5	j2|aj	j2|aj	PROPN
ejpam-5281	93	6	|2	|2	NUM
ejpam-5281	94	1	=	=	SYM
ejpam-5281	94	2	0	0	X
ejpam-5281	94	3	.	.	PUNCT
ejpam-5281	95	1	it	it	PRON
ejpam-5281	95	2	is	be	AUX
ejpam-5281	95	3	equivalent	equivalent	ADJ
ejpam-5281	95	4	of	of	ADP
ejpam-5281	95	5	finding	find	VERB
ejpam-5281	95	6	the	the	DET
ejpam-5281	95	7	maximum	maximum	NOUN
ejpam-5281	95	8	of	of	ADP
ejpam-5281	95	9	expression	expression	NOUN
ejpam-5281	95	10	m	m	NOUN
ejpam-5281	95	11	=	=	SYM
ejpam-5281	95	12	u	u	X
ejpam-5281	95	13	v	v	NOUN
ejpam-5281	95	14	,	,	PUNCT
ejpam-5281	95	15	where	where	SCONJ
ejpam-5281	95	16	u	u	NOUN
ejpam-5281	95	17	=	=	VERB
ejpam-5281	95	18	∞∑	∞∑	PROPN
ejpam-5281	95	19	j=0	j=0	PROPN
ejpam-5281	95	20	|aj	|aj	NUM
ejpam-5281	95	21	|2	|2	NUM
ejpam-5281	95	22	,	,	PUNCT
ejpam-5281	95	23	v	v	NOUN
ejpam-5281	95	24	=	=	SYM
ejpam-5281	96	1	∞∑	∞∑	NUM
ejpam-5281	96	2	j=0	j=0	PROPN
ejpam-5281	96	3	|bj	|bj	PROPN
ejpam-5281	96	4	|2	|2	NUM
ejpam-5281	96	5	under	under	ADP
ejpam-5281	96	6	the	the	DET
ejpam-5281	96	7	condition	condition	NOUN
ejpam-5281	96	8	h(a	h(a	PROPN
ejpam-5281	96	9	,	,	PUNCT
ejpam-5281	96	10	b	b	NOUN
ejpam-5281	96	11	)	)	PUNCT
ejpam-5281	96	12	=	=	SYM
ejpam-5281	97	1	0	0	X
ejpam-5281	97	2	.	.	PUNCT
ejpam-5281	98	1	the	the	DET
ejpam-5281	98	2	lagrangian	lagrangian	ADJ
ejpam-5281	98	3	is	be	AUX
ejpam-5281	98	4	l	l	NOUN
ejpam-5281	98	5	=	=	PUNCT
ejpam-5281	98	6	m	m	NOUN
ejpam-5281	98	7	−	−	NOUN
ejpam-5281	98	8	λh	λh	VERB
ejpam-5281	98	9	.	.	PROPN
ejpam-5281	98	10	assume	assume	VERB
ejpam-5281	98	11	without	without	ADP
ejpam-5281	98	12	loss	loss	NOUN
ejpam-5281	98	13	of	of	ADP
ejpam-5281	98	14	generality	generality	NOUN
ejpam-5281	98	15	that	that	PRON
ejpam-5281	98	16	aj	aj	PROPN
ejpam-5281	98	17	≥	≥	PRON
ejpam-5281	98	18	0	0	PUNCT
ejpam-5281	99	1	and	and	CCONJ
ejpam-5281	99	2	bj	bj	VERB
ejpam-5281	99	3	≥	≥	NOUN
ejpam-5281	99	4	0	0	NUM
ejpam-5281	99	5	.	.	PUNCT
ejpam-5281	100	1	also	also	ADV
ejpam-5281	100	2	we	we	PRON
ejpam-5281	100	3	have	have	VERB
ejpam-5281	100	4	a0	a0	NOUN
ejpam-5281	100	5	=	=	SYM
ejpam-5281	100	6	0	0	PROPN
ejpam-5281	100	7	.	.	PUNCT
ejpam-5281	101	1	then	then	ADV
ejpam-5281	101	2	laj	laj	PROPN
ejpam-5281	101	3	=	=	PROPN
ejpam-5281	101	4	0	0	PROPN
ejpam-5281	101	5	and	and	CCONJ
ejpam-5281	101	6	lbj	lbj	PROPN
ejpam-5281	101	7	=	=	SYM
ejpam-5281	101	8	0	0	PUNCT
ejpam-5281	101	9	imply	imply	VERB
ejpam-5281	101	10	that	that	PRON
ejpam-5281	101	11	bj	bj	VERB
ejpam-5281	101	12	u	u	NOUN
ejpam-5281	101	13	=	=	NOUN
ejpam-5281	101	14	λj2bj	λj2bj	NUM
ejpam-5281	101	15	,	,	PUNCT
ejpam-5281	101	16	ajv	ajv	PROPN
ejpam-5281	101	17	u2	u2	PROPN
ejpam-5281	101	18	=	=	PROPN
ejpam-5281	101	19	k2λj2aj	k2λj2aj	PROPN
ejpam-5281	101	20	,	,	PUNCT
ejpam-5281	101	21	j	j	PROPN
ejpam-5281	101	22	≥	≥	NUM
ejpam-5281	101	23	1	1	NUM
ejpam-5281	101	24	.	.	PUNCT
ejpam-5281	102	1	λ	λ	NOUN
ejpam-5281	102	2	can	can	AUX
ejpam-5281	102	3	not	not	PART
ejpam-5281	102	4	be	be	AUX
ejpam-5281	102	5	zero	zero	NUM
ejpam-5281	102	6	,	,	PUNCT
ejpam-5281	102	7	because	because	SCONJ
ejpam-5281	102	8	in	in	ADP
ejpam-5281	102	9	that	that	DET
ejpam-5281	102	10	case	case	NOUN
ejpam-5281	102	11	a	a	PRON
ejpam-5281	102	12	=	=	SYM
ejpam-5281	102	13	0	0	NUM
ejpam-5281	102	14	and	and	CCONJ
ejpam-5281	102	15	b	b	X
ejpam-5281	102	16	=	=	SYM
ejpam-5281	102	17	0	0	PROPN
ejpam-5281	102	18	.	.	PUNCT
ejpam-5281	103	1	if	if	SCONJ
ejpam-5281	103	2	λ	λ	PROPN
ejpam-5281	103	3	̸=	̸=	PROPN
ejpam-5281	103	4	0	0	NUM
ejpam-5281	103	5	,	,	PUNCT
ejpam-5281	103	6	then	then	ADV
ejpam-5281	103	7	there	there	PRON
ejpam-5281	103	8	exists	exist	VERB
ejpam-5281	103	9	j0	j0	PROPN
ejpam-5281	103	10	so	so	SCONJ
ejpam-5281	103	11	that	that	SCONJ
ejpam-5281	103	12	aj0	aj0	NOUN
ejpam-5281	103	13	̸=	̸=	PROPN
ejpam-5281	103	14	0	0	NUM
ejpam-5281	103	15	and	and	CCONJ
ejpam-5281	103	16	bj0	bj0	ADP
ejpam-5281	103	17	̸=	̸=	PROPN
ejpam-5281	103	18	0	0	NUM
ejpam-5281	103	19	,	,	PUNCT
ejpam-5281	103	20	aj	aj	PROPN
ejpam-5281	103	21	=	=	PROPN
ejpam-5281	103	22	bj	bj	NOUN
ejpam-5281	103	23	=	=	SYM
ejpam-5281	103	24	0	0	NUM
ejpam-5281	103	25	for	for	ADP
ejpam-5281	103	26	j	j	PROPN
ejpam-5281	103	27	̸=	̸=	PROPN
ejpam-5281	103	28	j0	j0	PROPN
ejpam-5281	103	29	and	and	CCONJ
ejpam-5281	103	30	1	1	NUM
ejpam-5281	103	31	u	u	NOUN
ejpam-5281	103	32	=	=	NOUN
ejpam-5281	103	33	k2v	k2v	NOUN
ejpam-5281	103	34	u2	u2	NOUN
ejpam-5281	103	35	.	.	PUNCT
ejpam-5281	104	1	in	in	ADP
ejpam-5281	104	2	this	this	DET
ejpam-5281	104	3	case	case	NOUN
ejpam-5281	104	4	we	we	PRON
ejpam-5281	104	5	get	get	VERB
ejpam-5281	104	6	m	m	NOUN
ejpam-5281	104	7	=	=	NOUN
ejpam-5281	104	8	k2	k2	PROPN
ejpam-5281	104	9	.	.	PUNCT
ejpam-5281	105	1	this	this	PRON
ejpam-5281	105	2	implies	imply	VERB
ejpam-5281	105	3	that	that	SCONJ
ejpam-5281	105	4	w	w	PROPN
ejpam-5281	105	5	≤	≤	NUM
ejpam-5281	105	6	1+k2	1+k2	NUM
ejpam-5281	106	1	+	+	NOUN
ejpam-5281	107	1	2k	2k	NOUN
ejpam-5281	107	2	1+k2−2k	1+k2−2k	NUM
ejpam-5281	107	3	=	=	SYM
ejpam-5281	107	4	k2	k2	PROPN
ejpam-5281	107	5	.	.	PUNCT
ejpam-5281	108	1	in	in	ADP
ejpam-5281	108	2	order	order	NOUN
ejpam-5281	108	3	to	to	PART
ejpam-5281	108	4	prove	prove	VERB
ejpam-5281	108	5	theorem	theorem	ADJ
ejpam-5281	108	6	2	2	NUM
ejpam-5281	108	7	,	,	PUNCT
ejpam-5281	108	8	we	we	PRON
ejpam-5281	108	9	will	will	AUX
ejpam-5281	108	10	need	need	VERB
ejpam-5281	108	11	next	next	ADJ
ejpam-5281	108	12	result	result	NOUN
ejpam-5281	108	13	.	.	PUNCT
ejpam-5281	109	1	lemma	lemma	PROPN
ejpam-5281	109	2	1	1	X
ejpam-5281	109	3	.	.	PUNCT
ejpam-5281	110	1	let	let	VERB
ejpam-5281	110	2	f	f	PRON
ejpam-5281	110	3	be	be	AUX
ejpam-5281	110	4	analytic	analytic	ADJ
ejpam-5281	110	5	function	function	NOUN
ejpam-5281	110	6	with	with	ADP
ejpam-5281	110	7	condition	condition	NOUN
ejpam-5281	110	8	f(0	f(0	NOUN
ejpam-5281	110	9	)	)	PUNCT
ejpam-5281	110	10	=	=	SYM
ejpam-5281	111	1	0	0	X
ejpam-5281	111	2	.	.	PUNCT
ejpam-5281	112	1	then∫	then∫	NOUN
ejpam-5281	112	2	u	u	NOUN
ejpam-5281	112	3	ℜ(f(z))|dz|	ℜ(f(z))|dz|	PROPN
ejpam-5281	112	4	=	=	SYM
ejpam-5281	112	5	0	0	X
ejpam-5281	112	6	.	.	PUNCT
ejpam-5281	113	1	proof	proof	NOUN
ejpam-5281	113	2	.	.	PUNCT
ejpam-5281	114	1	since	since	SCONJ
ejpam-5281	114	2	f(0	f(0	NOUN
ejpam-5281	114	3	)	)	PUNCT
ejpam-5281	114	4	=	=	SYM
ejpam-5281	114	5	0	0	NUM
ejpam-5281	114	6	,	,	PUNCT
ejpam-5281	114	7	this	this	DET
ejpam-5281	114	8	function	function	NOUN
ejpam-5281	114	9	can	can	AUX
ejpam-5281	114	10	be	be	AUX
ejpam-5281	114	11	expressed	express	VERB
ejpam-5281	114	12	as	as	ADP
ejpam-5281	114	13	f(z	f(z	NOUN
ejpam-5281	114	14	)	)	PUNCT
ejpam-5281	115	1	=	=	PUNCT
ejpam-5281	115	2	∑∞	∑∞	NOUN
ejpam-5281	115	3	k=1	k=1	X
ejpam-5281	115	4	akz	akz	PROPN
ejpam-5281	115	5	k.	k.	PROPN
ejpam-5281	115	6	integrating	integrate	VERB
ejpam-5281	115	7	last	last	ADJ
ejpam-5281	115	8	expression	expression	NOUN
ejpam-5281	115	9	in	in	ADP
ejpam-5281	115	10	unit	unit	NOUN
ejpam-5281	115	11	circle	circle	NOUN
ejpam-5281	115	12	,	,	PUNCT
ejpam-5281	115	13	we	we	PRON
ejpam-5281	115	14	get∫	get∫	VERB
ejpam-5281	115	15	u	u	NOUN
ejpam-5281	115	16	f(z)|dz|	f(z)|dz|	X
ejpam-5281	115	17	=	=	PUNCT
ejpam-5281	116	1	∞∑	∞∑	NUM
ejpam-5281	116	2	k=1	k=1	PRON
ejpam-5281	116	3	ak	ak	PROPN
ejpam-5281	116	4	∫	∫	PROPN
ejpam-5281	116	5	1	1	NUM
ejpam-5281	116	6	0	0	NUM
ejpam-5281	116	7	rkdr	rkdr	ADJ
ejpam-5281	116	8	∫	∫	PROPN
ejpam-5281	116	9	2π	2π	PROPN
ejpam-5281	116	10	0	0	NUM
ejpam-5281	116	11	eiktdt	eiktdt	PROPN
ejpam-5281	116	12	.	.	PUNCT
ejpam-5281	117	1	since	since	SCONJ
ejpam-5281	117	2	the	the	DET
ejpam-5281	117	3	integral	integral	ADJ
ejpam-5281	117	4	∫	∫	PROPN
ejpam-5281	117	5	2π	2π	PROPN
ejpam-5281	117	6	0	0	NUM
ejpam-5281	117	7	eiktdt	eiktdt	NOUN
ejpam-5281	117	8	=	=	SYM
ejpam-5281	117	9	0	0	PROPN
ejpam-5281	117	10	,	,	PUNCT
ejpam-5281	117	11	for	for	ADP
ejpam-5281	117	12	each	each	DET
ejpam-5281	117	13	k	k	PROPN
ejpam-5281	117	14	∈	∈	PROPN
ejpam-5281	117	15	n	n	CCONJ
ejpam-5281	117	16	,	,	PUNCT
ejpam-5281	117	17	we	we	PRON
ejpam-5281	117	18	get∫	get∫	VERB
ejpam-5281	117	19	u	u	NOUN
ejpam-5281	117	20	f(z)|dz|	f(z)|dz|	PROPN
ejpam-5281	117	21	=	=	SYM
ejpam-5281	117	22	0	0	X
ejpam-5281	117	23	.	.	PUNCT
ejpam-5281	118	1	similarly	similarly	ADV
ejpam-5281	118	2	∫	∫	PROPN
ejpam-5281	118	3	u	u	NOUN
ejpam-5281	118	4	f(z)|dz|	f(z)|dz|	PROPN
ejpam-5281	118	5	=	=	SYM
ejpam-5281	118	6	0	0	X
ejpam-5281	118	7	.	.	PUNCT
ejpam-5281	119	1	now	now	ADV
ejpam-5281	119	2	,	,	PUNCT
ejpam-5281	119	3	identity	identity	NOUN
ejpam-5281	119	4	ℜ(f(z	ℜ(f(z	NOUN
ejpam-5281	119	5	)	)	PUNCT
ejpam-5281	119	6	)	)	PUNCT
ejpam-5281	120	1	=	=	SYM
ejpam-5281	120	2	f(z)+f(z	f(z)+f(z	VERB
ejpam-5281	120	3	)	)	PUNCT
ejpam-5281	120	4	2	2	NUM
ejpam-5281	120	5	,	,	PUNCT
ejpam-5281	120	6	follows	follow	VERB
ejpam-5281	120	7	that	that	SCONJ
ejpam-5281	120	8	∫	∫	PROPN
ejpam-5281	120	9	uℜ(f(z))|dz|	uℜ(f(z))|dz|	PROPN
ejpam-5281	120	10	=	=	SYM
ejpam-5281	121	1	0	0	X
ejpam-5281	121	2	.	.	PUNCT
ejpam-5281	121	3	references	reference	NOUN
ejpam-5281	121	4	1495	1495	NUM
ejpam-5281	121	5	proof	proof	NOUN
ejpam-5281	121	6	.	.	PUNCT
ejpam-5281	122	1	[	[	X
ejpam-5281	122	2	proof	proof	NOUN
ejpam-5281	122	3	of	of	ADP
ejpam-5281	122	4	theorem	theorem	NOUN
ejpam-5281	122	5	2	2	NUM
ejpam-5281	122	6	]	]	PUNCT
ejpam-5281	122	7	let	let	VERB
ejpam-5281	122	8	f(z	f(z	NOUN
ejpam-5281	122	9	)	)	PUNCT
ejpam-5281	122	10	=	=	SYM
ejpam-5281	122	11	h(z	h(z	NOUN
ejpam-5281	122	12	)	)	PUNCT
ejpam-5281	123	1	+	+	PUNCT
ejpam-5281	123	2	g(z	g(z	ADJ
ejpam-5281	123	3	)	)	PUNCT
ejpam-5281	123	4	=	=	SYM
ejpam-5281	123	5	∑∞	∑∞	NOUN
ejpam-5281	123	6	k=0	k=0	PUNCT
ejpam-5281	123	7	akz	akz	PROPN
ejpam-5281	124	1	k	k	PROPN
ejpam-5281	124	2	+	+	PUNCT
ejpam-5281	124	3	∑∞	∑∞	X
ejpam-5281	124	4	k=1	k=1	X
ejpam-5281	124	5	bkz	bkz	VERB
ejpam-5281	124	6	k	k	PROPN
ejpam-5281	124	7	,	,	PUNCT
ejpam-5281	124	8	then∫	then∫	NOUN
ejpam-5281	124	9	u	u	NOUN
ejpam-5281	124	10	|f(z)|2|dz|	|f(z)|2|dz|	PROPN
ejpam-5281	124	11	=	=	SYM
ejpam-5281	124	12	∫	∫	PROPN
ejpam-5281	124	13	u	u	PROPN
ejpam-5281	124	14	|h(z)|2|dz|+	|h(z)|2|dz|+	PROPN
ejpam-5281	124	15	∫	∫	PROPN
ejpam-5281	124	16	u	u	PROPN
ejpam-5281	124	17	|g(z)|2|dz|+	|g(z)|2|dz|+	VERB
ejpam-5281	124	18	2	2	NUM
ejpam-5281	124	19	∫	∫	NOUN
ejpam-5281	124	20	u	u	NOUN
ejpam-5281	124	21	ℜ(h(z)g(z))|dz|	ℜ(h(z)g(z))|dz|	VERB
ejpam-5281	124	22	.	.	PUNCT
ejpam-5281	125	1	as	as	ADP
ejpam-5281	125	2	in	in	ADP
ejpam-5281	125	3	the	the	DET
ejpam-5281	125	4	proof	proof	NOUN
ejpam-5281	125	5	of	of	ADP
ejpam-5281	125	6	theorem	theorem	NOUN
ejpam-5281	125	7	1	1	NUM
ejpam-5281	125	8	,	,	PUNCT
ejpam-5281	125	9	using	use	VERB
ejpam-5281	125	10	cauchy	cauchy	PROPN
ejpam-5281	125	11	-	-	PUNCT
ejpam-5281	125	12	schwartz	schwartz	PROPN
ejpam-5281	125	13	inequality	inequality	PROPN
ejpam-5281	125	14	,	,	PUNCT
ejpam-5281	125	15	lemma	lemma	PROPN
ejpam-5281	125	16	1	1	NUM
ejpam-5281	125	17	,	,	PUNCT
ejpam-5281	125	18	we	we	PRON
ejpam-5281	125	19	get∫	get∫	VERB
ejpam-5281	125	20	u	u	PROPN
ejpam-5281	125	21	|f(z)|2|dz|	|f(z)|2|dz|	PROPN
ejpam-5281	125	22	≤	≤	NUM
ejpam-5281	125	23	(	(	PUNCT
ejpam-5281	125	24	1	1	NUM
ejpam-5281	125	25	+	+	CCONJ
ejpam-5281	125	26	k2	k2	ADJ
ejpam-5281	125	27	)	)	PUNCT
ejpam-5281	125	28	∫	∫	PROPN
ejpam-5281	125	29	t	t	PROPN
ejpam-5281	125	30	|h(z)|2|dz|+	|h(z)|2|dz|+	PROPN
ejpam-5281	125	31	2	2	NUM
ejpam-5281	125	32	∫	∫	NOUN
ejpam-5281	125	33	t	t	NOUN
ejpam-5281	125	34	ℜ(h(z)g(z))|dz|	ℜ(h(z)g(z))|dz|	NOUN
ejpam-5281	126	1	=	=	PUNCT
ejpam-5281	126	2	ck	ck	INTJ
ejpam-5281	126	3	∫	∫	PROPN
ejpam-5281	126	4	t	t	PROPN
ejpam-5281	126	5	|h(z)|2|dz|	|h(z)|2|dz|	PROPN
ejpam-5281	126	6	.	.	PROPN
ejpam-5281	127	1	which	which	PRON
ejpam-5281	127	2	give	give	VERB
ejpam-5281	127	3	required	require	VERB
ejpam-5281	127	4	results	result	NOUN
ejpam-5281	127	5	.	.	PUNCT
ejpam-5281	128	1	proof	proof	NOUN
ejpam-5281	128	2	.	.	PUNCT
ejpam-5281	129	1	[	[	X
ejpam-5281	129	2	proof	proof	NOUN
ejpam-5281	129	3	of	of	ADP
ejpam-5281	129	4	theorem	theorem	ADJ
ejpam-5281	129	5	3	3	NUM
ejpam-5281	129	6	]	]	PUNCT
ejpam-5281	129	7	let	let	VERB
ejpam-5281	129	8	f(z	f(z	NOUN
ejpam-5281	129	9	)	)	PUNCT
ejpam-5281	129	10	=	=	SYM
ejpam-5281	129	11	h(z	h(z	NOUN
ejpam-5281	129	12	)	)	PUNCT
ejpam-5281	130	1	+	+	PUNCT
ejpam-5281	130	2	g(z	g(z	ADJ
ejpam-5281	130	3	)	)	PUNCT
ejpam-5281	130	4	=	=	SYM
ejpam-5281	130	5	∑∞	∑∞	NOUN
ejpam-5281	130	6	k=0	k=0	PUNCT
ejpam-5281	130	7	akz	akz	PROPN
ejpam-5281	131	1	k	k	PROPN
ejpam-5281	131	2	+	+	PUNCT
ejpam-5281	131	3	∑∞	∑∞	X
ejpam-5281	131	4	k=1	k=1	X
ejpam-5281	131	5	bkz	bkz	AUX
ejpam-5281	131	6	k	k	PROPN
ejpam-5281	131	7	be	be	AUX
ejpam-5281	131	8	harmonic	harmonic	ADJ
ejpam-5281	131	9	k	k	NOUN
ejpam-5281	131	10	-	-	NOUN
ejpam-5281	131	11	quasiregular	quasiregular	ADJ
ejpam-5281	131	12	,	,	PUNCT
ejpam-5281	131	13	with	with	ADP
ejpam-5281	131	14	g(0	g(0	NOUN
ejpam-5281	131	15	)	)	PUNCT
ejpam-5281	131	16	=	=	SYM
ejpam-5281	132	1	0	0	X
ejpam-5281	132	2	.	.	PUNCT
ejpam-5281	133	1	we	we	PRON
ejpam-5281	133	2	have∫	have∫	VERB
ejpam-5281	133	3	u	u	PRON
ejpam-5281	133	4	|f(z)|n	|f(z)|n	PROPN
ejpam-5281	133	5	=	=	SYM
ejpam-5281	133	6	∫	∫	PROPN
ejpam-5281	133	7	u	u	PROPN
ejpam-5281	133	8	(	(	PUNCT
ejpam-5281	133	9	|g	|g	PROPN
ejpam-5281	133	10	+	+	X
ejpam-5281	133	11	h|2	h|2	ADJ
ejpam-5281	133	12	)	)	PUNCT
ejpam-5281	133	13	n	n	PRON
ejpam-5281	133	14	2	2	NUM
ejpam-5281	133	15	=	=	SYM
ejpam-5281	133	16	∫	∫	PROPN
ejpam-5281	133	17	u	u	NOUN
ejpam-5281	133	18	(	(	PUNCT
ejpam-5281	133	19	|g|2	|g|2	PROPN
ejpam-5281	133	20	+	+	CCONJ
ejpam-5281	133	21	|h|2	|h|2	PROPN
ejpam-5281	133	22	+	+	CCONJ
ejpam-5281	133	23	2ℜ(gh	2ℜ(gh	NUM
ejpam-5281	133	24	)	)	PUNCT
ejpam-5281	133	25	)	)	PUNCT
ejpam-5281	133	26	n	n	PRON
ejpam-5281	133	27	2	2	NUM
ejpam-5281	133	28	.	.	PUNCT
ejpam-5281	134	1	using	use	VERB
ejpam-5281	134	2	theorem	theorem	ADJ
ejpam-5281	134	3	2	2	NUM
ejpam-5281	134	4	and	and	CCONJ
ejpam-5281	134	5	inequality	inequality	NOUN
ejpam-5281	134	6	ℜ(gh	ℜ(gh	PROPN
ejpam-5281	134	7	)	)	PUNCT
ejpam-5281	134	8	≤	≤	NUM
ejpam-5281	134	9	|hg|	|hg|	NOUN
ejpam-5281	134	10	≤	≤	NOUN
ejpam-5281	134	11	1	1	NUM
ejpam-5281	134	12	2(|h|	2(|h|	NUM
ejpam-5281	134	13	2	2	NUM
ejpam-5281	134	14	+	+	CCONJ
ejpam-5281	134	15	|g|2	|g|2	PROPN
ejpam-5281	134	16	)	)	PUNCT
ejpam-5281	134	17	,	,	PUNCT
ejpam-5281	134	18	we	we	PRON
ejpam-5281	134	19	get∫	get∫	VERB
ejpam-5281	134	20	u	u	PRON
ejpam-5281	134	21	|f(z)|n	|f(z)|n	VERB
ejpam-5281	134	22	≤	≤	NUM
ejpam-5281	134	23	∫	∫	PROPN
ejpam-5281	134	24	u	u	NOUN
ejpam-5281	134	25	(	(	PUNCT
ejpam-5281	134	26	2(|h|2	2(|h|2	NUM
ejpam-5281	134	27	+	+	CCONJ
ejpam-5281	134	28	|g|2	|g|2	PROPN
ejpam-5281	134	29	)	)	PUNCT
ejpam-5281	134	30	)	)	PUNCT
ejpam-5281	134	31	n	n	CCONJ
ejpam-5281	134	32	2	2	NUM
ejpam-5281	134	33	≤	≤	NOUN
ejpam-5281	134	34	(	(	PUNCT
ejpam-5281	134	35	2(1	2(1	NUM
ejpam-5281	134	36	+	+	CCONJ
ejpam-5281	134	37	k2	k2	ADJ
ejpam-5281	134	38	)	)	PUNCT
ejpam-5281	134	39	)	)	PUNCT
ejpam-5281	134	40	n	n	CCONJ
ejpam-5281	134	41	2	2	NUM
ejpam-5281	134	42	∫	∫	NOUN
ejpam-5281	134	43	u	u	PROPN
ejpam-5281	134	44	|h|n	|h|n	PROPN
ejpam-5281	134	45	.	.	PROPN
ejpam-5281	135	1	3	3	X
ejpam-5281	135	2	.	.	X
ejpam-5281	135	3	conclusion	conclusion	NOUN
ejpam-5281	135	4	in	in	ADP
ejpam-5281	135	5	this	this	DET
ejpam-5281	135	6	paper	paper	NOUN
ejpam-5281	135	7	we	we	PRON
ejpam-5281	135	8	generalize	generalize	VERB
ejpam-5281	135	9	the	the	DET
ejpam-5281	135	10	riesz	riesz	NOUN
ejpam-5281	135	11	theorem	theorem	NOUN
ejpam-5281	135	12	for	for	ADP
ejpam-5281	135	13	harmonic	harmonic	ADJ
ejpam-5281	135	14	quasiregular	quasiregular	ADJ
ejpam-5281	135	15	mappings	mapping	NOUN
ejpam-5281	135	16	for	for	ADP
ejpam-5281	135	17	a	a	DET
ejpam-5281	135	18	special	special	ADJ
ejpam-5281	135	19	case	case	NOUN
ejpam-5281	135	20	in	in	ADP
ejpam-5281	135	21	the	the	DET
ejpam-5281	135	22	unit	unit	NOUN
ejpam-5281	135	23	disc	disc	NOUN
ejpam-5281	135	24	.	.	PUNCT
ejpam-5281	136	1	this	this	DET
ejpam-5281	136	2	result	result	NOUN
ejpam-5281	136	3	is	be	AUX
ejpam-5281	136	4	given	give	VERB
ejpam-5281	136	5	thought	thought	NOUN
ejpam-5281	136	6	theorem	theorem	VERB
ejpam-5281	136	7	1	1	NUM
ejpam-5281	136	8	.	.	PUNCT
ejpam-5281	137	1	in	in	ADP
ejpam-5281	137	2	order	order	NOUN
ejpam-5281	137	3	to	to	ADP
ejpam-5281	137	4	proving	prove	VERB
ejpam-5281	137	5	this	this	DET
ejpam-5281	137	6	result	result	NOUN
ejpam-5281	137	7	we	we	PRON
ejpam-5281	137	8	use	use	VERB
ejpam-5281	137	9	lagrange	lagrange	NOUN
ejpam-5281	137	10	multipliers	multiplier	NOUN
ejpam-5281	137	11	.	.	PUNCT
ejpam-5281	138	1	probably	probably	ADV
ejpam-5281	138	2	this	this	DET
ejpam-5281	138	3	method	method	NOUN
ejpam-5281	138	4	can	can	AUX
ejpam-5281	138	5	be	be	AUX
ejpam-5281	138	6	used	use	VERB
ejpam-5281	138	7	to	to	PART
ejpam-5281	138	8	prove	prove	VERB
ejpam-5281	138	9	also	also	ADV
ejpam-5281	138	10	for	for	ADP
ejpam-5281	138	11	other	other	ADJ
ejpam-5281	138	12	cases	case	NOUN
ejpam-5281	138	13	,	,	PUNCT
ejpam-5281	138	14	to	to	PART
ejpam-5281	138	15	make	make	VERB
ejpam-5281	138	16	a	a	DET
ejpam-5281	138	17	generalization	generalization	NOUN
ejpam-5281	138	18	of	of	ADP
ejpam-5281	138	19	riesz	riesz	PROPN
ejpam-5281	138	20	theorem	theorem	VERB
ejpam-5281	138	21	.	.	PUNCT
ejpam-5281	139	1	moreover	moreover	ADV
ejpam-5281	139	2	,	,	PUNCT
ejpam-5281	139	3	thought	thought	NOUN
ejpam-5281	139	4	theorem	theorem	ADJ
ejpam-5281	139	5	2	2	NUM
ejpam-5281	139	6	and	and	CCONJ
ejpam-5281	139	7	3	3	NUM
ejpam-5281	139	8	,	,	PUNCT
ejpam-5281	139	9	we	we	PRON
ejpam-5281	139	10	prove	prove	VERB
ejpam-5281	139	11	another	another	DET
ejpam-5281	139	12	variant	variant	ADJ
ejpam-5281	139	13	forms	form	NOUN
ejpam-5281	139	14	of	of	ADP
ejpam-5281	139	15	riesz	riesz	NOUN
ejpam-5281	139	16	inequality	inequality	NOUN
ejpam-5281	139	17	for	for	ADP
ejpam-5281	139	18	harmonic	harmonic	ADJ
ejpam-5281	139	19	quasiregular	quasiregular	ADJ
ejpam-5281	139	20	functions	function	NOUN
ejpam-5281	139	21	.	.	PUNCT
ejpam-5281	140	1	references	reference	NOUN
ejpam-5281	140	2	[	[	X
ejpam-5281	140	3	1	1	X
ejpam-5281	140	4	]	]	PUNCT
ejpam-5281	140	5	e.	e.	PROPN
ejpam-5281	140	6	f.	f.	PROPN
ejpam-5281	140	7	beckenbach	beckenbach	PROPN
ejpam-5281	140	8	.	.	PUNCT
ejpam-5281	141	1	on	on	ADP
ejpam-5281	141	2	a	a	DET
ejpam-5281	141	3	theorem	theorem	NOUN
ejpam-5281	141	4	of	of	ADP
ejpam-5281	141	5	fejér	fejér	NOUN
ejpam-5281	141	6	and	and	CCONJ
ejpam-5281	141	7	riesz	riesz	NOUN
ejpam-5281	141	8	.	.	PUNCT
ejpam-5281	142	1	j.	j.	PROPN
ejpam-5281	142	2	london	london	PROPN
ejpam-5281	142	3	math	math	PROPN
ejpam-5281	142	4	.	.	PUNCT
ejpam-5281	143	1	soc	soc	PROPN
ejpam-5281	143	2	.	.	PROPN
ejpam-5281	143	3	,	,	PUNCT
ejpam-5281	143	4	13:82–86	13:82–86	NUM
ejpam-5281	143	5	,	,	PUNCT
ejpam-5281	143	6	1938	1938	NUM
ejpam-5281	143	7	.	.	PUNCT
ejpam-5281	144	1	[	[	X
ejpam-5281	144	2	2	2	NUM
ejpam-5281	144	3	]	]	PUNCT
ejpam-5281	144	4	m.	m.	PROPN
ejpam-5281	144	5	stein	stein	PROPN
ejpam-5281	144	6	c.	c.	PROPN
ejpam-5281	144	7	efferman	efferman	PROPN
ejpam-5281	144	8	.	.	PUNCT
ejpam-5281	145	1	hp	hp	ADJ
ejpam-5281	145	2	spaces	space	NOUN
ejpam-5281	145	3	of	of	ADP
ejpam-5281	145	4	several	several	ADJ
ejpam-5281	145	5	variables	variable	NOUN
ejpam-5281	145	6	.	.	PUNCT
ejpam-5281	146	1	acta	acta	PROPN
ejpam-5281	146	2	math	math	PROPN
ejpam-5281	146	3	.	.	PUNCT
ejpam-5281	146	4	,	,	PUNCT
ejpam-5281	146	5	129:137–193	129:137–193	NUM
ejpam-5281	146	6	,	,	PUNCT
ejpam-5281	146	7	1972	1972	NUM
ejpam-5281	146	8	.	.	PUNCT
ejpam-5281	147	1	[	[	X
ejpam-5281	147	2	3	3	X
ejpam-5281	147	3	]	]	PUNCT
ejpam-5281	147	4	t.	t.	PROPN
ejpam-5281	147	5	tao	tao	PROPN
ejpam-5281	147	6	s.	s.	PROPN
ejpam-5281	147	7	wainger	wainger	PROPN
ejpam-5281	147	8	c.	c.	PROPN
ejpam-5281	147	9	efferman	efferman	PROPN
ejpam-5281	147	10	,	,	PUNCT
ejpam-5281	147	11	a.	a.	NOUN
ejpam-5281	147	12	lonescu	lonescu	PROPN
ejpam-5281	147	13	.	.	PUNCT
ejpam-5281	148	1	analysis	analysis	NOUN
ejpam-5281	148	2	and	and	CCONJ
ejpam-5281	148	3	its	its	PRON
ejpam-5281	148	4	applications	application	NOUN
ejpam-5281	148	5	:	:	PUNCT
ejpam-5281	148	6	the	the	DET
ejpam-5281	148	7	mathematical	mathematical	ADJ
ejpam-5281	148	8	work	work	NOUN
ejpam-5281	148	9	of	of	ADP
ejpam-5281	148	10	elias	elias	PROPN
ejpam-5281	148	11	stein	stein	PROPN
ejpam-5281	148	12	.	.	PUNCT
ejpam-5281	149	1	bull	bull	PROPN
ejpam-5281	149	2	.	.	PUNCT
ejpam-5281	150	1	amer	amer	PROPN
ejpam-5281	150	2	.	.	PUNCT
ejpam-5281	150	3	math	math	PROPN
ejpam-5281	150	4	.	.	PUNCT
ejpam-5281	151	1	soc	soc	PROPN
ejpam-5281	151	2	.	.	PUNCT
ejpam-5281	152	1	new	new	ADJ
ejpam-5281	152	2	ser	ser	PROPN
ejpam-5281	152	3	.	.	PROPN
ejpam-5281	152	4	,	,	PUNCT
ejpam-5281	152	5	57:523–594	57:523–594	PROPN
ejpam-5281	152	6	,	,	PUNCT
ejpam-5281	152	7	2020	2020	NUM
ejpam-5281	152	8	.	.	PUNCT
ejpam-5281	153	1	[	[	X
ejpam-5281	153	2	4	4	X
ejpam-5281	153	3	]	]	PUNCT
ejpam-5281	153	4	p.	p.	NOUN
ejpam-5281	153	5	l.	l.	PROPN
ejpam-5281	153	6	duren	duren	PROPN
ejpam-5281	153	7	.	.	PUNCT
ejpam-5281	153	8	theory	theory	NOUN
ejpam-5281	153	9	of	of	ADP
ejpam-5281	153	10	hp	hp	ADJ
ejpam-5281	153	11	spaces	space	NOUN
ejpam-5281	153	12	.	.	PUNCT
ejpam-5281	154	1	pure	pure	ADJ
ejpam-5281	154	2	and	and	CCONJ
ejpam-5281	154	3	applied	applied	ADJ
ejpam-5281	154	4	mathematics	mathematic	NOUN
ejpam-5281	154	5	,	,	PUNCT
ejpam-5281	154	6	38	38	NUM
ejpam-5281	154	7	:	:	PUNCT
ejpam-5281	154	8	xii+25	xii+25	PROPN
ejpam-5281	154	9	,	,	PUNCT
ejpam-5281	154	10	1970	1970	NUM
ejpam-5281	154	11	.	.	PUNCT
ejpam-5281	155	1	references	reference	NOUN
ejpam-5281	155	2	1496	1496	NUM
ejpam-5281	156	1	[	[	X
ejpam-5281	156	2	5	5	NUM
ejpam-5281	156	3	]	]	PUNCT
ejpam-5281	157	1	p.	p.	NOUN
ejpam-5281	157	2	l.	l.	PROPN
ejpam-5281	157	3	duren	duren	PROPN
ejpam-5281	157	4	.	.	PUNCT
ejpam-5281	158	1	harmonic	harmonic	ADJ
ejpam-5281	158	2	mappings	mapping	NOUN
ejpam-5281	158	3	in	in	ADP
ejpam-5281	158	4	the	the	DET
ejpam-5281	158	5	plane	plane	NOUN
ejpam-5281	158	6	.	.	PUNCT
ejpam-5281	159	1	cambridge	cambridge	PROPN
ejpam-5281	159	2	univ	univ	PROPN
ejpam-5281	159	3	.	.	PUNCT
ejpam-5281	160	1	press	press	PROPN
ejpam-5281	160	2	,	,	PUNCT
ejpam-5281	160	3	new	new	PROPN
ejpam-5281	160	4	york	york	PROPN
ejpam-5281	160	5	,	,	PUNCT
ejpam-5281	160	6	2004	2004	NUM
ejpam-5281	160	7	.	.	PUNCT
ejpam-5281	161	1	[	[	X
ejpam-5281	161	2	6	6	NUM
ejpam-5281	161	3	]	]	PUNCT
ejpam-5281	161	4	j.	j.	PROPN
ejpam-5281	161	5	b.	b.	PROPN
ejpam-5281	161	6	garnett	garnett	PROPN
ejpam-5281	161	7	.	.	PUNCT
ejpam-5281	162	1	bounded	bound	VERB
ejpam-5281	162	2	analytic	analytic	ADJ
ejpam-5281	162	3	functions	function	NOUN
ejpam-5281	162	4	.	.	PUNCT
ejpam-5281	163	1	springer	springer	NOUN
ejpam-5281	163	2	,	,	PUNCT
ejpam-5281	163	3	new	new	PROPN
ejpam-5281	163	4	york	york	PROPN
ejpam-5281	163	5	,	,	PUNCT
ejpam-5281	163	6	2007	2007	NUM
ejpam-5281	163	7	.	.	PUNCT
ejpam-5281	164	1	[	[	X
ejpam-5281	164	2	7	7	X
ejpam-5281	164	3	]	]	PUNCT
ejpam-5281	164	4	j.	j.	PROPN
ejpam-5281	164	5	zhu	zhu	PROPN
ejpam-5281	164	6	j.	j.	PROPN
ejpam-5281	164	7	liu	liu	PROPN
ejpam-5281	164	8	.	.	PROPN
ejpam-5281	165	1	riesz	riesz	VERB
ejpam-5281	165	2	conjugate	conjugate	ADJ
ejpam-5281	165	3	functions	function	NOUN
ejpam-5281	165	4	theorem	theorem	VERB
ejpam-5281	165	5	for	for	ADP
ejpam-5281	165	6	harmonic	harmonic	ADJ
ejpam-5281	165	7	quasiconformal	quasiconformal	ADJ
ejpam-5281	165	8	mappings	mapping	NOUN
ejpam-5281	165	9	.	.	PUNCT
ejpam-5281	166	1	advances	advance	NOUN
ejpam-5281	166	2	in	in	ADP
ejpam-5281	166	3	mathematics	mathematic	NOUN
ejpam-5281	166	4	,	,	PUNCT
ejpam-5281	166	5	434:109321	434:109321	NUM
ejpam-5281	166	6	,	,	PUNCT
ejpam-5281	166	7	2023	2023	NUM
ejpam-5281	166	8	.	.	PUNCT
ejpam-5281	167	1	[	[	X
ejpam-5281	167	2	8	8	NUM
ejpam-5281	167	3	]	]	X
ejpam-5281	167	4	p.	p.	NOUN
ejpam-5281	167	5	koskela	koskela	PROPN
ejpam-5281	167	6	k.	k.	PROPN
ejpam-5281	167	7	astala	astala	PROPN
ejpam-5281	167	8	.	.	PUNCT
ejpam-5281	168	1	hp	hp	PROPN
ejpam-5281	168	2	theory	theory	NOUN
ejpam-5281	168	3	for	for	ADP
ejpam-5281	168	4	quasiconformal	quasiconformal	ADJ
ejpam-5281	168	5	mappings	mapping	NOUN
ejpam-5281	168	6	.	.	PUNCT
ejpam-5281	169	1	pure	pure	ADJ
ejpam-5281	169	2	appl	appl	PROPN
ejpam-5281	169	3	.	.	PUNCT
ejpam-5281	169	4	math	math	PROPN
ejpam-5281	169	5	.	.	PUNCT
ejpam-5281	169	6	,	,	PUNCT
ejpam-5281	169	7	1:19–50	1:19–50	NUM
ejpam-5281	169	8	,	,	PUNCT
ejpam-5281	169	9	2011	2011	NUM
ejpam-5281	169	10	.	.	PUNCT
ejpam-5281	170	1	[	[	X
ejpam-5281	170	2	9	9	NUM
ejpam-5281	170	3	]	]	X
ejpam-5281	170	4	d.	d.	PROPN
ejpam-5281	170	5	kalaj	kalaj	PROPN
ejpam-5281	170	6	.	.	PUNCT
ejpam-5281	171	1	on	on	ADP
ejpam-5281	171	2	riesz	riesz	PROPN
ejpam-5281	171	3	type	type	NOUN
ejpam-5281	171	4	inequalities	inequality	NOUN
ejpam-5281	171	5	for	for	ADP
ejpam-5281	171	6	harmonic	harmonic	ADJ
ejpam-5281	171	7	mappings	mapping	NOUN
ejpam-5281	171	8	in	in	ADP
ejpam-5281	171	9	the	the	DET
ejpam-5281	171	10	unit	unit	NOUN
ejpam-5281	171	11	disk	disk	NOUN
ejpam-5281	171	12	.	.	PUNCT
ejpam-5281	172	1	trans	trans	PROPN
ejpam-5281	172	2	.	.	PUNCT
ejpam-5281	173	1	amer	amer	PROPN
ejpam-5281	173	2	.	.	PUNCT
ejpam-5281	173	3	math	math	PROPN
ejpam-5281	173	4	.	.	PUNCT
ejpam-5281	174	1	soc	soc	PROPN
ejpam-5281	174	2	.	.	PUNCT
ejpam-5281	174	3	,	,	PUNCT
ejpam-5281	174	4	372(6):4031–4051	372(6):4031–4051	NUM
ejpam-5281	174	5	,	,	PUNCT
ejpam-5281	174	6	2019	2019	NUM
ejpam-5281	174	7	.	.	PUNCT
ejpam-5281	175	1	[	[	X
ejpam-5281	175	2	10	10	NUM
ejpam-5281	175	3	]	]	PUNCT
ejpam-5281	175	4	s.	s.	PROPN
ejpam-5281	175	5	k.	k.	PROPN
ejpam-5281	175	6	pichorides	pichorides	PROPN
ejpam-5281	175	7	.	.	PUNCT
ejpam-5281	176	1	on	on	ADP
ejpam-5281	176	2	the	the	DET
ejpam-5281	176	3	best	good	ADJ
ejpam-5281	176	4	value	value	NOUN
ejpam-5281	176	5	of	of	ADP
ejpam-5281	176	6	the	the	DET
ejpam-5281	176	7	constants	constant	NOUN
ejpam-5281	176	8	in	in	ADP
ejpam-5281	176	9	the	the	DET
ejpam-5281	176	10	theorem	theorem	NOUN
ejpam-5281	176	11	of	of	ADP
ejpam-5281	176	12	m.	m.	NOUN
ejpam-5281	176	13	riesz	riesz	PROPN
ejpam-5281	176	14	,	,	PUNCT
ejpam-5281	176	15	zygmund	zygmund	NOUN
ejpam-5281	176	16	and	and	CCONJ
ejpam-5281	176	17	kolmogorov	kolmogorov	PROPN
ejpam-5281	176	18	.	.	PROPN
ejpam-5281	176	19	stud	stud	PROPN
ejpam-5281	176	20	.	.	PUNCT
ejpam-5281	176	21	math	math	NOUN
ejpam-5281	176	22	.	.	PUNCT
ejpam-5281	176	23	,	,	PUNCT
ejpam-5281	176	24	44:165–179	44:165–179	PROPN
ejpam-5281	176	25	,	,	PUNCT
ejpam-5281	176	26	1972	1972	NUM
ejpam-5281	176	27	.	.	PUNCT
ejpam-5281	177	1	[	[	X
ejpam-5281	177	2	11	11	NUM
ejpam-5281	177	3	]	]	PUNCT
ejpam-5281	177	4	s.	s.	PROPN
ejpam-5281	177	5	rickman	rickman	PROPN
ejpam-5281	177	6	.	.	PUNCT
ejpam-5281	178	1	quasiregular	quasiregular	ADJ
ejpam-5281	178	2	mappings	mapping	NOUN
ejpam-5281	178	3	.	.	PUNCT
ejpam-5281	179	1	springer	springer	NOUN
ejpam-5281	179	2	,	,	PUNCT
ejpam-5281	179	3	berlin	berlin	PROPN
ejpam-5281	179	4	,	,	PUNCT
ejpam-5281	179	5	1993	1993	NUM
ejpam-5281	179	6	.	.	PUNCT
ejpam-5281	180	1	[	[	X
ejpam-5281	180	2	12	12	NUM
ejpam-5281	180	3	]	]	X
ejpam-5281	180	4	w.	w.	PROPN
ejpam-5281	180	5	ramey	ramey	PROPN
ejpam-5281	180	6	s.	s.	PROPN
ejpam-5281	180	7	axler	axler	PROPN
ejpam-5281	180	8	,	,	PUNCT
ejpam-5281	180	9	p.	p.	PROPN
ejpam-5281	180	10	bourdon	bourdon	PROPN
ejpam-5281	180	11	.	.	PUNCT
ejpam-5281	181	1	harmonic	harmonic	ADJ
ejpam-5281	181	2	function	function	NOUN
ejpam-5281	181	3	theory	theory	NOUN
ejpam-5281	181	4	.	.	PUNCT
ejpam-5281	182	1	springer	springer	PROPN
ejpam-5281	182	2	verlag	verlag	PROPN
ejpam-5281	182	3	,	,	PUNCT
ejpam-5281	182	4	new	new	PROPN
ejpam-5281	182	5	york	york	PROPN
ejpam-5281	182	6	,	,	PUNCT
ejpam-5281	182	7	1992	1992	NUM
ejpam-5281	182	8	.	.	PUNCT
ejpam-5281	183	1	[	[	X
ejpam-5281	183	2	13	13	NUM
ejpam-5281	183	3	]	]	PUNCT
ejpam-5281	183	4	i.	i.	PROPN
ejpam-5281	183	5	e.	e.	PROPN
ejpam-5281	183	6	verbitsky	verbitsky	PROPN
ejpam-5281	183	7	.	.	PUNCT
ejpam-5281	184	1	esimate	esimate	NOUN
ejpam-5281	184	2	of	of	ADP
ejpam-5281	184	3	the	the	DET
ejpam-5281	184	4	norm	norm	NOUN
ejpam-5281	184	5	of	of	ADP
ejpam-5281	184	6	a	a	DET
ejpam-5281	184	7	function	function	NOUN
ejpam-5281	184	8	in	in	ADP
ejpam-5281	184	9	hardy	hardy	ADJ
ejpam-5281	184	10	space	space	NOUN
ejpam-5281	184	11	in	in	ADP
ejpam-5281	184	12	terms	term	NOUN
ejpam-5281	184	13	of	of	ADP
ejpam-5281	184	14	a	a	DET
ejpam-5281	184	15	norms	norm	NOUN
ejpam-5281	184	16	of	of	ADP
ejpam-5281	184	17	its	its	PRON
ejpam-5281	184	18	real	real	ADJ
ejpam-5281	184	19	and	and	CCONJ
ejpam-5281	184	20	imaginary	imaginary	ADJ
ejpam-5281	184	21	parts	part	NOUN
ejpam-5281	184	22	.	.	PUNCT
ejpam-5281	185	1	linear	linear	PROPN
ejpam-5281	185	2	operators	operator	NOUN
ejpam-5281	185	3	.	.	PUNCT
ejpam-5281	186	1	mat	mat	PROPN
ejpam-5281	186	2	.	.	PROPN
ejpam-5281	186	3	issled	issle	VERB
ejpam-5281	186	4	.	.	PUNCT
ejpam-5281	186	5	,	,	PUNCT
ejpam-5281	186	6	54:16–20	54:16–20	NUM
ejpam-5281	186	7	,	,	PUNCT
ejpam-5281	186	8	164–165	164–165	NUM
ejpam-5281	186	9	,	,	PUNCT
ejpam-5281	186	10	1980	1980	NUM
ejpam-5281	186	11	.	.	PUNCT
ejpam-5281	187	1	[	[	X
ejpam-5281	187	2	14	14	NUM
ejpam-5281	187	3	]	]	PUNCT
ejpam-5281	187	4	m.	m.	NOUN
ejpam-5281	187	5	vuorinen	vuorinen	NOUN
ejpam-5281	187	6	.	.	PUNCT
ejpam-5281	188	1	conformal	conformal	ADJ
ejpam-5281	188	2	geometry	geometry	NOUN
ejpam-5281	188	3	and	and	CCONJ
ejpam-5281	188	4	quasiregular	quasiregular	ADJ
ejpam-5281	188	5	mappings	mapping	NOUN
ejpam-5281	188	6	.	.	PUNCT
ejpam-5281	189	1	springer	springer	NOUN
ejpam-5281	189	2	,	,	PUNCT
ejpam-5281	189	3	berlin	berlin	PROPN
ejpam-5281	189	4	,	,	PUNCT
ejpam-5281	189	5	heidelberg	heidelberg	PROPN
ejpam-5281	189	6	,	,	PUNCT
ejpam-5281	189	7	,	,	PUNCT
ejpam-5281	189	8	1988	1988	NUM
ejpam-5281	189	9	.	.	PUNCT