id	sid	tid	token	lemma	pos
ejpam-5282	1	1	european	european	PROPN
ejpam-5282	1	2	journal	journal	PROPN
ejpam-5282	1	3	of	of	ADP
ejpam-5282	1	4	pure	pure	ADJ
ejpam-5282	1	5	and	and	CCONJ
ejpam-5282	1	6	applied	apply	VERB
ejpam-5282	1	7	mathematics	mathematic	NOUN
ejpam-5282	1	8	vol	vol	NOUN
ejpam-5282	1	9	.	.	PROPN
ejpam-5282	2	1	17	17	NUM
ejpam-5282	2	2	,	,	PUNCT
ejpam-5282	2	3	no	no	INTJ
ejpam-5282	2	4	.	.	NOUN
ejpam-5282	2	5	3	3	NUM
ejpam-5282	2	6	,	,	PUNCT
ejpam-5282	2	7	2024	2024	NUM
ejpam-5282	2	8	,	,	PUNCT
ejpam-5282	2	9	1685	1685	NUM
ejpam-5282	2	10	-	-	SYM
ejpam-5282	2	11	1690	1690	NUM
ejpam-5282	2	12	issn	issn	PROPN
ejpam-5282	2	13	1307	1307	NUM
ejpam-5282	2	14	-	-	SYM
ejpam-5282	2	15	5543	5543	NUM
ejpam-5282	2	16	–	–	PUNCT
ejpam-5282	3	1	ejpam.com	ejpam.com	X
ejpam-5282	3	2	published	publish	VERB
ejpam-5282	3	3	by	by	ADP
ejpam-5282	3	4	new	new	PROPN
ejpam-5282	3	5	york	york	PROPN
ejpam-5282	3	6	business	business	PROPN
ejpam-5282	3	7	global	global	ADJ
ejpam-5282	3	8	some	some	DET
ejpam-5282	3	9	generalization	generalization	NOUN
ejpam-5282	3	10	of	of	ADP
ejpam-5282	3	11	riesz	riesz	PROPN
ejpam-5282	3	12	type	type	NOUN
ejpam-5282	3	13	inequalities	inequality	NOUN
ejpam-5282	3	14	for	for	ADP
ejpam-5282	3	15	harmonic	harmonic	ADJ
ejpam-5282	3	16	mappings	mapping	NOUN
ejpam-5282	3	17	on	on	ADP
ejpam-5282	3	18	the	the	DET
ejpam-5282	3	19	unit	unit	NOUN
ejpam-5282	3	20	disk	disk	NOUN
ejpam-5282	3	21	elver	elver	PROPN
ejpam-5282	3	22	bajrami	bajrami	PROPN
ejpam-5282	3	23	department	department	PROPN
ejpam-5282	3	24	of	of	ADP
ejpam-5282	3	25	mathematics	mathematics	PROPN
ejpam-5282	3	26	,	,	PUNCT
ejpam-5282	3	27	university	university	PROPN
ejpam-5282	3	28	of	of	ADP
ejpam-5282	3	29	prishtina	prishtina	PROPN
ejpam-5282	3	30	,	,	PUNCT
ejpam-5282	3	31	mother	mother	NOUN
ejpam-5282	3	32	teresa	teresa	PROPN
ejpam-5282	3	33	,	,	PUNCT
ejpam-5282	3	34	no	no	INTJ
ejpam-5282	3	35	.	.	NOUN
ejpam-5282	3	36	5	5	NUM
ejpam-5282	3	37	,	,	PUNCT
ejpam-5282	3	38	10000	10000	NUM
ejpam-5282	3	39	,	,	PUNCT
ejpam-5282	3	40	prishtina	prishtina	PROPN
ejpam-5282	3	41	,	,	PUNCT
ejpam-5282	3	42	kosovo	kosovo	PROPN
ejpam-5282	3	43	abstract	abstract	PROPN
ejpam-5282	3	44	.	.	PUNCT
ejpam-5282	4	1	in	in	ADP
ejpam-5282	4	2	this	this	DET
ejpam-5282	4	3	paper	paper	NOUN
ejpam-5282	4	4	a	a	DET
ejpam-5282	4	5	new	new	ADJ
ejpam-5282	4	6	generalized	generalized	ADJ
ejpam-5282	4	7	norm	norm	NOUN
ejpam-5282	4	8	is	be	AUX
ejpam-5282	4	9	defined	define	VERB
ejpam-5282	4	10	and	and	CCONJ
ejpam-5282	4	11	riesz	riesz	NOUN
ejpam-5282	4	12	type	type	NOUN
ejpam-5282	4	13	inequalities	inequality	NOUN
ejpam-5282	4	14	for	for	ADP
ejpam-5282	4	15	harmonic	harmonic	ADJ
ejpam-5282	4	16	functions	function	NOUN
ejpam-5282	4	17	on	on	ADP
ejpam-5282	4	18	the	the	DET
ejpam-5282	4	19	unit	unit	NOUN
ejpam-5282	4	20	disk	disk	NOUN
ejpam-5282	4	21	are	be	AUX
ejpam-5282	4	22	discussed	discuss	VERB
ejpam-5282	4	23	by	by	ADP
ejpam-5282	4	24	applying	apply	VERB
ejpam-5282	4	25	it	it	PRON
ejpam-5282	4	26	.	.	PUNCT
ejpam-5282	5	1	also	also	ADV
ejpam-5282	5	2	sharp	sharp	ADJ
ejpam-5282	5	3	constants	constant	NOUN
ejpam-5282	5	4	are	be	AUX
ejpam-5282	5	5	obtained	obtain	VERB
ejpam-5282	5	6	for	for	ADP
ejpam-5282	5	7	certain	certain	ADJ
ejpam-5282	5	8	special	special	ADJ
ejpam-5282	5	9	values	value	NOUN
ejpam-5282	5	10	considered	consider	VERB
ejpam-5282	5	11	in	in	ADP
ejpam-5282	5	12	the	the	DET
ejpam-5282	5	13	reverse	reverse	ADJ
ejpam-5282	5	14	case	case	NOUN
ejpam-5282	5	15	of	of	ADP
ejpam-5282	5	16	the	the	DET
ejpam-5282	5	17	standard	standard	ADJ
ejpam-5282	5	18	riesz	riesz	NOUN
ejpam-5282	5	19	inequality	inequality	NOUN
ejpam-5282	5	20	.	.	PUNCT
ejpam-5282	6	1	2020	2020	NUM
ejpam-5282	6	2	mathematics	mathematic	NOUN
ejpam-5282	6	3	subject	subject	NOUN
ejpam-5282	6	4	classifications	classification	NOUN
ejpam-5282	6	5	:	:	PUNCT
ejpam-5282	6	6	30h05	30h05	NUM
ejpam-5282	6	7	,	,	PUNCT
ejpam-5282	6	8	30h10	30h10	NUM
ejpam-5282	6	9	,	,	PUNCT
ejpam-5282	6	10	47b06	47b06	NUM
ejpam-5282	6	11	key	key	ADJ
ejpam-5282	6	12	words	word	NOUN
ejpam-5282	6	13	and	and	CCONJ
ejpam-5282	6	14	phrases	phrase	NOUN
ejpam-5282	6	15	:	:	PUNCT
ejpam-5282	6	16	harmonic	harmonic	ADJ
ejpam-5282	6	17	functions	function	NOUN
ejpam-5282	6	18	,	,	PUNCT
ejpam-5282	6	19	riesz	riesz	NOUN
ejpam-5282	6	20	inequality	inequality	NOUN
ejpam-5282	6	21	,	,	PUNCT
ejpam-5282	6	22	isoperimetric	isoperimetric	ADJ
ejpam-5282	6	23	inequality	inequality	NOUN
ejpam-5282	6	24	1	1	NUM
ejpam-5282	6	25	.	.	PUNCT
ejpam-5282	7	1	introduction	introduction	NOUN
ejpam-5282	7	2	and	and	CCONJ
ejpam-5282	7	3	statement	statement	NOUN
ejpam-5282	7	4	of	of	ADP
ejpam-5282	7	5	main	main	ADJ
ejpam-5282	7	6	results	result	NOUN
ejpam-5282	7	7	let	let	VERB
ejpam-5282	7	8	u	u	PRON
ejpam-5282	7	9	=	=	PUNCT
ejpam-5282	7	10	{	{	PUNCT
ejpam-5282	7	11	z	z	PROPN
ejpam-5282	7	12	∈	∈	PROPN
ejpam-5282	7	13	c	c	NOUN
ejpam-5282	7	14	:	:	PUNCT
ejpam-5282	7	15	|z|	|z|	NOUN
ejpam-5282	7	16	<	<	X
ejpam-5282	7	17	1	1	NUM
ejpam-5282	7	18	}	}	PUNCT
ejpam-5282	7	19	be	be	AUX
ejpam-5282	7	20	the	the	DET
ejpam-5282	7	21	unit	unit	NOUN
ejpam-5282	7	22	disk	disk	NOUN
ejpam-5282	7	23	and	and	CCONJ
ejpam-5282	7	24	let	let	VERB
ejpam-5282	7	25	t	t	NOUN
ejpam-5282	7	26	=	=	SYM
ejpam-5282	7	27	{	{	PUNCT
ejpam-5282	7	28	z	z	NOUN
ejpam-5282	7	29	∈	∈	PROPN
ejpam-5282	7	30	c	c	NOUN
ejpam-5282	7	31	:	:	PUNCT
ejpam-5282	7	32	|z|	|z|	NOUN
ejpam-5282	7	33	=	=	SYM
ejpam-5282	7	34	1	1	X
ejpam-5282	7	35	}	}	PUNCT
ejpam-5282	7	36	be	be	AUX
ejpam-5282	7	37	the	the	DET
ejpam-5282	7	38	unit	unit	NOUN
ejpam-5282	7	39	circle	circle	NOUN
ejpam-5282	7	40	in	in	ADP
ejpam-5282	7	41	the	the	DET
ejpam-5282	7	42	complex	complex	ADJ
ejpam-5282	7	43	plane	plane	NOUN
ejpam-5282	7	44	.	.	PUNCT
ejpam-5282	8	1	for	for	ADP
ejpam-5282	8	2	p	p	PROPN
ejpam-5282	8	3	>	>	X
ejpam-5282	8	4	1	1	NUM
ejpam-5282	8	5	we	we	PRON
ejpam-5282	8	6	define	define	VERB
ejpam-5282	8	7	the	the	DET
ejpam-5282	8	8	hardy	hardy	ADJ
ejpam-5282	8	9	class	class	NOUN
ejpam-5282	8	10	hp	hp	NOUN
ejpam-5282	8	11	as	as	ADP
ejpam-5282	8	12	the	the	DET
ejpam-5282	8	13	class	class	NOUN
ejpam-5282	8	14	of	of	ADP
ejpam-5282	8	15	harmonic	harmonic	ADJ
ejpam-5282	8	16	mappings	mapping	NOUN
ejpam-5282	9	1	f	f	NOUN
ejpam-5282	9	2	=	=	SYM
ejpam-5282	9	3	g	g	PROPN
ejpam-5282	9	4	+	+	CCONJ
ejpam-5282	9	5	h	h	NOUN
ejpam-5282	9	6	,	,	PUNCT
ejpam-5282	9	7	where	where	SCONJ
ejpam-5282	9	8	h	h	NOUN
ejpam-5282	9	9	and	and	CCONJ
ejpam-5282	9	10	g	g	PROPN
ejpam-5282	9	11	are	be	AUX
ejpam-5282	9	12	holomorphic	holomorphic	ADJ
ejpam-5282	9	13	mappings	mapping	NOUN
ejpam-5282	9	14	defined	define	VERB
ejpam-5282	9	15	on	on	ADP
ejpam-5282	9	16	unit	unit	NOUN
ejpam-5282	9	17	disk	disk	NOUN
ejpam-5282	9	18	u	u	PROPN
ejpam-5282	9	19	⊂	⊂	PROPN
ejpam-5282	9	20	c.	c.	PROPN
ejpam-5282	9	21	norm	norm	NOUN
ejpam-5282	9	22	in	in	ADP
ejpam-5282	9	23	this	this	DET
ejpam-5282	9	24	space	space	NOUN
ejpam-5282	9	25	is	be	AUX
ejpam-5282	9	26	defined	define	VERB
ejpam-5282	9	27	as	as	ADP
ejpam-5282	9	28	:	:	PUNCT
ejpam-5282	9	29	||f	||f	NOUN
ejpam-5282	9	30	||p	||p	NOUN
ejpam-5282	9	31	=	=	SYM
ejpam-5282	9	32	||f	||f	NOUN
ejpam-5282	9	33	||hp	||hp	NUM
ejpam-5282	9	34	=	=	NOUN
ejpam-5282	9	35	sup	sup	NOUN
ejpam-5282	9	36	0	0	NUM
ejpam-5282	9	37	<	<	NOUN
ejpam-5282	9	38	r<1	r<1	NOUN
ejpam-5282	9	39	mp(f	mp(f	NOUN
ejpam-5282	9	40	,	,	PUNCT
ejpam-5282	9	41	r	r	NOUN
ejpam-5282	9	42	)	)	PUNCT
ejpam-5282	9	43	<	<	X
ejpam-5282	9	44	∞	∞	PROPN
ejpam-5282	9	45	,	,	PUNCT
ejpam-5282	9	46	where	where	SCONJ
ejpam-5282	9	47	mp(f	mp(f	NOUN
ejpam-5282	9	48	,	,	PUNCT
ejpam-5282	9	49	r	r	NOUN
ejpam-5282	9	50	)	)	PUNCT
ejpam-5282	9	51	=	=	SYM
ejpam-5282	10	1	(	(	PUNCT
ejpam-5282	10	2	∫	∫	PROPN
ejpam-5282	10	3	t	t	PROPN
ejpam-5282	10	4	|f(rζ)|pdσ(ζ	|f(rζ)|pdσ(ζ	NUM
ejpam-5282	10	5	)	)	PUNCT
ejpam-5282	10	6	)	)	PUNCT
ejpam-5282	10	7	1	1	X
ejpam-5282	10	8	/	/	SYM
ejpam-5282	10	9	p	p	NOUN
ejpam-5282	10	10	.	.	PUNCT
ejpam-5282	11	1	here	here	ADV
ejpam-5282	11	2	σ	σ	PROPN
ejpam-5282	11	3	is	be	AUX
ejpam-5282	11	4	probability	probability	NOUN
ejpam-5282	11	5	measure	measure	NOUN
ejpam-5282	11	6	on	on	ADP
ejpam-5282	11	7	t.	t.	PROPN
ejpam-5282	11	8	with	with	ADP
ejpam-5282	11	9	hp	hp	PROPN
ejpam-5282	11	10	,	,	PUNCT
ejpam-5282	11	11	we	we	PRON
ejpam-5282	11	12	denote	denote	VERB
ejpam-5282	11	13	the	the	DET
ejpam-5282	11	14	subclass	subclass	NOUN
ejpam-5282	11	15	of	of	ADP
ejpam-5282	11	16	holomorphic	holomorphic	ADJ
ejpam-5282	11	17	mappings	mapping	NOUN
ejpam-5282	11	18	that	that	PRON
ejpam-5282	11	19	belong	belong	VERB
ejpam-5282	11	20	to	to	ADP
ejpam-5282	11	21	the	the	DET
ejpam-5282	11	22	class	class	NOUN
ejpam-5282	11	23	hp	hp	PROPN
ejpam-5282	11	24	.	.	PROPN
ejpam-5282	12	1	for	for	ADP
ejpam-5282	12	2	the	the	DET
ejpam-5282	12	3	theory	theory	NOUN
ejpam-5282	12	4	of	of	ADP
ejpam-5282	12	5	hardy	hardy	ADJ
ejpam-5282	12	6	spaces	space	NOUN
ejpam-5282	12	7	in	in	ADP
ejpam-5282	12	8	the	the	DET
ejpam-5282	12	9	unit	unit	NOUN
ejpam-5282	12	10	disk	disk	NOUN
ejpam-5282	12	11	we	we	PRON
ejpam-5282	12	12	refer	refer	VERB
ejpam-5282	12	13	to	to	ADP
ejpam-5282	12	14	[	[	X
ejpam-5282	12	15	11	11	NUM
ejpam-5282	12	16	]	]	PUNCT
ejpam-5282	12	17	,	,	PUNCT
ejpam-5282	12	18	[	[	X
ejpam-5282	12	19	7	7	X
ejpam-5282	12	20	]	]	PUNCT
ejpam-5282	12	21	and	and	CCONJ
ejpam-5282	12	22	[	[	X
ejpam-5282	12	23	8	8	NUM
ejpam-5282	12	24	]	]	PUNCT
ejpam-5282	12	25	.	.	PUNCT
ejpam-5282	13	1	based	base	VERB
ejpam-5282	13	2	on	on	ADP
ejpam-5282	13	3	results	result	NOUN
ejpam-5282	13	4	of	of	ADP
ejpam-5282	13	5	verbitsky	verbitsky	NOUN
ejpam-5282	13	6	[	[	X
ejpam-5282	13	7	12	12	NUM
ejpam-5282	13	8	]	]	PUNCT
ejpam-5282	13	9	,	,	PUNCT
ejpam-5282	13	10	kalaj	kalaj	NOUN
ejpam-5282	13	11	in	in	ADP
ejpam-5282	13	12	[	[	PUNCT
ejpam-5282	13	13	9	9	NUM
ejpam-5282	13	14	]	]	PUNCT
ejpam-5282	13	15	proved	prove	VERB
ejpam-5282	13	16	these	these	DET
ejpam-5282	13	17	inequalities	inequality	NOUN
ejpam-5282	13	18	|||f	|||f	NOUN
ejpam-5282	13	19	|||p	|||p	PROPN
ejpam-5282	13	20	≤	≤	ADJ
ejpam-5282	13	21	ap||f	ap||f	ADJ
ejpam-5282	13	22	||p	||p	NOUN
ejpam-5282	13	23	,	,	PUNCT
ejpam-5282	13	24	||f	||f	ADJ
ejpam-5282	13	25	||p	||p	NOUN
ejpam-5282	13	26	≤	≤	NUM
ejpam-5282	13	27	bp|||f	bp|||f	PROPN
ejpam-5282	13	28	|||p	|||p	NOUN
ejpam-5282	13	29	,	,	PUNCT
ejpam-5282	13	30	doi	doi	PROPN
ejpam-5282	13	31	:	:	PUNCT
ejpam-5282	13	32	https://doi.org/10.29020/nybg.ejpam.v17i3.5282	https://doi.org/10.29020/nybg.ejpam.v17i3.5282	PROPN
ejpam-5282	13	33	email	email	NOUN
ejpam-5282	13	34	address	address	NOUN
ejpam-5282	13	35	:	:	PUNCT
ejpam-5282	13	36	elver.bajrami@uni-pr.edu	elver.bajrami@uni-pr.edu	PROPN
ejpam-5282	13	37	(	(	PUNCT
ejpam-5282	13	38	e.	e.	PROPN
ejpam-5282	13	39	bajrami	bajrami	PROPN
ejpam-5282	13	40	)	)	PUNCT
ejpam-5282	13	41	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5282	13	42	1685	1685	NUM
ejpam-5282	13	43	©	©	ADP
ejpam-5282	13	44	2024	2024	NUM
ejpam-5282	13	45	ejpam	ejpam	NOUN
ejpam-5282	13	46	all	all	DET
ejpam-5282	13	47	rights	right	NOUN
ejpam-5282	13	48	reserved	reserve	VERB
ejpam-5282	13	49	.	.	PUNCT
ejpam-5282	14	1	e.	e.	PROPN
ejpam-5282	14	2	bajrami	bajrami	PROPN
ejpam-5282	14	3	/	/	SYM
ejpam-5282	14	4	eur	eur	PROPN
ejpam-5282	14	5	.	.	PUNCT
ejpam-5282	15	1	j.	j.	PROPN
ejpam-5282	15	2	pure	pure	PROPN
ejpam-5282	15	3	appl	appl	PROPN
ejpam-5282	15	4	.	.	PROPN
ejpam-5282	15	5	math	math	PROPN
ejpam-5282	15	6	,	,	PUNCT
ejpam-5282	15	7	17	17	NUM
ejpam-5282	15	8	(	(	PUNCT
ejpam-5282	15	9	3	3	NUM
ejpam-5282	15	10	)	)	PUNCT
ejpam-5282	15	11	(	(	PUNCT
ejpam-5282	15	12	2024	2024	NUM
ejpam-5282	15	13	)	)	PUNCT
ejpam-5282	15	14	,	,	PUNCT
ejpam-5282	15	15	1685	1685	NUM
ejpam-5282	15	16	-	-	SYM
ejpam-5282	15	17	1690	1690	NUM
ejpam-5282	15	18	1686	1686	NUM
ejpam-5282	15	19	where	where	SCONJ
ejpam-5282	15	20	ap	ap	PROPN
ejpam-5282	15	21	=	=	PRON
ejpam-5282	16	1	(	(	PUNCT
ejpam-5282	16	2	1−	1−	NUM
ejpam-5282	16	3	|	|	INTJ
ejpam-5282	16	4	cos	cos	INTJ
ejpam-5282	16	5	p	p	PROPN
ejpam-5282	16	6	π	π	PROPN
ejpam-5282	16	7	|	|	ADV
ejpam-5282	16	8	)	)	PUNCT
ejpam-5282	16	9	−1/2	−1/2	ADJ
ejpam-5282	16	10	,	,	PUNCT
ejpam-5282	16	11	bp	bp	PROPN
ejpam-5282	16	12	=	=	SYM
ejpam-5282	16	13	√	√	PROPN
ejpam-5282	16	14	2	2	NUM
ejpam-5282	16	15	cos	cos	ADP
ejpam-5282	16	16	π	π	PROPN
ejpam-5282	16	17	2p	2p	NOUN
ejpam-5282	16	18	and	and	CCONJ
ejpam-5282	16	19	|||f	|||f	NOUN
ejpam-5282	16	20	|||p	|||p	NOUN
ejpam-5282	17	1	=	=	SYM
ejpam-5282	17	2	sup	sup	NOUN
ejpam-5282	17	3	0	0	NUM
ejpam-5282	17	4	<	<	NOUN
ejpam-5282	17	5	r<1	r<1	NOUN
ejpam-5282	17	6	(	(	PUNCT
ejpam-5282	17	7	∫	∫	PROPN
ejpam-5282	17	8	t	t	PROPN
ejpam-5282	17	9	(	(	PUNCT
ejpam-5282	17	10	|g(z)|2	|g(z)|2	X
ejpam-5282	17	11	+	+	CCONJ
ejpam-5282	17	12	|h(z)|2)p/2dσ	|h(z)|2)p/2dσ	NOUN
ejpam-5282	17	13	)	)	PUNCT
ejpam-5282	17	14	1	1	X
ejpam-5282	17	15	/	/	SYM
ejpam-5282	17	16	p	p	NOUN
ejpam-5282	17	17	.	.	PUNCT
ejpam-5282	18	1	these	these	DET
ejpam-5282	18	2	results	result	NOUN
ejpam-5282	18	3	are	be	AUX
ejpam-5282	18	4	used	use	VERB
ejpam-5282	18	5	to	to	PART
ejpam-5282	18	6	prove	prove	VERB
ejpam-5282	18	7	and	and	CCONJ
ejpam-5282	18	8	improve	improve	VERB
ejpam-5282	18	9	some	some	DET
ejpam-5282	18	10	results	result	NOUN
ejpam-5282	18	11	about	about	ADP
ejpam-5282	18	12	isoperimetric	isoperimetric	ADJ
ejpam-5282	18	13	inequalities	inequality	NOUN
ejpam-5282	18	14	which	which	PRON
ejpam-5282	18	15	are	be	AUX
ejpam-5282	18	16	given	give	VERB
ejpam-5282	18	17	in	in	ADP
ejpam-5282	18	18	[	[	X
ejpam-5282	18	19	2	2	NUM
ejpam-5282	18	20	]	]	PUNCT
ejpam-5282	18	21	and	and	CCONJ
ejpam-5282	18	22	generalized	generalize	VERB
ejpam-5282	18	23	in	in	ADP
ejpam-5282	18	24	[	[	X
ejpam-5282	18	25	6	6	NUM
ejpam-5282	18	26	]	]	PUNCT
ejpam-5282	18	27	for	for	ADP
ejpam-5282	18	28	a	a	DET
ejpam-5282	18	29	special	special	ADJ
ejpam-5282	18	30	case	case	NOUN
ejpam-5282	18	31	.	.	PUNCT
ejpam-5282	19	1	also	also	ADV
ejpam-5282	19	2	,	,	PUNCT
ejpam-5282	19	3	this	this	DET
ejpam-5282	19	4	inequality	inequality	NOUN
ejpam-5282	19	5	was	be	AUX
ejpam-5282	19	6	generalized	generalize	VERB
ejpam-5282	19	7	in	in	ADP
ejpam-5282	19	8	several	several	ADJ
ejpam-5282	19	9	directions	direction	NOUN
ejpam-5282	19	10	.	.	PUNCT
ejpam-5282	20	1	let	let	VERB
ejpam-5282	20	2	us	we	PRON
ejpam-5282	20	3	mention	mention	VERB
ejpam-5282	20	4	beckenbach	beckenbach	NOUN
ejpam-5282	20	5	’s	’s	PART
ejpam-5282	20	6	results	result	NOUN
ejpam-5282	20	7	:	:	PUNCT
ejpam-5282	20	8	the	the	DET
ejpam-5282	20	9	same	same	ADJ
ejpam-5282	20	10	inequality	inequality	NOUN
ejpam-5282	20	11	holds	hold	VERB
ejpam-5282	20	12	where	where	SCONJ
ejpam-5282	20	13	in	in	ADP
ejpam-5282	20	14	place	place	NOUN
ejpam-5282	20	15	of	of	ADP
ejpam-5282	20	16	|f	|f	PROPN
ejpam-5282	20	17	|p	|p	X
ejpam-5282	20	18	we	we	PRON
ejpam-5282	20	19	have	have	VERB
ejpam-5282	20	20	a	a	DET
ejpam-5282	20	21	positive	positive	ADJ
ejpam-5282	20	22	logarithmically	logarithmically	ADV
ejpam-5282	20	23	subharmonic	subharmonic	ADJ
ejpam-5282	20	24	function	function	NOUN
ejpam-5282	20	25	.	.	PUNCT
ejpam-5282	21	1	this	this	DET
ejpam-5282	21	2	kind	kind	NOUN
ejpam-5282	21	3	of	of	ADP
ejpam-5282	21	4	generalizations	generalization	NOUN
ejpam-5282	21	5	can	can	AUX
ejpam-5282	21	6	be	be	AUX
ejpam-5282	21	7	found	find	VERB
ejpam-5282	21	8	in	in	ADP
ejpam-5282	21	9	[	[	X
ejpam-5282	21	10	3	3	NUM
ejpam-5282	21	11	]	]	PUNCT
ejpam-5282	21	12	.	.	PUNCT
ejpam-5282	22	1	we	we	PRON
ejpam-5282	22	2	refer	refer	VERB
ejpam-5282	22	3	interested	interested	ADJ
ejpam-5282	22	4	readers	reader	NOUN
ejpam-5282	22	5	to	to	ADP
ejpam-5282	22	6	[	[	X
ejpam-5282	22	7	4	4	NUM
ejpam-5282	22	8	]	]	PUNCT
ejpam-5282	22	9	,	,	PUNCT
ejpam-5282	22	10	[	[	X
ejpam-5282	22	11	5	5	NUM
ejpam-5282	22	12	]	]	PUNCT
ejpam-5282	22	13	and	and	CCONJ
ejpam-5282	22	14	[	[	X
ejpam-5282	22	15	9	9	NUM
ejpam-5282	22	16	]	]	PUNCT
ejpam-5282	22	17	.	.	PUNCT
ejpam-5282	23	1	the	the	DET
ejpam-5282	23	2	following	follow	VERB
ejpam-5282	23	3	definition	definition	NOUN
ejpam-5282	23	4	for	for	ADP
ejpam-5282	23	5	a	a	DET
ejpam-5282	23	6	generalized	generalized	ADJ
ejpam-5282	23	7	norm	norm	NOUN
ejpam-5282	23	8	of	of	ADP
ejpam-5282	23	9	this	this	DET
ejpam-5282	23	10	kind	kind	NOUN
ejpam-5282	23	11	is	be	AUX
ejpam-5282	23	12	next	next	ADJ
ejpam-5282	23	13	given	give	VERB
ejpam-5282	23	14	:	:	PUNCT
ejpam-5282	23	15	for	for	ADP
ejpam-5282	23	16	harmonic	harmonic	ADJ
ejpam-5282	23	17	mapping	mapping	NOUN
ejpam-5282	23	18	f	f	NOUN
ejpam-5282	23	19	=	=	SYM
ejpam-5282	23	20	g	g	PROPN
ejpam-5282	23	21	+	+	CCONJ
ejpam-5282	23	22	h̄	h̄	X
ejpam-5282	23	23	∈	∈	PROPN
ejpam-5282	23	24	hp	hp	PROPN
ejpam-5282	23	25	,	,	PUNCT
ejpam-5282	23	26	(	(	PUNCT
ejpam-5282	23	27	hg)(0	hg)(0	NOUN
ejpam-5282	23	28	)	)	PUNCT
ejpam-5282	23	29	=	=	SYM
ejpam-5282	23	30	0	0	NUM
ejpam-5282	23	31	,	,	PUNCT
ejpam-5282	23	32	q	q	ADJ
ejpam-5282	23	33	>	>	X
ejpam-5282	23	34	1	1	NUM
ejpam-5282	23	35	we	we	PRON
ejpam-5282	23	36	define	define	VERB
ejpam-5282	23	37	new	new	ADJ
ejpam-5282	23	38	norm	norm	NOUN
ejpam-5282	23	39	|||	|||	NOUN
ejpam-5282	23	40	·	·	PUNCT
ejpam-5282	23	41	|||p	|||p	NOUN
ejpam-5282	23	42	,	,	PUNCT
ejpam-5282	23	43	q	q	NOUN
ejpam-5282	23	44	=	=	PUNCT
ejpam-5282	23	45	|||	|||	NOUN
ejpam-5282	23	46	·	·	PUNCT
ejpam-5282	23	47	|||hp	|||hp	NOUN
ejpam-5282	23	48	as	as	SCONJ
ejpam-5282	23	49	follows	follow	VERB
ejpam-5282	23	50	|||f	|||f	NOUN
ejpam-5282	23	51	|||p	|||p	NOUN
ejpam-5282	23	52	,	,	PUNCT
ejpam-5282	23	53	q	q	NOUN
ejpam-5282	24	1	=	=	PUNCT
ejpam-5282	24	2	sup	sup	NOUN
ejpam-5282	24	3	0	0	NUM
ejpam-5282	24	4	<	<	NOUN
ejpam-5282	24	5	r<1	r<1	NOUN
ejpam-5282	24	6	(	(	PUNCT
ejpam-5282	24	7	∫	∫	PROPN
ejpam-5282	24	8	t	t	PROPN
ejpam-5282	24	9	(	(	PUNCT
ejpam-5282	24	10	|g(rz)|q	|g(rz)|q	PROPN
ejpam-5282	24	11	+	+	CCONJ
ejpam-5282	24	12	|h(rz)|q)p	|h(rz)|q)p	PROPN
ejpam-5282	24	13	/	/	SYM
ejpam-5282	24	14	qdσ(z	qdσ(z	NOUN
ejpam-5282	24	15	)	)	PUNCT
ejpam-5282	24	16	)	)	PUNCT
ejpam-5282	24	17	1	1	X
ejpam-5282	24	18	/	/	SYM
ejpam-5282	24	19	p	p	NOUN
ejpam-5282	24	20	.	.	PUNCT
ejpam-5282	25	1	or	or	CCONJ
ejpam-5282	25	2	using	use	VERB
ejpam-5282	25	3	limr→1	limr→1	PROPN
ejpam-5282	25	4	in	in	ADP
ejpam-5282	25	5	last	last	ADJ
ejpam-5282	25	6	expression	expression	NOUN
ejpam-5282	25	7	we	we	PRON
ejpam-5282	25	8	have	have	VERB
ejpam-5282	25	9	that	that	DET
ejpam-5282	25	10	|||f	|||f	NOUN
ejpam-5282	25	11	|||p	|||p	NOUN
ejpam-5282	25	12	,	,	PUNCT
ejpam-5282	25	13	q	q	X
ejpam-5282	25	14	=	=	SYM
ejpam-5282	25	15	(	(	PUNCT
ejpam-5282	25	16	∫	∫	PROPN
ejpam-5282	25	17	t	t	PROPN
ejpam-5282	25	18	(	(	PUNCT
ejpam-5282	25	19	|g(z)|q	|g(z)|q	PROPN
ejpam-5282	25	20	+	+	CCONJ
ejpam-5282	25	21	|h(z)|q)p	|h(z)|q)p	NOUN
ejpam-5282	25	22	/	/	SYM
ejpam-5282	25	23	qdσ(z	qdσ(z	NOUN
ejpam-5282	25	24	)	)	PUNCT
ejpam-5282	25	25	)	)	PUNCT
ejpam-5282	26	1	1	1	X
ejpam-5282	26	2	/	/	SYM
ejpam-5282	26	3	p	p	NOUN
ejpam-5282	26	4	.	.	PUNCT
ejpam-5282	27	1	we	we	PRON
ejpam-5282	27	2	see	see	VERB
ejpam-5282	27	3	that	that	SCONJ
ejpam-5282	27	4	the	the	DET
ejpam-5282	27	5	norm	norm	NOUN
ejpam-5282	27	6	defined	define	VERB
ejpam-5282	27	7	in	in	ADP
ejpam-5282	27	8	[	[	X
ejpam-5282	27	9	9	9	NUM
ejpam-5282	27	10	]	]	PUNCT
ejpam-5282	27	11	is	be	AUX
ejpam-5282	27	12	a	a	DET
ejpam-5282	27	13	special	special	ADJ
ejpam-5282	27	14	case	case	NOUN
ejpam-5282	27	15	where	where	SCONJ
ejpam-5282	27	16	q	q	NOUN
ejpam-5282	27	17	=	=	NOUN
ejpam-5282	27	18	2	2	X
ejpam-5282	27	19	.	.	PUNCT
ejpam-5282	28	1	in	in	ADP
ejpam-5282	28	2	the	the	DET
ejpam-5282	28	3	same	same	ADJ
ejpam-5282	28	4	paper	paper	NOUN
ejpam-5282	28	5	,	,	PUNCT
ejpam-5282	28	6	this	this	DET
ejpam-5282	28	7	inequality	inequality	NOUN
ejpam-5282	28	8	is	be	AUX
ejpam-5282	28	9	proved	prove	VERB
ejpam-5282	28	10	for	for	ADP
ejpam-5282	28	11	the	the	DET
ejpam-5282	28	12	special	special	ADJ
ejpam-5282	28	13	value	value	NOUN
ejpam-5282	28	14	(	(	PUNCT
ejpam-5282	28	15	q	q	NOUN
ejpam-5282	28	16	=	=	SYM
ejpam-5282	28	17	2	2	NUM
ejpam-5282	28	18	)	)	PUNCT
ejpam-5282	28	19	.	.	PUNCT
ejpam-5282	29	1	in	in	ADP
ejpam-5282	29	2	this	this	DET
ejpam-5282	29	3	paper	paper	NOUN
ejpam-5282	29	4	our	our	PRON
ejpam-5282	29	5	main	main	ADJ
ejpam-5282	29	6	aim	aim	NOUN
ejpam-5282	29	7	is	be	AUX
ejpam-5282	29	8	to	to	PART
ejpam-5282	29	9	find	find	VERB
ejpam-5282	29	10	best	good	ADJ
ejpam-5282	29	11	constant	constant	ADJ
ejpam-5282	29	12	ap	ap	PROPN
ejpam-5282	29	13	,	,	PUNCT
ejpam-5282	29	14	q	q	NOUN
ejpam-5282	29	15	in	in	ADP
ejpam-5282	29	16	the	the	DET
ejpam-5282	29	17	inequality	inequality	NOUN
ejpam-5282	29	18	||f	||f	PROPN
ejpam-5282	29	19	||p	||p	PROPN
ejpam-5282	29	20	≤	≤	X
ejpam-5282	29	21	ap	ap	PROPN
ejpam-5282	29	22	,	,	PUNCT
ejpam-5282	29	23	q|||f	q|||f	ADP
ejpam-5282	29	24	|||p	|||p	NOUN
ejpam-5282	29	25	,	,	PUNCT
ejpam-5282	29	26	q.	q.	PROPN
ejpam-5282	29	27	(	(	PUNCT
ejpam-5282	29	28	1.1	1.1	NUM
ejpam-5282	29	29	)	)	PUNCT
ejpam-5282	29	30	a	a	DET
ejpam-5282	29	31	reverse	reverse	ADJ
ejpam-5282	29	32	case	case	NOUN
ejpam-5282	29	33	of	of	ADP
ejpam-5282	29	34	this	this	DET
ejpam-5282	29	35	kind	kind	NOUN
ejpam-5282	29	36	of	of	ADP
ejpam-5282	29	37	inequalities	inequality	NOUN
ejpam-5282	29	38	is	be	AUX
ejpam-5282	29	39	generalized	generalize	VERB
ejpam-5282	29	40	from	from	ADP
ejpam-5282	29	41	melentijević	melentijević	ADJ
ejpam-5282	29	42	in	in	ADP
ejpam-5282	29	43	[	[	X
ejpam-5282	29	44	10	10	NUM
ejpam-5282	29	45	]	]	PUNCT
ejpam-5282	29	46	for	for	ADP
ejpam-5282	29	47	a	a	DET
ejpam-5282	29	48	special	special	ADJ
ejpam-5282	29	49	value	value	NOUN
ejpam-5282	29	50	of	of	ADP
ejpam-5282	29	51	p	p	PROPN
ejpam-5282	29	52	,	,	PUNCT
ejpam-5282	29	53	t	t	PROPN
ejpam-5282	29	54	and	and	CCONJ
ejpam-5282	29	55	q.	q.	PROPN
ejpam-5282	29	56	there	there	ADV
ejpam-5282	29	57	,	,	PUNCT
ejpam-5282	29	58	these	these	DET
ejpam-5282	29	59	inequalities	inequality	NOUN
ejpam-5282	29	60	are	be	AUX
ejpam-5282	29	61	analyzed	analyze	VERB
ejpam-5282	29	62	using	use	VERB
ejpam-5282	29	63	riesz	riesz	PROPN
ejpam-5282	29	64	’s	’s	PART
ejpam-5282	29	65	projection	projection	NOUN
ejpam-5282	29	66	operator	operator	NOUN
ejpam-5282	29	67	.	.	PUNCT
ejpam-5282	30	1	let	let	VERB
ejpam-5282	30	2	us	we	PRON
ejpam-5282	30	3	say	say	VERB
ejpam-5282	30	4	that	that	SCONJ
ejpam-5282	30	5	the	the	DET
ejpam-5282	30	6	riesz	riesz	PROPN
ejpam-5282	30	7	projection	projection	NOUN
ejpam-5282	30	8	operator	operator	NOUN
ejpam-5282	30	9	is	be	AUX
ejpam-5282	30	10	not	not	PART
ejpam-5282	30	11	bounded	bound	VERB
ejpam-5282	30	12	on	on	ADP
ejpam-5282	30	13	l1(t	l1(t	NOUN
ejpam-5282	30	14	)	)	PUNCT
ejpam-5282	30	15	.	.	PUNCT
ejpam-5282	31	1	2	2	X
ejpam-5282	31	2	.	.	X
ejpam-5282	31	3	main	main	ADJ
ejpam-5282	31	4	results	result	NOUN
ejpam-5282	31	5	and	and	CCONJ
ejpam-5282	31	6	strategy	strategy	NOUN
ejpam-5282	31	7	of	of	ADP
ejpam-5282	31	8	proofs	proof	NOUN
ejpam-5282	31	9	as	as	SCONJ
ejpam-5282	31	10	the	the	DET
ejpam-5282	31	11	authors	author	NOUN
ejpam-5282	31	12	of	of	ADP
ejpam-5282	31	13	paper	paper	NOUN
ejpam-5282	31	14	did	do	VERB
ejpam-5282	31	15	in	in	ADP
ejpam-5282	31	16	[	[	X
ejpam-5282	31	17	9	9	NUM
ejpam-5282	31	18	]	]	PUNCT
ejpam-5282	31	19	and	and	CCONJ
ejpam-5282	31	20	[	[	X
ejpam-5282	31	21	1	1	NUM
ejpam-5282	31	22	]	]	PUNCT
ejpam-5282	31	23	,	,	PUNCT
ejpam-5282	31	24	in	in	ADP
ejpam-5282	31	25	order	order	NOUN
ejpam-5282	31	26	to	to	PART
ejpam-5282	31	27	prove	prove	VERB
ejpam-5282	31	28	results	result	NOUN
ejpam-5282	31	29	we	we	PRON
ejpam-5282	31	30	use	use	VERB
ejpam-5282	31	31	pluri	pluri	ADJ
ejpam-5282	31	32	subharmonic	subharmonic	ADJ
ejpam-5282	31	33	function	function	NOUN
ejpam-5282	31	34	.	.	PUNCT
ejpam-5282	32	1	first	first	ADV
ejpam-5282	32	2	,	,	PUNCT
ejpam-5282	32	3	a	a	DET
ejpam-5282	32	4	lemma	lemma	PROPN
ejpam-5282	32	5	is	be	AUX
ejpam-5282	32	6	proved	prove	VERB
ejpam-5282	32	7	,	,	PUNCT
ejpam-5282	32	8	which	which	PRON
ejpam-5282	32	9	is	be	AUX
ejpam-5282	32	10	applied	apply	VERB
ejpam-5282	32	11	for	for	ADP
ejpam-5282	32	12	the	the	DET
ejpam-5282	32	13	proof	proof	NOUN
ejpam-5282	32	14	of	of	ADP
ejpam-5282	32	15	the	the	DET
ejpam-5282	32	16	main	main	ADJ
ejpam-5282	32	17	theorem	theorem	NOUN
ejpam-5282	32	18	.	.	PUNCT
ejpam-5282	33	1	lemma	lemma	PROPN
ejpam-5282	33	2	1	1	X
ejpam-5282	33	3	.	.	PUNCT
ejpam-5282	34	1	let	let	VERB
ejpam-5282	34	2	p	p	PRON
ejpam-5282	34	3	>	>	X
ejpam-5282	34	4	2	2	NUM
ejpam-5282	34	5	and	and	CCONJ
ejpam-5282	34	6	q	q	ADJ
ejpam-5282	34	7	>	>	X
ejpam-5282	35	1	1	1	X
ejpam-5282	35	2	.	.	PUNCT
ejpam-5282	35	3	then	then	ADV
ejpam-5282	35	4	for	for	ADP
ejpam-5282	35	5	complex	complex	ADJ
ejpam-5282	35	6	numbers	number	NOUN
ejpam-5282	35	7	z	z	NOUN
ejpam-5282	35	8	=	=	SYM
ejpam-5282	35	9	|z|eit	|z|eit	PUNCT
ejpam-5282	35	10	and	and	CCONJ
ejpam-5282	35	11	w	w	PROPN
ejpam-5282	35	12	=	=	NOUN
ejpam-5282	35	13	|w|eis	|w|eis	PROPN
ejpam-5282	36	1	we	we	PRON
ejpam-5282	36	2	have	have	VERB
ejpam-5282	36	3	|z	|z	PROPN
ejpam-5282	37	1	+	+	NUM
ejpam-5282	37	2	w|	w|	PROPN
ejpam-5282	37	3	≤	≤	NUM
ejpam-5282	37	4	cp	cp	NUM
ejpam-5282	37	5	,	,	PUNCT
ejpam-5282	37	6	q(|z|q	q(|z|q	PROPN
ejpam-5282	37	7	+	+	CCONJ
ejpam-5282	37	8	|w|q)p	|w|q)p	NUM
ejpam-5282	37	9	/	/	SYM
ejpam-5282	37	10	q	q	NOUN
ejpam-5282	37	11	−dp	−dp	PROPN
ejpam-5282	37	12	,	,	PUNCT
ejpam-5282	37	13	q|zw|	q|zw|	ADJ
ejpam-5282	37	14	p	p	ADJ
ejpam-5282	37	15	2	2	NUM
ejpam-5282	37	16	cos	cos	X
ejpam-5282	37	17	(	(	PUNCT
ejpam-5282	37	18	π	π	PROPN
ejpam-5282	37	19	−	−	PROPN
ejpam-5282	37	20	|t+	|t+	PROPN
ejpam-5282	37	21	s|)p	s|)p	NOUN
ejpam-5282	37	22	2	2	NUM
ejpam-5282	37	23	.	.	PUNCT
ejpam-5282	38	1	where	where	SCONJ
ejpam-5282	38	2	cp	cp	NOUN
ejpam-5282	38	3	,	,	PUNCT
ejpam-5282	38	4	q	q	NOUN
ejpam-5282	38	5	and	and	CCONJ
ejpam-5282	38	6	dp	dp	PROPN
ejpam-5282	38	7	,	,	PUNCT
ejpam-5282	38	8	q	q	X
ejpam-5282	38	9	are	be	AUX
ejpam-5282	38	10	defined	define	VERB
ejpam-5282	38	11	as	as	ADP
ejpam-5282	38	12	below	below	ADP
ejpam-5282	38	13	cp	cp	NUM
ejpam-5282	38	14	,	,	PUNCT
ejpam-5282	38	15	q	q	NOUN
ejpam-5282	38	16	=	=	SYM
ejpam-5282	38	17	2	2	NUM
ejpam-5282	38	18	p−	p−	NOUN
ejpam-5282	38	19	p	p	X
ejpam-5282	38	20	q	q	X
ejpam-5282	38	21	sinp	sinp	VERB
ejpam-5282	38	22	π	π	X
ejpam-5282	38	23	2p	2p	NUM
ejpam-5282	38	24	,	,	PUNCT
ejpam-5282	38	25	and	and	CCONJ
ejpam-5282	38	26	dp	dp	NOUN
ejpam-5282	38	27	,	,	PUNCT
ejpam-5282	38	28	q	q	NOUN
ejpam-5282	38	29	=	=	SYM
ejpam-5282	38	30	2	2	NUM
ejpam-5282	38	31	3p	3p	NUM
ejpam-5282	38	32	2	2	NUM
ejpam-5282	38	33	−	−	NOUN
ejpam-5282	39	1	p	p	X
ejpam-5282	39	2	q	q	X
ejpam-5282	39	3	sinp	sinp	VERB
ejpam-5282	39	4	π	π	X
ejpam-5282	39	5	2p	2p	NUM
ejpam-5282	39	6	cot	cot	NOUN
ejpam-5282	39	7	π	π	NOUN
ejpam-5282	39	8	2p	2p	NUM
ejpam-5282	39	9	.	.	PUNCT
ejpam-5282	40	1	e.	e.	PROPN
ejpam-5282	40	2	bajrami	bajrami	PROPN
ejpam-5282	40	3	/	/	SYM
ejpam-5282	40	4	eur	eur	PROPN
ejpam-5282	40	5	.	.	PUNCT
ejpam-5282	41	1	j.	j.	PROPN
ejpam-5282	41	2	pure	pure	PROPN
ejpam-5282	41	3	appl	appl	PROPN
ejpam-5282	41	4	.	.	PROPN
ejpam-5282	41	5	math	math	PROPN
ejpam-5282	41	6	,	,	PUNCT
ejpam-5282	41	7	17	17	NUM
ejpam-5282	41	8	(	(	PUNCT
ejpam-5282	41	9	3	3	NUM
ejpam-5282	41	10	)	)	PUNCT
ejpam-5282	41	11	(	(	PUNCT
ejpam-5282	41	12	2024	2024	NUM
ejpam-5282	41	13	)	)	PUNCT
ejpam-5282	41	14	,	,	PUNCT
ejpam-5282	41	15	1685	1685	NUM
ejpam-5282	41	16	-	-	SYM
ejpam-5282	41	17	1690	1690	NUM
ejpam-5282	41	18	1687	1687	NUM
ejpam-5282	41	19	based	base	VERB
ejpam-5282	41	20	on	on	ADP
ejpam-5282	41	21	homogeneity	homogeneity	NOUN
ejpam-5282	41	22	of	of	ADP
ejpam-5282	41	23	expression	expression	NOUN
ejpam-5282	41	24	(	(	PUNCT
ejpam-5282	41	25	as	as	ADP
ejpam-5282	41	26	in	in	ADP
ejpam-5282	41	27	proof	proof	NOUN
ejpam-5282	41	28	of	of	ADP
ejpam-5282	41	29	lemma	lemma	PROPN
ejpam-5282	41	30	2	2	NUM
ejpam-5282	41	31	in	in	ADP
ejpam-5282	41	32	[	[	X
ejpam-5282	41	33	1	1	NUM
ejpam-5282	41	34	]	]	NUM
ejpam-5282	41	35	)	)	PUNCT
ejpam-5282	42	1	,	,	PUNCT
ejpam-5282	42	2	we	we	PRON
ejpam-5282	42	3	can	can	AUX
ejpam-5282	42	4	assume	assume	VERB
ejpam-5282	42	5	that	that	SCONJ
ejpam-5282	42	6	|z|	|z|	VERB
ejpam-5282	42	7	=	=	SYM
ejpam-5282	42	8	r	r	NOUN
ejpam-5282	42	9	<	<	X
ejpam-5282	42	10	1	1	NUM
ejpam-5282	42	11	and	and	CCONJ
ejpam-5282	42	12	w	w	NOUN
ejpam-5282	42	13	=	=	NOUN
ejpam-5282	42	14	1	1	X
ejpam-5282	42	15	.	.	PUNCT
ejpam-5282	43	1	so	so	ADV
ejpam-5282	43	2	,	,	PUNCT
ejpam-5282	43	3	rather	rather	ADV
ejpam-5282	43	4	than	than	ADP
ejpam-5282	43	5	proving	prove	VERB
ejpam-5282	43	6	the	the	DET
ejpam-5282	43	7	last	last	ADJ
ejpam-5282	43	8	lemma	lemma	PROPN
ejpam-5282	43	9	,	,	PUNCT
ejpam-5282	43	10	we	we	PRON
ejpam-5282	43	11	will	will	AUX
ejpam-5282	43	12	present	present	VERB
ejpam-5282	43	13	and	and	CCONJ
ejpam-5282	43	14	prove	prove	VERB
ejpam-5282	43	15	the	the	DET
ejpam-5282	43	16	next	next	ADJ
ejpam-5282	43	17	lemma	lemma	PROPN
ejpam-5282	43	18	.	.	PUNCT
ejpam-5282	44	1	lemma	lemma	PROPN
ejpam-5282	44	2	2	2	X
ejpam-5282	44	3	.	.	PUNCT
ejpam-5282	44	4	let	let	VERB
ejpam-5282	44	5	p	p	PRON
ejpam-5282	44	6	>	>	X
ejpam-5282	44	7	2	2	NUM
ejpam-5282	44	8	and	and	CCONJ
ejpam-5282	44	9	q	q	ADJ
ejpam-5282	44	10	>	>	X
ejpam-5282	45	1	1	1	X
ejpam-5282	45	2	.	.	PUNCT
ejpam-5282	46	1	then	then	ADV
ejpam-5282	46	2	this	this	DET
ejpam-5282	46	3	sharp	sharp	ADJ
ejpam-5282	46	4	inequality	inequality	NOUN
ejpam-5282	46	5	hold	hold	NOUN
ejpam-5282	46	6	(	(	PUNCT
ejpam-5282	46	7	1	1	NUM
ejpam-5282	46	8	+	+	NUM
ejpam-5282	46	9	r2	r2	PROPN
ejpam-5282	46	10	+	+	CCONJ
ejpam-5282	46	11	2r	2r	NUM
ejpam-5282	46	12	cos	cos	ADP
ejpam-5282	46	13	t)p/2	t)p/2	ADJ
ejpam-5282	46	14	≤	≤	NUM
ejpam-5282	46	15	2p	2p	NUM
ejpam-5282	46	16	sinp	sinp	VERB
ejpam-5282	46	17	π	π	X
ejpam-5282	46	18	2p	2p	NUM
ejpam-5282	46	19	(	(	PUNCT
ejpam-5282	46	20	1	1	NUM
ejpam-5282	46	21	+	+	CCONJ
ejpam-5282	46	22	rq	rq	VERB
ejpam-5282	46	23	2	2	NUM
ejpam-5282	46	24	)	)	PUNCT
ejpam-5282	46	25	p	p	X
ejpam-5282	46	26	/	/	SYM
ejpam-5282	46	27	q	q	NOUN
ejpam-5282	46	28	−	−	PROPN
ejpam-5282	46	29	2	2	NUM
ejpam-5282	46	30	3p	3p	NUM
ejpam-5282	46	31	2	2	NUM
ejpam-5282	46	32	−	−	NOUN
ejpam-5282	46	33	p	p	NOUN
ejpam-5282	46	34	q	q	NOUN
ejpam-5282	46	35	r	r	NOUN
ejpam-5282	46	36	p	p	NOUN
ejpam-5282	46	37	2	2	NUM
ejpam-5282	46	38	sinp	sinp	NOUN
ejpam-5282	46	39	π	π	NOUN
ejpam-5282	46	40	2p	2p	NUM
ejpam-5282	46	41	cot	cot	NOUN
ejpam-5282	46	42	π	π	X
ejpam-5282	46	43	2p	2p	NUM
ejpam-5282	46	44	cos	cos	PROPN
ejpam-5282	46	45	(	(	PUNCT
ejpam-5282	46	46	π	π	PROPN
ejpam-5282	46	47	−	−	PROPN
ejpam-5282	46	48	|t+	|t+	PROPN
ejpam-5282	46	49	s|)p	s|)p	NOUN
ejpam-5282	46	50	2	2	NUM
ejpam-5282	46	51	for	for	ADP
ejpam-5282	46	52	0	0	NUM
ejpam-5282	46	53	≤	≤	NUM
ejpam-5282	46	54	r	r	NOUN
ejpam-5282	46	55	≤	≤	NUM
ejpam-5282	46	56	1	1	NUM
ejpam-5282	46	57	,	,	PUNCT
ejpam-5282	46	58	0	0	NUM
ejpam-5282	46	59	≤	≤	NUM
ejpam-5282	46	60	t	t	PROPN
ejpam-5282	46	61	≤	≤	NUM
ejpam-5282	46	62	π	π	PROPN
ejpam-5282	46	63	.	.	PUNCT
ejpam-5282	47	1	proof	proof	NOUN
ejpam-5282	47	2	.	.	PUNCT
ejpam-5282	48	1	define	define	VERB
ejpam-5282	48	2	p	p	X
ejpam-5282	48	3	(	(	PUNCT
ejpam-5282	48	4	r	r	NOUN
ejpam-5282	48	5	,	,	PUNCT
ejpam-5282	48	6	t	t	PROPN
ejpam-5282	48	7	)	)	PUNCT
ejpam-5282	48	8	=	=	PUNCT
ejpam-5282	49	1	(	(	PUNCT
ejpam-5282	49	2	1	1	NUM
ejpam-5282	49	3	+	+	NUM
ejpam-5282	49	4	r2	r2	PROPN
ejpam-5282	49	5	+	+	CCONJ
ejpam-5282	49	6	2r	2r	NUM
ejpam-5282	49	7	cos	cos	SCONJ
ejpam-5282	49	8	t)p/2	t)p/2	NOUN
ejpam-5282	49	9	−	−	PROPN
ejpam-5282	49	10	2p	2p	NUM
ejpam-5282	49	11	sinp	sinp	VERB
ejpam-5282	49	12	π	π	X
ejpam-5282	49	13	2p	2p	NUM
ejpam-5282	49	14	(	(	PUNCT
ejpam-5282	49	15	1+rq	1+rq	NUM
ejpam-5282	49	16	2	2	NUM
ejpam-5282	49	17	)	)	PUNCT
ejpam-5282	49	18	p	p	X
ejpam-5282	49	19	/	/	SYM
ejpam-5282	49	20	q	q	NOUN
ejpam-5282	49	21	+2	+2	PROPN
ejpam-5282	49	22	3p	3p	NUM
ejpam-5282	49	23	2	2	NUM
ejpam-5282	49	24	−	−	NOUN
ejpam-5282	49	25	p	p	X
ejpam-5282	49	26	q	q	X
ejpam-5282	49	27	sinp	sinp	VERB
ejpam-5282	49	28	π	π	X
ejpam-5282	49	29	2p	2p	NUM
ejpam-5282	49	30	cot	cot	NOUN
ejpam-5282	49	31	π	π	PROPN
ejpam-5282	49	32	2pr	2pr	NOUN
ejpam-5282	50	1	p	p	ADJ
ejpam-5282	50	2	2	2	NUM
ejpam-5282	50	3	cos	cos	PROPN
ejpam-5282	50	4	(	(	PUNCT
ejpam-5282	50	5	π−|t+s|)p	π−|t+s|)p	ADJ
ejpam-5282	50	6	2	2	NUM
ejpam-5282	50	7	(	(	PUNCT
ejpam-5282	50	8	2.1	2.1	NUM
ejpam-5282	50	9	)	)	PUNCT
ejpam-5282	50	10	we	we	PRON
ejpam-5282	50	11	must	must	AUX
ejpam-5282	50	12	prove	prove	VERB
ejpam-5282	50	13	that	that	SCONJ
ejpam-5282	50	14	p	p	X
ejpam-5282	50	15	(	(	PUNCT
ejpam-5282	50	16	r	r	NOUN
ejpam-5282	50	17	,	,	PUNCT
ejpam-5282	50	18	t	t	PROPN
ejpam-5282	50	19	)	)	PUNCT
ejpam-5282	50	20	≤	≤	NOUN
ejpam-5282	50	21	0	0	NUM
ejpam-5282	50	22	.	.	PUNCT
ejpam-5282	51	1	calculate	calculate	VERB
ejpam-5282	51	2	partial	partial	ADJ
ejpam-5282	51	3	derivative	derivative	ADJ
ejpam-5282	51	4	2	2	NUM
ejpam-5282	51	5	p	p	NOUN
ejpam-5282	51	6	∂p	∂p	NOUN
ejpam-5282	51	7	(	(	PUNCT
ejpam-5282	51	8	r	r	NOUN
ejpam-5282	51	9	,	,	PUNCT
ejpam-5282	51	10	t	t	NOUN
ejpam-5282	51	11	)	)	PUNCT
ejpam-5282	52	1	∂r	∂r	PROPN
ejpam-5282	52	2	=	=	PUNCT
ejpam-5282	53	1	2(r	2(r	NUM
ejpam-5282	53	2	+	+	CCONJ
ejpam-5282	53	3	cos	co	NOUN
ejpam-5282	53	4	t)(1	t)(1	X
ejpam-5282	53	5	+	+	CCONJ
ejpam-5282	53	6	2r	2r	NUM
ejpam-5282	53	7	cos	cos	PROPN
ejpam-5282	53	8	t+	t+	NOUN
ejpam-5282	53	9	r2	r2	NOUN
ejpam-5282	53	10	)	)	PUNCT
ejpam-5282	53	11	p	p	NOUN
ejpam-5282	53	12	2	2	NUM
ejpam-5282	53	13	−1	−1	NOUN
ejpam-5282	53	14	−	−	NOUN
ejpam-5282	53	15	2p	2p	NUM
ejpam-5282	53	16	sinp	sinp	VERB
ejpam-5282	53	17	π	π	X
ejpam-5282	53	18	2p	2p	NUM
ejpam-5282	53	19	rq−1	rq−1	PROPN
ejpam-5282	53	20	(	(	PUNCT
ejpam-5282	53	21	1	1	X
ejpam-5282	53	22	+	+	CCONJ
ejpam-5282	53	23	rq	rq	VERB
ejpam-5282	53	24	2	2	NUM
ejpam-5282	53	25	)	)	PUNCT
ejpam-5282	53	26	p	p	X
ejpam-5282	53	27	q	q	NOUN
ejpam-5282	53	28	−1	−1	NOUN
ejpam-5282	53	29	+	+	CCONJ
ejpam-5282	53	30	2	2	NUM
ejpam-5282	53	31	3p	3p	NUM
ejpam-5282	53	32	2	2	NUM
ejpam-5282	53	33	−	−	NOUN
ejpam-5282	54	1	p	p	X
ejpam-5282	55	1	q	q	X
ejpam-5282	55	2	sinp	sinp	VERB
ejpam-5282	55	3	π	π	X
ejpam-5282	55	4	2p	2p	NUM
ejpam-5282	55	5	cot	cot	NOUN
ejpam-5282	56	1	π	π	NOUN
ejpam-5282	56	2	2p	2p	NUM
ejpam-5282	57	1	r	r	NOUN
ejpam-5282	57	2	p	p	NOUN
ejpam-5282	57	3	2	2	NUM
ejpam-5282	57	4	−1	−1	NOUN
ejpam-5282	57	5	cos	cos	PROPN
ejpam-5282	57	6	(	(	PUNCT
ejpam-5282	57	7	π	π	PROPN
ejpam-5282	57	8	−	−	PROPN
ejpam-5282	57	9	|t|)p	|t|)p	ADV
ejpam-5282	57	10	2	2	NUM
ejpam-5282	57	11	and	and	CCONJ
ejpam-5282	57	12	∂p	∂p	ADJ
ejpam-5282	57	13	(	(	PUNCT
ejpam-5282	57	14	r	r	NOUN
ejpam-5282	57	15	,	,	PUNCT
ejpam-5282	57	16	t	t	PROPN
ejpam-5282	57	17	)	)	PUNCT
ejpam-5282	57	18	∂t	∂t	PROPN
ejpam-5282	57	19	=	=	PUNCT
ejpam-5282	58	1	p	p	ADJ
ejpam-5282	58	2	2	2	NUM
ejpam-5282	58	3	(	(	PUNCT
ejpam-5282	58	4	1	1	NUM
ejpam-5282	58	5	+	+	NUM
ejpam-5282	58	6	2r	2r	NUM
ejpam-5282	58	7	cos	cos	PROPN
ejpam-5282	58	8	t+	t+	NOUN
ejpam-5282	58	9	r2	r2	NOUN
ejpam-5282	58	10	)	)	PUNCT
ejpam-5282	58	11	p	p	NOUN
ejpam-5282	58	12	2	2	NUM
ejpam-5282	58	13	−1(−2r	−1(−2r	PROPN
ejpam-5282	58	14	sin	sin	NOUN
ejpam-5282	58	15	t	t	NOUN
ejpam-5282	58	16	)	)	PUNCT
ejpam-5282	58	17	+	+	CCONJ
ejpam-5282	58	18	2	2	NUM
ejpam-5282	58	19	3p	3p	NUM
ejpam-5282	58	20	2	2	NUM
ejpam-5282	58	21	−	−	NOUN
ejpam-5282	58	22	p	p	X
ejpam-5282	59	1	q	q	X
ejpam-5282	59	2	sinp	sinp	VERB
ejpam-5282	59	3	π	π	NOUN
ejpam-5282	59	4	2p	2p	NUM
ejpam-5282	60	1	r	r	NOUN
ejpam-5282	60	2	p	p	NOUN
ejpam-5282	60	3	2	2	NUM
ejpam-5282	60	4	cot	cot	NOUN
ejpam-5282	60	5	π	π	PROPN
ejpam-5282	60	6	2p	2p	NUM
ejpam-5282	60	7	sin	sin	NOUN
ejpam-5282	60	8	(	(	PUNCT
ejpam-5282	60	9	π	π	PROPN
ejpam-5282	60	10	−	−	PROPN
ejpam-5282	60	11	t)p	t)p	ADJ
ejpam-5282	60	12	2	2	NUM
ejpam-5282	60	13	.	.	PUNCT
ejpam-5282	61	1	using	use	VERB
ejpam-5282	61	2	equality	equality	NOUN
ejpam-5282	61	3	∂p	∂p	PROPN
ejpam-5282	61	4	∂t	∂t	PROPN
ejpam-5282	61	5	=	=	PUNCT
ejpam-5282	61	6	0	0	PROPN
ejpam-5282	61	7	,	,	PUNCT
ejpam-5282	61	8	from	from	ADP
ejpam-5282	61	9	the	the	DET
ejpam-5282	61	10	last	last	ADJ
ejpam-5282	61	11	equation	equation	NOUN
ejpam-5282	61	12	we	we	PRON
ejpam-5282	61	13	have	have	VERB
ejpam-5282	61	14	(	(	PUNCT
ejpam-5282	61	15	1	1	NUM
ejpam-5282	61	16	+	+	NUM
ejpam-5282	61	17	2r	2r	NUM
ejpam-5282	61	18	cos	cos	PROPN
ejpam-5282	61	19	t+	t+	NOUN
ejpam-5282	61	20	r2	r2	NOUN
ejpam-5282	61	21	)	)	PUNCT
ejpam-5282	61	22	p	p	NOUN
ejpam-5282	61	23	2	2	NUM
ejpam-5282	61	24	−1	−1	NOUN
ejpam-5282	61	25	=	=	NOUN
ejpam-5282	61	26	2	2	NUM
ejpam-5282	61	27	3p	3p	NUM
ejpam-5282	61	28	2	2	NUM
ejpam-5282	61	29	−	−	NOUN
ejpam-5282	62	1	p	p	X
ejpam-5282	63	1	q	q	X
ejpam-5282	63	2	sinp	sinp	VERB
ejpam-5282	63	3	π	π	PROPN
ejpam-5282	63	4	2pr	2pr	NOUN
ejpam-5282	64	1	p	p	ADJ
ejpam-5282	64	2	2	2	NUM
ejpam-5282	64	3	cot	cot	NOUN
ejpam-5282	64	4	π	π	PROPN
ejpam-5282	64	5	2p	2p	NUM
ejpam-5282	64	6	sin	sin	NOUN
ejpam-5282	64	7	(	(	PUNCT
ejpam-5282	64	8	π−t)p	π−t)p	PROPN
ejpam-5282	64	9	2	2	NUM
ejpam-5282	64	10	pr	pr	NOUN
ejpam-5282	64	11	sin	sin	NOUN
ejpam-5282	64	12	t	t	PROPN
ejpam-5282	64	13	(	(	PUNCT
ejpam-5282	64	14	2.2	2.2	NUM
ejpam-5282	64	15	)	)	PUNCT
ejpam-5282	64	16	and	and	CCONJ
ejpam-5282	64	17	substitute	substitute	NOUN
ejpam-5282	64	18	in	in	ADP
ejpam-5282	64	19	equation	equation	NOUN
ejpam-5282	64	20	2	2	NUM
ejpam-5282	64	21	p	p	NOUN
ejpam-5282	64	22	∂p	∂p	PROPN
ejpam-5282	64	23	∂r	∂r	PROPN
ejpam-5282	64	24	=	=	NOUN
ejpam-5282	64	25	0	0	PROPN
ejpam-5282	64	26	to	to	PART
ejpam-5282	64	27	get	get	VERB
ejpam-5282	64	28	2(r	2(r	PRON
ejpam-5282	64	29	+	+	CCONJ
ejpam-5282	64	30	cos	cos	PROPN
ejpam-5282	64	31	t	t	PROPN
ejpam-5282	64	32	)	)	PUNCT
ejpam-5282	64	33	2	2	NUM
ejpam-5282	64	34	3p	3p	NUM
ejpam-5282	64	35	2	2	NUM
ejpam-5282	64	36	−	−	NOUN
ejpam-5282	65	1	p	p	X
ejpam-5282	66	1	q	q	X
ejpam-5282	66	2	sinp	sinp	VERB
ejpam-5282	66	3	π	π	PROPN
ejpam-5282	66	4	2pr	2pr	NOUN
ejpam-5282	67	1	p	p	ADJ
ejpam-5282	67	2	2	2	NUM
ejpam-5282	67	3	cot	cot	NOUN
ejpam-5282	67	4	π	π	PROPN
ejpam-5282	67	5	2p	2p	NUM
ejpam-5282	67	6	sin	sin	NOUN
ejpam-5282	67	7	(	(	PUNCT
ejpam-5282	67	8	π−t)p	π−t)p	PROPN
ejpam-5282	67	9	2	2	NUM
ejpam-5282	67	10	pr	pr	NOUN
ejpam-5282	67	11	sin	sin	NOUN
ejpam-5282	67	12	t	t	PROPN
ejpam-5282	67	13	−	−	PROPN
ejpam-5282	67	14	2p	2p	NUM
ejpam-5282	67	15	sinp	sinp	VERB
ejpam-5282	67	16	π	π	X
ejpam-5282	67	17	2p	2p	NUM
ejpam-5282	67	18	rq−1	rq−1	PROPN
ejpam-5282	67	19	(	(	PUNCT
ejpam-5282	67	20	1	1	X
ejpam-5282	67	21	+	+	CCONJ
ejpam-5282	67	22	rq	rq	VERB
ejpam-5282	67	23	2	2	NUM
ejpam-5282	67	24	)	)	PUNCT
ejpam-5282	67	25	p	p	NOUN
ejpam-5282	67	26	q	q	NOUN
ejpam-5282	67	27	−1	−1	NOUN
ejpam-5282	67	28	+2	+2	ADV
ejpam-5282	67	29	3p	3p	NUM
ejpam-5282	67	30	2	2	NUM
ejpam-5282	67	31	−	−	NOUN
ejpam-5282	67	32	p	p	X
ejpam-5282	68	1	q	q	X
ejpam-5282	68	2	sinp	sinp	VERB
ejpam-5282	68	3	π	π	X
ejpam-5282	68	4	2p	2p	NUM
ejpam-5282	68	5	cot	cot	NOUN
ejpam-5282	69	1	π	π	NOUN
ejpam-5282	69	2	2p	2p	NUM
ejpam-5282	70	1	r	r	NOUN
ejpam-5282	70	2	p	p	NOUN
ejpam-5282	70	3	2	2	NUM
ejpam-5282	70	4	−1	−1	NOUN
ejpam-5282	70	5	cos	cos	PROPN
ejpam-5282	70	6	(	(	PUNCT
ejpam-5282	70	7	π	π	PROPN
ejpam-5282	70	8	−	−	PROPN
ejpam-5282	70	9	t)p	t)p	ADJ
ejpam-5282	70	10	2	2	NUM
ejpam-5282	70	11	=	=	SYM
ejpam-5282	70	12	0	0	NUM
ejpam-5282	70	13	e.	e.	PROPN
ejpam-5282	70	14	bajrami	bajrami	PROPN
ejpam-5282	70	15	/	/	SYM
ejpam-5282	70	16	eur	eur	PROPN
ejpam-5282	70	17	.	.	PUNCT
ejpam-5282	71	1	j.	j.	PROPN
ejpam-5282	71	2	pure	pure	PROPN
ejpam-5282	71	3	appl	appl	PROPN
ejpam-5282	71	4	.	.	PROPN
ejpam-5282	71	5	math	math	PROPN
ejpam-5282	71	6	,	,	PUNCT
ejpam-5282	71	7	17	17	NUM
ejpam-5282	71	8	(	(	PUNCT
ejpam-5282	71	9	3	3	NUM
ejpam-5282	71	10	)	)	PUNCT
ejpam-5282	71	11	(	(	PUNCT
ejpam-5282	71	12	2024	2024	NUM
ejpam-5282	71	13	)	)	PUNCT
ejpam-5282	71	14	,	,	PUNCT
ejpam-5282	71	15	1685	1685	NUM
ejpam-5282	71	16	-	-	SYM
ejpam-5282	71	17	1690	1690	NUM
ejpam-5282	71	18	1688	1688	NUM
ejpam-5282	71	19	or	or	CCONJ
ejpam-5282	71	20	(	(	PUNCT
ejpam-5282	71	21	1	1	NUM
ejpam-5282	71	22	+	+	NUM
ejpam-5282	71	23	rq	rq	VERB
ejpam-5282	71	24	2	2	NUM
ejpam-5282	71	25	)	)	PUNCT
ejpam-5282	72	1	p	p	X
ejpam-5282	72	2	q	q	X
ejpam-5282	72	3	−1	−1	NOUN
ejpam-5282	72	4	=	=	SYM
ejpam-5282	72	5	2	2	NUM
ejpam-5282	72	6	p	p	NOUN
ejpam-5282	72	7	2	2	NUM
ejpam-5282	72	8	−	−	NOUN
ejpam-5282	72	9	p	p	NOUN
ejpam-5282	72	10	q	q	X
ejpam-5282	72	11	cot	cot	NOUN
ejpam-5282	72	12	π	π	NOUN
ejpam-5282	72	13	2p	2p	NUM
ejpam-5282	72	14	r	r	NOUN
ejpam-5282	72	15	p	p	NOUN
ejpam-5282	72	16	2	2	NUM
ejpam-5282	72	17	−q	−q	NOUN
ejpam-5282	72	18	(	(	PUNCT
ejpam-5282	72	19	(	(	PUNCT
ejpam-5282	72	20	r	r	NOUN
ejpam-5282	72	21	+	+	PROPN
ejpam-5282	72	22	cos	cos	PROPN
ejpam-5282	72	23	t	t	PROPN
ejpam-5282	72	24	)	)	PUNCT
ejpam-5282	72	25	sin	sin	NOUN
ejpam-5282	72	26	(	(	PUNCT
ejpam-5282	72	27	π−t)p	π−t)p	PROPN
ejpam-5282	72	28	2	2	NUM
ejpam-5282	72	29	p	p	NOUN
ejpam-5282	72	30	sin	sin	NOUN
ejpam-5282	72	31	t	t	PROPN
ejpam-5282	72	32	−	−	PROPN
ejpam-5282	72	33	cos	cos	PROPN
ejpam-5282	72	34	(	(	PUNCT
ejpam-5282	72	35	π	π	PROPN
ejpam-5282	72	36	−	−	PROPN
ejpam-5282	72	37	t)p	t)p	ADJ
ejpam-5282	72	38	2	2	NUM
ejpam-5282	72	39	)	)	PUNCT
ejpam-5282	72	40	.	.	PUNCT
ejpam-5282	73	1	(	(	PUNCT
ejpam-5282	73	2	2.3	2.3	NUM
ejpam-5282	73	3	)	)	PUNCT
ejpam-5282	73	4	now	now	ADV
ejpam-5282	73	5	,	,	PUNCT
ejpam-5282	73	6	if	if	SCONJ
ejpam-5282	73	7	we	we	PRON
ejpam-5282	73	8	substitute	substitute	VERB
ejpam-5282	73	9	expressions	expression	NOUN
ejpam-5282	73	10	from	from	ADP
ejpam-5282	73	11	(	(	PUNCT
ejpam-5282	73	12	2.2	2.2	NUM
ejpam-5282	73	13	)	)	PUNCT
ejpam-5282	73	14	and	and	CCONJ
ejpam-5282	73	15	(	(	PUNCT
ejpam-5282	73	16	2.3	2.3	NUM
ejpam-5282	73	17	)	)	PUNCT
ejpam-5282	73	18	in	in	ADP
ejpam-5282	73	19	(	(	PUNCT
ejpam-5282	73	20	2.1	2.1	NUM
ejpam-5282	73	21	)	)	PUNCT
ejpam-5282	73	22	and	and	CCONJ
ejpam-5282	73	23	avoid	avoid	VERB
ejpam-5282	73	24	the	the	DET
ejpam-5282	73	25	factor	factor	NOUN
ejpam-5282	73	26	2	2	NUM
ejpam-5282	73	27	3p	3p	NUM
ejpam-5282	73	28	2	2	NUM
ejpam-5282	73	29	−	−	NOUN
ejpam-5282	74	1	p	p	X
ejpam-5282	75	1	q	q	X
ejpam-5282	75	2	sinp	sinp	VERB
ejpam-5282	75	3	π	π	NOUN
ejpam-5282	75	4	2p	2p	X
ejpam-5282	75	5	>	>	X
ejpam-5282	75	6	0	0	NUM
ejpam-5282	75	7	,	,	PUNCT
ejpam-5282	75	8	we	we	PRON
ejpam-5282	75	9	get	get	VERB
ejpam-5282	75	10	p	p	NOUN
ejpam-5282	75	11	(	(	PUNCT
ejpam-5282	75	12	r	r	NOUN
ejpam-5282	75	13	,	,	PUNCT
ejpam-5282	75	14	t	t	PROPN
ejpam-5282	75	15	)	)	PUNCT
ejpam-5282	76	1	=	=	PUNCT
ejpam-5282	76	2	r	r	NOUN
ejpam-5282	76	3	p	p	NOUN
ejpam-5282	76	4	2	2	NUM
ejpam-5282	76	5	cot	cot	NOUN
ejpam-5282	76	6	π	π	NOUN
ejpam-5282	76	7	2p	2p	NUM
ejpam-5282	76	8	pr	pr	ADP
ejpam-5282	76	9	sin	sin	PROPN
ejpam-5282	76	10	t	t	PROPN
ejpam-5282	76	11	(	(	PUNCT
ejpam-5282	76	12	(	(	PUNCT
ejpam-5282	76	13	1	1	NUM
ejpam-5282	76	14	+	+	NUM
ejpam-5282	76	15	r2	r2	PROPN
ejpam-5282	76	16	+	+	CCONJ
ejpam-5282	76	17	2r	2r	NUM
ejpam-5282	76	18	cos	cos	PROPN
ejpam-5282	76	19	t	t	PROPN
ejpam-5282	76	20	)	)	PUNCT
ejpam-5282	76	21	sin	sin	NOUN
ejpam-5282	76	22	(	(	PUNCT
ejpam-5282	76	23	π	π	NOUN
ejpam-5282	76	24	−	−	PROPN
ejpam-5282	76	25	t)p	t)p	ADJ
ejpam-5282	76	26	2	2	NUM
ejpam-5282	76	27	−1	−1	NOUN
ejpam-5282	76	28	+	+	NOUN
ejpam-5282	76	29	rq	rq	X
ejpam-5282	76	30	2rq−1	2rq−1	NUM
ejpam-5282	76	31	(	(	PUNCT
ejpam-5282	76	32	r	r	NOUN
ejpam-5282	76	33	sin	sin	NOUN
ejpam-5282	76	34	(	(	PUNCT
ejpam-5282	76	35	π	π	PROPN
ejpam-5282	76	36	−	−	PROPN
ejpam-5282	76	37	t)p	t)p	ADJ
ejpam-5282	76	38	2	2	NUM
ejpam-5282	76	39	+	+	CCONJ
ejpam-5282	76	40	sin(t−	sin(t−	PROPN
ejpam-5282	76	41	tp	tp	ADP
ejpam-5282	76	42	2	2	NUM
ejpam-5282	76	43	)	)	PUNCT
ejpam-5282	76	44	)	)	PUNCT
ejpam-5282	77	1	+	+	CCONJ
ejpam-5282	77	2	r	r	X
ejpam-5282	77	3	cos	cos	PROPN
ejpam-5282	77	4	(	(	PUNCT
ejpam-5282	77	5	π	π	PROPN
ejpam-5282	77	6	−	−	PROPN
ejpam-5282	77	7	t)p	t)p	ADJ
ejpam-5282	77	8	2	2	NUM
ejpam-5282	77	9	sin	sin	NOUN
ejpam-5282	77	10	t	t	NOUN
ejpam-5282	77	11	)	)	PUNCT
ejpam-5282	77	12	.	.	PUNCT
ejpam-5282	78	1	after	after	ADP
ejpam-5282	78	2	some	some	DET
ejpam-5282	78	3	transformation	transformation	NOUN
ejpam-5282	78	4	we	we	PRON
ejpam-5282	78	5	obtain	obtain	VERB
ejpam-5282	78	6	p	p	NOUN
ejpam-5282	78	7	(	(	PUNCT
ejpam-5282	78	8	r	r	NOUN
ejpam-5282	78	9	,	,	PUNCT
ejpam-5282	78	10	t	t	PROPN
ejpam-5282	78	11	)	)	PUNCT
ejpam-5282	78	12	=	=	PUNCT
ejpam-5282	79	1	r	r	NOUN
ejpam-5282	79	2	p	p	NOUN
ejpam-5282	79	3	2	2	NUM
ejpam-5282	79	4	cot	cot	NOUN
ejpam-5282	79	5	π	π	NOUN
ejpam-5282	79	6	2p	2p	NUM
ejpam-5282	79	7	pr	pr	NOUN
ejpam-5282	79	8	sin	sin	NOUN
ejpam-5282	79	9	t	t	PROPN
ejpam-5282	79	10	(	(	PUNCT
ejpam-5282	79	11	sin(t−	sin(t−	PROPN
ejpam-5282	79	12	tp	tp	PROPN
ejpam-5282	79	13	2	2	NUM
ejpam-5282	79	14	)	)	PUNCT
ejpam-5282	79	15	(	(	PUNCT
ejpam-5282	79	16	2r	2r	NUM
ejpam-5282	80	1	+	+	CCONJ
ejpam-5282	80	2	1	1	NUM
ejpam-5282	80	3	+	+	NUM
ejpam-5282	80	4	rq	rq	VERB
ejpam-5282	80	5	2rq−1	2rq−1	PROPN
ejpam-5282	80	6	)	)	PUNCT
ejpam-5282	81	1	+	+	CCONJ
ejpam-5282	81	2	sin	sin	NOUN
ejpam-5282	81	3	tp	tp	ADP
ejpam-5282	81	4	2	2	NUM
ejpam-5282	81	5	(	(	PUNCT
ejpam-5282	81	6	1	1	NUM
ejpam-5282	81	7	+	+	NUM
ejpam-5282	81	8	r2	r2	PROPN
ejpam-5282	81	9	−	−	PROPN
ejpam-5282	81	10	1	1	NUM
ejpam-5282	81	11	+	+	CCONJ
ejpam-5282	81	12	rq	rq	VERB
ejpam-5282	81	13	2rq	2rq	NOUN
ejpam-5282	81	14	)	)	PUNCT
ejpam-5282	81	15	)	)	PUNCT
ejpam-5282	81	16	.	.	PUNCT
ejpam-5282	82	1	finally	finally	ADV
ejpam-5282	82	2	,	,	PUNCT
ejpam-5282	82	3	for	for	ADP
ejpam-5282	82	4	such	such	ADJ
ejpam-5282	82	5	r	r	NOUN
ejpam-5282	82	6	,	,	PUNCT
ejpam-5282	82	7	t	t	PROPN
ejpam-5282	82	8	and	and	CCONJ
ejpam-5282	82	9	p	p	X
ejpam-5282	82	10	,	,	PUNCT
ejpam-5282	82	11	we	we	PRON
ejpam-5282	82	12	have	have	VERB
ejpam-5282	82	13	(	(	PUNCT
ejpam-5282	82	14	3rq	3rq	ADJ
ejpam-5282	82	15	+	+	CCONJ
ejpam-5282	82	16	1	1	NUM
ejpam-5282	82	17	2rq−1	2rq−1	NUM
ejpam-5282	82	18	)	)	PUNCT
ejpam-5282	83	1	sin(t−	sin(t−	PROPN
ejpam-5282	83	2	tp	tp	ADP
ejpam-5282	83	3	2	2	NUM
ejpam-5282	83	4	)	)	PUNCT
ejpam-5282	84	1	+	+	CCONJ
ejpam-5282	84	2	(	(	PUNCT
ejpam-5282	84	3	rq(1	rq(1	VERB
ejpam-5282	84	4	+	+	NOUN
ejpam-5282	84	5	2r2)−	2r2)−	NUM
ejpam-5282	84	6	1	1	NUM
ejpam-5282	84	7	2rq	2rq	NOUN
ejpam-5282	84	8	)	)	PUNCT
ejpam-5282	84	9	sin	sin	NOUN
ejpam-5282	84	10	tp	tp	ADP
ejpam-5282	84	11	2	2	NUM
ejpam-5282	84	12	≤	≤	NUM
ejpam-5282	84	13	0	0	NUM
ejpam-5282	85	1	and	and	CCONJ
ejpam-5282	85	2	r	r	NOUN
ejpam-5282	85	3	p	p	X
ejpam-5282	85	4	2	2	NUM
ejpam-5282	85	5	cot	cot	NOUN
ejpam-5282	85	6	π	π	NOUN
ejpam-5282	85	7	2p	2p	NUM
ejpam-5282	85	8	pr	pr	NOUN
ejpam-5282	85	9	sin	sin	PROPN
ejpam-5282	85	10	t	t	PROPN
ejpam-5282	85	11	≥	≥	PROPN
ejpam-5282	85	12	0	0	NUM
ejpam-5282	85	13	.	.	PUNCT
ejpam-5282	86	1	which	which	PRON
ejpam-5282	86	2	give	give	VERB
ejpam-5282	86	3	p	p	NOUN
ejpam-5282	86	4	(	(	PUNCT
ejpam-5282	86	5	r	r	NOUN
ejpam-5282	86	6	,	,	PUNCT
ejpam-5282	86	7	t	t	PROPN
ejpam-5282	86	8	)	)	PUNCT
ejpam-5282	86	9	≤	≤	NOUN
ejpam-5282	86	10	0	0	PUNCT
ejpam-5282	86	11	and	and	CCONJ
ejpam-5282	86	12	prove	prove	VERB
ejpam-5282	86	13	the	the	DET
ejpam-5282	86	14	lemma	lemma	PROPN
ejpam-5282	86	15	.	.	PUNCT
ejpam-5282	87	1	at	at	ADP
ejpam-5282	87	2	finish	finish	NOUN
ejpam-5282	87	3	,	,	PUNCT
ejpam-5282	87	4	we	we	PRON
ejpam-5282	87	5	analyze	analyze	VERB
ejpam-5282	87	6	inequality	inequality	NOUN
ejpam-5282	87	7	p	p	NOUN
ejpam-5282	87	8	(	(	PUNCT
ejpam-5282	87	9	r	r	NOUN
ejpam-5282	87	10	,	,	PUNCT
ejpam-5282	87	11	t	t	PROPN
ejpam-5282	87	12	)	)	PUNCT
ejpam-5282	87	13	≤	≤	NOUN
ejpam-5282	87	14	0	0	NUM
ejpam-5282	88	1	at	at	ADP
ejpam-5282	88	2	the	the	DET
ejpam-5282	88	3	boundary	boundary	ADJ
ejpam-5282	88	4	points	point	NOUN
ejpam-5282	88	5	.	.	PUNCT
ejpam-5282	89	1	for	for	ADP
ejpam-5282	89	2	r	r	NOUN
ejpam-5282	89	3	=	=	SYM
ejpam-5282	89	4	0	0	NOUN
ejpam-5282	89	5	our	our	PRON
ejpam-5282	89	6	inequality	inequality	NOUN
ejpam-5282	89	7	is	be	AUX
ejpam-5282	89	8	transformed	transform	VERB
ejpam-5282	89	9	as	as	ADP
ejpam-5282	89	10	p	p	PROPN
ejpam-5282	89	11	(	(	PUNCT
ejpam-5282	89	12	0	0	NUM
ejpam-5282	89	13	,	,	PUNCT
ejpam-5282	89	14	t	t	PROPN
ejpam-5282	89	15	)	)	PUNCT
ejpam-5282	89	16	=	=	SYM
ejpam-5282	90	1	1−	1−	NUM
ejpam-5282	90	2	2p	2p	NUM
ejpam-5282	90	3	sinp	sinp	VERB
ejpam-5282	90	4	π	π	X
ejpam-5282	90	5	2p	2p	NUM
ejpam-5282	90	6	(	(	PUNCT
ejpam-5282	90	7	1	1	NUM
ejpam-5282	90	8	2	2	NUM
ejpam-5282	90	9	)	)	PUNCT
ejpam-5282	90	10	p	p	X
ejpam-5282	90	11	q	q	PUNCT
ejpam-5282	90	12	≤	≤	NUM
ejpam-5282	90	13	1−	1−	NUM
ejpam-5282	90	14	2	2	NUM
ejpam-5282	90	15	p	p	SYM
ejpam-5282	90	16	2	2	NUM
ejpam-5282	90	17	sinp	sinp	NOUN
ejpam-5282	90	18	π	π	NOUN
ejpam-5282	90	19	2p	2p	NOUN
ejpam-5282	90	20	≤	≤	NUM
ejpam-5282	90	21	0	0	PUNCT
ejpam-5282	90	22	and	and	CCONJ
ejpam-5282	90	23	hold	hold	VERB
ejpam-5282	90	24	for	for	ADP
ejpam-5282	90	25	this	this	DET
ejpam-5282	90	26	case	case	NOUN
ejpam-5282	90	27	.	.	PUNCT
ejpam-5282	91	1	for	for	ADP
ejpam-5282	91	2	r	r	NOUN
ejpam-5282	91	3	=	=	SYM
ejpam-5282	91	4	1	1	NUM
ejpam-5282	91	5	we	we	PRON
ejpam-5282	91	6	have	have	VERB
ejpam-5282	91	7	p	p	NOUN
ejpam-5282	91	8	(	(	PUNCT
ejpam-5282	91	9	1	1	NUM
ejpam-5282	91	10	,	,	PUNCT
ejpam-5282	91	11	t	t	PROPN
ejpam-5282	91	12	)	)	PUNCT
ejpam-5282	91	13	=	=	SYM
ejpam-5282	92	1	2p	2p	NUM
ejpam-5282	92	2	sinp	sinp	VERB
ejpam-5282	92	3	π	π	X
ejpam-5282	92	4	2p	2p	NUM
ejpam-5282	92	5	(	(	PUNCT
ejpam-5282	92	6	cosp	cosp	PROPN
ejpam-5282	92	7	t	t	PROPN
ejpam-5282	92	8	2	2	NUM
ejpam-5282	92	9	sinp	sinp	NOUN
ejpam-5282	92	10	π	π	NOUN
ejpam-5282	92	11	2p	2p	NOUN
ejpam-5282	92	12	−	−	NOUN
ejpam-5282	92	13	1	1	NUM
ejpam-5282	93	1	+	+	SYM
ejpam-5282	93	2	2	2	NUM
ejpam-5282	93	3	p	p	NOUN
ejpam-5282	93	4	2	2	NUM
ejpam-5282	93	5	−	−	NOUN
ejpam-5282	93	6	p	p	NOUN
ejpam-5282	94	1	q	q	X
ejpam-5282	94	2	cot	cot	NOUN
ejpam-5282	94	3	π	π	PROPN
ejpam-5282	94	4	2p	2p	NUM
ejpam-5282	94	5	cos	cos	ADP
ejpam-5282	94	6	p(π	p(π	PROPN
ejpam-5282	94	7	−	−	PROPN
ejpam-5282	94	8	t	t	PROPN
ejpam-5282	94	9	)	)	PUNCT
ejpam-5282	94	10	2	2	NUM
ejpam-5282	94	11	)	)	PUNCT
ejpam-5282	94	12	≤	≤	NOUN
ejpam-5282	94	13	0	0	NUM
ejpam-5282	94	14	with	with	ADP
ejpam-5282	94	15	substitute	substitute	NOUN
ejpam-5282	94	16	of	of	ADP
ejpam-5282	94	17	variable	variable	ADJ
ejpam-5282	94	18	t	t	NOUN
ejpam-5282	95	1	=	=	PUNCT
ejpam-5282	95	2	π	π	X
ejpam-5282	95	3	−	−	PROPN
ejpam-5282	95	4	2y	2y	PROPN
ejpam-5282	95	5	and	and	CCONJ
ejpam-5282	95	6	using	use	VERB
ejpam-5282	95	7	derivative	derivative	NOUN
ejpam-5282	95	8	on	on	ADP
ejpam-5282	95	9	variable	variable	ADJ
ejpam-5282	95	10	y	y	PROPN
ejpam-5282	95	11	,	,	PUNCT
ejpam-5282	95	12	this	this	DET
ejpam-5282	95	13	inequality	inequality	NOUN
ejpam-5282	95	14	also	also	ADV
ejpam-5282	95	15	hold	hold	VERB
ejpam-5282	95	16	.	.	PUNCT
ejpam-5282	96	1	e.	e.	PROPN
ejpam-5282	96	2	bajrami	bajrami	PROPN
ejpam-5282	96	3	/	/	SYM
ejpam-5282	96	4	eur	eur	PROPN
ejpam-5282	96	5	.	.	PUNCT
ejpam-5282	97	1	j.	j.	PROPN
ejpam-5282	97	2	pure	pure	PROPN
ejpam-5282	97	3	appl	appl	PROPN
ejpam-5282	97	4	.	.	PROPN
ejpam-5282	97	5	math	math	PROPN
ejpam-5282	97	6	,	,	PUNCT
ejpam-5282	97	7	17	17	NUM
ejpam-5282	97	8	(	(	PUNCT
ejpam-5282	97	9	3	3	NUM
ejpam-5282	97	10	)	)	PUNCT
ejpam-5282	97	11	(	(	PUNCT
ejpam-5282	97	12	2024	2024	NUM
ejpam-5282	97	13	)	)	PUNCT
ejpam-5282	97	14	,	,	PUNCT
ejpam-5282	97	15	1685	1685	NUM
ejpam-5282	97	16	-	-	SYM
ejpam-5282	97	17	1690	1690	NUM
ejpam-5282	97	18	1689	1689	NUM
ejpam-5282	97	19	for	for	ADP
ejpam-5282	97	20	t	t	NOUN
ejpam-5282	97	21	=	=	SYM
ejpam-5282	97	22	0	0	PROPN
ejpam-5282	97	23	our	our	PRON
ejpam-5282	97	24	inequality	inequality	NOUN
ejpam-5282	97	25	has	have	VERB
ejpam-5282	97	26	a	a	DET
ejpam-5282	97	27	form	form	NOUN
ejpam-5282	97	28	p	p	NOUN
ejpam-5282	97	29	(	(	PUNCT
ejpam-5282	97	30	r	r	NOUN
ejpam-5282	97	31	,	,	PUNCT
ejpam-5282	97	32	0	0	NUM
ejpam-5282	97	33	)	)	PUNCT
ejpam-5282	97	34	=	=	SYM
ejpam-5282	97	35	(	(	PUNCT
ejpam-5282	97	36	1−	1−	NUM
ejpam-5282	97	37	r)p	r)p	NOUN
ejpam-5282	97	38	−	−	NOUN
ejpam-5282	97	39	2p	2p	NUM
ejpam-5282	97	40	sinp	sinp	VERB
ejpam-5282	97	41	π	π	X
ejpam-5282	97	42	2p	2p	NUM
ejpam-5282	97	43	(	(	PUNCT
ejpam-5282	97	44	1	1	NUM
ejpam-5282	97	45	+	+	NUM
ejpam-5282	97	46	r2	r2	PROPN
ejpam-5282	97	47	2	2	NUM
ejpam-5282	97	48	)	)	PUNCT
ejpam-5282	97	49	p	p	X
ejpam-5282	97	50	q	q	X
ejpam-5282	97	51	.	.	PUNCT
ejpam-5282	98	1	as	as	ADP
ejpam-5282	98	2	in	in	ADP
ejpam-5282	98	3	the	the	DET
ejpam-5282	98	4	case	case	NOUN
ejpam-5282	98	5	of	of	ADP
ejpam-5282	98	6	r	r	NOUN
ejpam-5282	98	7	=	=	SYM
ejpam-5282	98	8	0	0	NUM
ejpam-5282	98	9	,	,	PUNCT
ejpam-5282	98	10	we	we	PRON
ejpam-5282	98	11	can	can	AUX
ejpam-5282	98	12	transform	transform	VERB
ejpam-5282	98	13	and	and	CCONJ
ejpam-5282	98	14	prove	prove	VERB
ejpam-5282	98	15	inequality	inequality	NOUN
ejpam-5282	98	16	p	p	NOUN
ejpam-5282	98	17	(	(	PUNCT
ejpam-5282	98	18	r	r	NOUN
ejpam-5282	98	19	,	,	PUNCT
ejpam-5282	98	20	0	0	NUM
ejpam-5282	98	21	)	)	PUNCT
ejpam-5282	98	22	=	=	SYM
ejpam-5282	99	1	(	(	PUNCT
ejpam-5282	99	2	1	1	NUM
ejpam-5282	99	3	+	+	NUM
ejpam-5282	99	4	r2	r2	NOUN
ejpam-5282	99	5	)	)	PUNCT
ejpam-5282	99	6	(	(	PUNCT
ejpam-5282	99	7	1−	1−	NUM
ejpam-5282	99	8	2	2	NUM
ejpam-5282	99	9	p	p	SYM
ejpam-5282	99	10	2	2	NUM
ejpam-5282	99	11	sinp	sinp	NOUN
ejpam-5282	99	12	π	π	NOUN
ejpam-5282	99	13	2	2	X
ejpam-5282	99	14	)	)	PUNCT
ejpam-5282	99	15	≤	≤	NOUN
ejpam-5282	99	16	0	0	NUM
ejpam-5282	99	17	.	.	PUNCT
ejpam-5282	100	1	for	for	ADP
ejpam-5282	100	2	t	t	NOUN
ejpam-5282	100	3	=	=	PUNCT
ejpam-5282	100	4	π	π	NOUN
ejpam-5282	100	5	we	we	PRON
ejpam-5282	100	6	see	see	VERB
ejpam-5282	100	7	that	that	SCONJ
ejpam-5282	101	1	p	p	X
ejpam-5282	101	2	(	(	PUNCT
ejpam-5282	101	3	r	r	NOUN
ejpam-5282	101	4	,	,	PUNCT
ejpam-5282	101	5	π	π	NOUN
ejpam-5282	101	6	)	)	PUNCT
ejpam-5282	101	7	=	=	SYM
ejpam-5282	101	8	2pr	2pr	NOUN
ejpam-5282	102	1	p	p	NOUN
ejpam-5282	102	2	2	2	NUM
ejpam-5282	102	3	sinp	sinp	NOUN
ejpam-5282	102	4	π	π	PROPN
ejpam-5282	102	5	2p	2p	NUM
ejpam-5282	102	6			X
ejpam-5282	102	7	(	(	PUNCT
ejpam-5282	102	8	1+r2	1+r2	NUM
ejpam-5282	102	9	r	r	NOUN
ejpam-5282	102	10	−	−	NOUN
ejpam-5282	102	11	2	2	NUM
ejpam-5282	102	12	)	)	PUNCT
ejpam-5282	102	13	p	p	NOUN
ejpam-5282	102	14	2	2	NUM
ejpam-5282	102	15	sinp	sinp	NOUN
ejpam-5282	102	16	π	π	X
ejpam-5282	102	17	2p	2p	X
ejpam-5282	102	18	+	+	CCONJ
ejpam-5282	102	19	cot	cot	NOUN
ejpam-5282	102	20	π	π	X
ejpam-5282	102	21	2p	2p	NUM
ejpam-5282	102	22	−	−	PROPN
ejpam-5282	102	23	(	(	PUNCT
ejpam-5282	102	24	1	1	NUM
ejpam-5282	102	25	+	+	NUM
ejpam-5282	102	26	r2	r2	PROPN
ejpam-5282	102	27	2r	2r	NUM
ejpam-5282	102	28	)	)	PUNCT
ejpam-5282	103	1	p	p	X
ejpam-5282	103	2	2	2	NUM
ejpam-5282	103	3			PROPN
ejpam-5282	103	4	.	.	PUNCT
ejpam-5282	104	1	as	as	ADP
ejpam-5282	104	2	in	in	ADP
ejpam-5282	104	3	the	the	PRON
ejpam-5282	104	4	[	[	X
ejpam-5282	104	5	9	9	NUM
ejpam-5282	104	6	]	]	PUNCT
ejpam-5282	104	7	,	,	PUNCT
ejpam-5282	104	8	using	use	VERB
ejpam-5282	104	9	transformation	transformation	NOUN
ejpam-5282	104	10	a	a	DET
ejpam-5282	104	11	=	=	SYM
ejpam-5282	104	12	1+r2	1+r2	NUM
ejpam-5282	104	13	2r	2r	NUM
ejpam-5282	104	14	≥	≥	NOUN
ejpam-5282	104	15	0	0	NUM
ejpam-5282	104	16	we	we	PRON
ejpam-5282	104	17	get	get	VERB
ejpam-5282	104	18	r(a	r(a	PRON
ejpam-5282	104	19	)	)	PUNCT
ejpam-5282	105	1	=	=	SYM
ejpam-5282	105	2	(	(	PUNCT
ejpam-5282	105	3	2a−2	2a−2	NUM
ejpam-5282	105	4	)	)	PUNCT
ejpam-5282	105	5	p	p	NOUN
ejpam-5282	105	6	2	2	NUM
ejpam-5282	105	7	sinp	sinp	NOUN
ejpam-5282	105	8	π	π	NOUN
ejpam-5282	105	9	2	2	NUM
ejpam-5282	105	10	+	+	CCONJ
ejpam-5282	105	11	cot	cot	NOUN
ejpam-5282	105	12	π	π	X
ejpam-5282	105	13	2p	2p	NOUN
ejpam-5282	105	14	−	−	PROPN
ejpam-5282	105	15	a	a	DET
ejpam-5282	105	16	p	p	NOUN
ejpam-5282	105	17	2	2	NUM
ejpam-5282	105	18	.	.	PUNCT
ejpam-5282	106	1	it	it	PRON
ejpam-5282	106	2	is	be	AUX
ejpam-5282	106	3	easy	easy	ADJ
ejpam-5282	106	4	to	to	PART
ejpam-5282	106	5	see	see	VERB
ejpam-5282	106	6	that	that	DET
ejpam-5282	106	7	r(a	r(a	PROPN
ejpam-5282	106	8	)	)	PUNCT
ejpam-5282	106	9	is	be	AUX
ejpam-5282	106	10	increasing	increase	VERB
ejpam-5282	106	11	,	,	PUNCT
ejpam-5282	106	12	and	and	CCONJ
ejpam-5282	106	13	finally	finally	ADV
ejpam-5282	106	14	p	p	X
ejpam-5282	106	15	(	(	PUNCT
ejpam-5282	106	16	r	r	NOUN
ejpam-5282	106	17	,	,	PUNCT
ejpam-5282	106	18	π	π	NOUN
ejpam-5282	106	19	)	)	PUNCT
ejpam-5282	106	20	≤	≤	NOUN
ejpam-5282	106	21	0	0	NUM
ejpam-5282	106	22	.	.	PUNCT
ejpam-5282	107	1	the	the	DET
ejpam-5282	107	2	main	main	ADJ
ejpam-5282	107	3	outcome	outcome	NOUN
ejpam-5282	107	4	of	of	ADP
ejpam-5282	107	5	this	this	DET
ejpam-5282	107	6	paper	paper	NOUN
ejpam-5282	107	7	is	be	AUX
ejpam-5282	107	8	given	give	VERB
ejpam-5282	107	9	in	in	ADP
ejpam-5282	107	10	the	the	DET
ejpam-5282	107	11	next	next	ADJ
ejpam-5282	107	12	theorem	theorem	PROPN
ejpam-5282	107	13	.	.	PUNCT
ejpam-5282	107	14	theorem	theorem	NOUN
ejpam-5282	107	15	1	1	NUM
ejpam-5282	107	16	.	.	PUNCT
ejpam-5282	108	1	let	let	VERB
ejpam-5282	108	2	1	1	NUM
ejpam-5282	108	3	<	<	X
ejpam-5282	108	4	p	p	X
ejpam-5282	108	5	,	,	PUNCT
ejpam-5282	108	6	q	q	X
ejpam-5282	108	7	<	<	X
ejpam-5282	108	8	∞	∞	PROPN
ejpam-5282	108	9	and	and	CCONJ
ejpam-5282	108	10	assume	assume	VERB
ejpam-5282	108	11	that	that	SCONJ
ejpam-5282	108	12	f	f	PROPN
ejpam-5282	108	13	=	=	SYM
ejpam-5282	108	14	g	g	PROPN
ejpam-5282	108	15	+	+	CCONJ
ejpam-5282	108	16	h̄	h̄	X
ejpam-5282	109	1	∈	∈	NOUN
ejpam-5282	109	2	hp	hp	NOUN
ejpam-5282	109	3	is	be	AUX
ejpam-5282	109	4	a	a	DET
ejpam-5282	109	5	harmonic	harmonic	ADJ
ejpam-5282	109	6	mapping	mapping	NOUN
ejpam-5282	109	7	on	on	ADP
ejpam-5282	109	8	the	the	DET
ejpam-5282	109	9	unit	unit	NOUN
ejpam-5282	109	10	disk	disk	NOUN
ejpam-5282	109	11	with	with	ADP
ejpam-5282	109	12	ℜ(g(0)h(0	ℜ(g(0)h(0	NOUN
ejpam-5282	109	13	)	)	PUNCT
ejpam-5282	109	14	)	)	PUNCT
ejpam-5282	110	1	≤	≤	ADV
ejpam-5282	110	2	0	0	X
ejpam-5282	110	3	.	.	PUNCT
ejpam-5282	111	1	then	then	ADV
ejpam-5282	111	2	we	we	PRON
ejpam-5282	111	3	have	have	VERB
ejpam-5282	111	4	the	the	DET
ejpam-5282	111	5	following	follow	VERB
ejpam-5282	111	6	sharp	sharp	ADJ
ejpam-5282	111	7	inequality	inequality	NOUN
ejpam-5282	111	8	∥f∥hp	∥f∥hp	PROPN
ejpam-5282	111	9	≤	≤	NUM
ejpam-5282	111	10	2	2	NUM
ejpam-5282	111	11	1−	1−	NUM
ejpam-5282	111	12	1	1	NUM
ejpam-5282	111	13	q	q	NOUN
ejpam-5282	111	14	max{sin	max{sin	NOUN
ejpam-5282	111	15	π	π	PROPN
ejpam-5282	111	16	2p	2p	NUM
ejpam-5282	111	17	,	,	PUNCT
ejpam-5282	111	18	cos	cos	PROPN
ejpam-5282	111	19	π	π	PROPN
ejpam-5282	111	20	2p	2p	NUM
ejpam-5282	111	21	}	}	PUNCT
ejpam-5282	111	22	(	(	PUNCT
ejpam-5282	111	23	∫	∫	PROPN
ejpam-5282	111	24	t	t	PROPN
ejpam-5282	111	25	(	(	PUNCT
ejpam-5282	111	26	|g|q	|g|q	VERB
ejpam-5282	111	27	+	+	NOUN
ejpam-5282	111	28	|h|q)p	|h|q)p	NUM
ejpam-5282	111	29	/	/	SYM
ejpam-5282	111	30	q	q	NOUN
ejpam-5282	111	31	)	)	PUNCT
ejpam-5282	111	32	1	1	NUM
ejpam-5282	111	33	/	/	SYM
ejpam-5282	111	34	p	p	NOUN
ejpam-5282	111	35	.	.	PUNCT
ejpam-5282	112	1	proof	proof	NOUN
ejpam-5282	112	2	.	.	PUNCT
ejpam-5282	113	1	applying	apply	VERB
ejpam-5282	113	2	lemma	lemma	PROPN
ejpam-5282	113	3	2.1	2.1	NUM
ejpam-5282	113	4	,	,	PUNCT
ejpam-5282	113	5	lemma	lemma	PROPN
ejpam-5282	113	6	2.2	2.2	NUM
ejpam-5282	113	7	and	and	CCONJ
ejpam-5282	113	8	integrating	integrate	VERB
ejpam-5282	113	9	over	over	ADP
ejpam-5282	113	10	t	t	PROPN
ejpam-5282	113	11	,	,	PUNCT
ejpam-5282	113	12	0	0	PUNCT
ejpam-5282	113	13	<	<	X
ejpam-5282	113	14	r	r	X
ejpam-5282	113	15	<	<	X
ejpam-5282	113	16	1	1	NUM
ejpam-5282	113	17	and	and	CCONJ
ejpam-5282	113	18	letting	let	VERB
ejpam-5282	113	19	r	r	NOUN
ejpam-5282	113	20	→	→	SYM
ejpam-5282	113	21	1−	1−	NUM
ejpam-5282	113	22	we	we	PRON
ejpam-5282	113	23	get∫	get∫	PROPN
ejpam-5282	113	24	t	t	PROPN
ejpam-5282	113	25	|g(z	|g(z	NOUN
ejpam-5282	113	26	)	)	PUNCT
ejpam-5282	114	1	+	+	CCONJ
ejpam-5282	114	2	h(z)|p	h(z)|p	PROPN
ejpam-5282	114	3	≤	≤	NUM
ejpam-5282	114	4	2	2	NUM
ejpam-5282	114	5	p−	p−	NOUN
ejpam-5282	114	6	p	p	X
ejpam-5282	114	7	q	q	X
ejpam-5282	114	8	sinp	sinp	VERB
ejpam-5282	114	9	π	π	X
ejpam-5282	114	10	2p	2p	NUM
ejpam-5282	114	11	∫	∫	PROPN
ejpam-5282	114	12	t	t	PROPN
ejpam-5282	114	13	(	(	PUNCT
ejpam-5282	114	14	|z|q	|z|q	PROPN
ejpam-5282	114	15	+	+	NUM
ejpam-5282	114	16	|w|q)p	|w|q)p	NUM
ejpam-5282	114	17	/	/	SYM
ejpam-5282	114	18	q	q	NOUN
ejpam-5282	114	19	−dp	−dp	PROPN
ejpam-5282	114	20	,	,	PUNCT
ejpam-5282	114	21	qt	qt	NOUN
ejpam-5282	114	22	(	(	PUNCT
ejpam-5282	114	23	z	z	NOUN
ejpam-5282	114	24	)	)	PUNCT
ejpam-5282	114	25	,	,	PUNCT
ejpam-5282	114	26	in	in	ADP
ejpam-5282	114	27	case	case	NOUN
ejpam-5282	114	28	of	of	ADP
ejpam-5282	114	29	p	p	X
ejpam-5282	114	30	>	>	X
ejpam-5282	114	31	2	2	NUM
ejpam-5282	114	32	.	.	PUNCT
ejpam-5282	114	33	for	for	ADP
ejpam-5282	114	34	1	1	NUM
ejpam-5282	114	35	<	<	X
ejpam-5282	114	36	p	p	X
ejpam-5282	114	37	<	<	X
ejpam-5282	114	38	2∫	2∫	PROPN
ejpam-5282	114	39	t	t	PROPN
ejpam-5282	114	40	|g(z	|g(z	NOUN
ejpam-5282	114	41	)	)	PUNCT
ejpam-5282	115	1	+	+	CCONJ
ejpam-5282	115	2	h(z)|p	h(z)|p	PROPN
ejpam-5282	115	3	≤	≤	NUM
ejpam-5282	115	4	2	2	NUM
ejpam-5282	115	5	p−	p−	NOUN
ejpam-5282	115	6	p	p	NOUN
ejpam-5282	115	7	q	q	X
ejpam-5282	115	8	cosp	cosp	NOUN
ejpam-5282	115	9	π	π	PROPN
ejpam-5282	115	10	2p	2p	NUM
ejpam-5282	115	11	∫	∫	PROPN
ejpam-5282	115	12	t	t	PROPN
ejpam-5282	115	13	(	(	PUNCT
ejpam-5282	115	14	|z|q	|z|q	PROPN
ejpam-5282	115	15	+	+	NUM
ejpam-5282	115	16	|w|q)p	|w|q)p	NUM
ejpam-5282	115	17	/	/	SYM
ejpam-5282	115	18	q	q	NOUN
ejpam-5282	115	19	−dp	−dp	PROPN
ejpam-5282	115	20	,	,	PUNCT
ejpam-5282	115	21	qt	qt	NOUN
ejpam-5282	115	22	(	(	PUNCT
ejpam-5282	115	23	z	z	NOUN
ejpam-5282	115	24	)	)	PUNCT
ejpam-5282	115	25	.	.	PUNCT
ejpam-5282	116	1	since	since	SCONJ
ejpam-5282	116	2	∫	∫	PROPN
ejpam-5282	116	3	t	t	PROPN
ejpam-5282	116	4	t	t	PROPN
ejpam-5282	116	5	(	(	PUNCT
ejpam-5282	116	6	z	z	NOUN
ejpam-5282	116	7	)	)	PUNCT
ejpam-5282	116	8	≥	≥	NOUN
ejpam-5282	116	9	0	0	NUM
ejpam-5282	116	10	(	(	PUNCT
ejpam-5282	116	11	because	because	SCONJ
ejpam-5282	116	12	of	of	ADP
ejpam-5282	116	13	subharmonicity	subharmonicity	NOUN
ejpam-5282	116	14	)	)	PUNCT
ejpam-5282	116	15	.	.	PUNCT
ejpam-5282	117	1	we	we	PRON
ejpam-5282	117	2	conclude	conclude	VERB
ejpam-5282	117	3	that	that	SCONJ
ejpam-5282	117	4	∥f∥hp	∥f∥hp	PROPN
ejpam-5282	117	5	≤	≤	NUM
ejpam-5282	117	6	2	2	NUM
ejpam-5282	117	7	1−	1−	NUM
ejpam-5282	117	8	1	1	NUM
ejpam-5282	117	9	q	q	NOUN
ejpam-5282	117	10	max{sin	max{sin	NOUN
ejpam-5282	117	11	π	π	PROPN
ejpam-5282	117	12	2p	2p	NUM
ejpam-5282	117	13	,	,	PUNCT
ejpam-5282	117	14	cos	cos	PROPN
ejpam-5282	117	15	π	π	PROPN
ejpam-5282	117	16	2p	2p	NUM
ejpam-5282	117	17	}	}	PUNCT
ejpam-5282	117	18	(	(	PUNCT
ejpam-5282	117	19	∫	∫	PROPN
ejpam-5282	117	20	t	t	PROPN
ejpam-5282	117	21	(	(	PUNCT
ejpam-5282	117	22	|g|q	|g|q	VERB
ejpam-5282	117	23	+	+	NOUN
ejpam-5282	117	24	|h|q)p	|h|q)p	NUM
ejpam-5282	117	25	/	/	SYM
ejpam-5282	117	26	q	q	NOUN
ejpam-5282	117	27	)	)	PUNCT
ejpam-5282	117	28	1	1	X
ejpam-5282	117	29	/	/	SYM
ejpam-5282	117	30	p	p	NOUN
ejpam-5282	117	31	.	.	PUNCT
ejpam-5282	118	1	finally	finally	ADV
ejpam-5282	118	2	,	,	PUNCT
ejpam-5282	118	3	we	we	PRON
ejpam-5282	118	4	see	see	VERB
ejpam-5282	118	5	that	that	PRON
ejpam-5282	118	6	constant	constant	ADJ
ejpam-5282	118	7	in	in	ADP
ejpam-5282	118	8	the	the	DET
ejpam-5282	118	9	norm	norm	NOUN
ejpam-5282	118	10	(	(	PUNCT
ejpam-5282	118	11	1.1	1.1	NUM
ejpam-5282	118	12	)	)	PUNCT
ejpam-5282	118	13	has	have	VERB
ejpam-5282	118	14	a	a	DET
ejpam-5282	118	15	form	form	NOUN
ejpam-5282	118	16	ap	ap	PROPN
ejpam-5282	118	17	,	,	PUNCT
ejpam-5282	118	18	q	q	NOUN
ejpam-5282	118	19	=	=	SYM
ejpam-5282	118	20	2	2	NUM
ejpam-5282	118	21	1−	1−	NUM
ejpam-5282	118	22	1	1	NUM
ejpam-5282	118	23	q	q	NOUN
ejpam-5282	118	24	max{sin	max{sin	NOUN
ejpam-5282	118	25	π	π	PROPN
ejpam-5282	118	26	2p	2p	NUM
ejpam-5282	118	27	,	,	PUNCT
ejpam-5282	118	28	cos	cos	PROPN
ejpam-5282	118	29	π	π	PROPN
ejpam-5282	118	30	2p	2p	NUM
ejpam-5282	118	31	}	}	PUNCT
ejpam-5282	118	32	which	which	PRON
ejpam-5282	118	33	coincide	coincide	VERB
ejpam-5282	118	34	with	with	ADP
ejpam-5282	118	35	result	result	NOUN
ejpam-5282	118	36	in	in	ADP
ejpam-5282	118	37	[	[	X
ejpam-5282	118	38	9	9	NUM
ejpam-5282	118	39	]	]	PUNCT
ejpam-5282	118	40	,	,	PUNCT
ejpam-5282	118	41	for	for	ADP
ejpam-5282	118	42	a	a	DET
ejpam-5282	118	43	special	special	ADJ
ejpam-5282	118	44	case	case	NOUN
ejpam-5282	118	45	when	when	SCONJ
ejpam-5282	118	46	q	q	PROPN
ejpam-5282	118	47	=	=	SYM
ejpam-5282	118	48	2	2	NUM
ejpam-5282	118	49	.	.	NUM
ejpam-5282	118	50	references	reference	NOUN
ejpam-5282	118	51	1690	1690	NUM
ejpam-5282	118	52	acknowledgements	acknowledgement	NOUN
ejpam-5282	118	53	i	i	PRON
ejpam-5282	118	54	would	would	AUX
ejpam-5282	118	55	like	like	VERB
ejpam-5282	118	56	to	to	PART
ejpam-5282	118	57	express	express	VERB
ejpam-5282	118	58	my	my	PRON
ejpam-5282	118	59	gratitude	gratitude	NOUN
ejpam-5282	118	60	to	to	ADP
ejpam-5282	118	61	the	the	DET
ejpam-5282	118	62	anonymous	anonymous	ADJ
ejpam-5282	118	63	referees	referee	NOUN
ejpam-5282	118	64	for	for	ADP
ejpam-5282	118	65	their	their	PRON
ejpam-5282	118	66	helpful	helpful	ADJ
ejpam-5282	118	67	comments	comment	NOUN
ejpam-5282	118	68	that	that	PRON
ejpam-5282	118	69	have	have	AUX
ejpam-5282	118	70	improved	improve	VERB
ejpam-5282	118	71	the	the	DET
ejpam-5282	118	72	quality	quality	NOUN
ejpam-5282	118	73	of	of	ADP
ejpam-5282	118	74	the	the	DET
ejpam-5282	118	75	paper	paper	NOUN
ejpam-5282	118	76	.	.	PUNCT
ejpam-5282	119	1	references	reference	NOUN
ejpam-5282	119	2	[	[	X
ejpam-5282	119	3	1	1	NUM
ejpam-5282	119	4	]	]	PUNCT
ejpam-5282	119	5	i.	i.	PROPN
ejpam-5282	119	6	e.	e.	PROPN
ejpam-5282	119	7	verbitsky	verbitsky	PROPN
ejpam-5282	119	8	b.	b.	PROPN
ejpam-5282	119	9	hollenbeck	hollenbeck	PROPN
ejpam-5282	119	10	.	.	PUNCT
ejpam-5282	120	1	best	good	ADJ
ejpam-5282	120	2	constants	constant	NOUN
ejpam-5282	120	3	for	for	ADP
ejpam-5282	120	4	the	the	DET
ejpam-5282	120	5	riesz	riesz	PROPN
ejpam-5282	120	6	projection	projection	NOUN
ejpam-5282	120	7	.	.	PUNCT
ejpam-5282	121	1	j.	j.	PROPN
ejpam-5282	121	2	funct	funct	PROPN
ejpam-5282	121	3	.	.	PUNCT
ejpam-5282	122	1	anal	anal	PROPN
ejpam-5282	122	2	.	.	PROPN
ejpam-5282	122	3	,	,	PUNCT
ejpam-5282	122	4	175(2):370–392	175(2):370–392	NUM
ejpam-5282	122	5	,	,	PUNCT
ejpam-5282	122	6	2000	2000	NUM
ejpam-5282	122	7	.	.	PUNCT
ejpam-5282	123	1	[	[	X
ejpam-5282	123	2	2	2	X
ejpam-5282	123	3	]	]	PUNCT
ejpam-5282	123	4	e.	e.	PROPN
ejpam-5282	123	5	bajrami	bajrami	PROPN
ejpam-5282	123	6	.	.	PUNCT
ejpam-5282	124	1	improvement	improvement	NOUN
ejpam-5282	124	2	of	of	ADP
ejpam-5282	124	3	isoperimetric	isoperimetric	ADJ
ejpam-5282	124	4	type	type	NOUN
ejpam-5282	124	5	inequality	inequality	NOUN
ejpam-5282	124	6	for	for	ADP
ejpam-5282	124	7	harmonic	harmonic	ADJ
ejpam-5282	124	8	functions	function	NOUN
ejpam-5282	124	9	in	in	ADP
ejpam-5282	124	10	the	the	DET
ejpam-5282	124	11	case	case	NOUN
ejpam-5282	124	12	p	p	X
ejpam-5282	124	13	=	=	NOUN
ejpam-5282	124	14	4	4	X
ejpam-5282	124	15	.	.	X
ejpam-5282	124	16	indagationes	indagatione	NOUN
ejpam-5282	124	17	mathematicae	mathematicae	PROPN
ejpam-5282	124	18	,	,	PUNCT
ejpam-5282	124	19	28(2):383–389	28(2):383–389	NOUN
ejpam-5282	124	20	,	,	PUNCT
ejpam-5282	124	21	2017	2017	NUM
ejpam-5282	124	22	.	.	PUNCT
ejpam-5282	125	1	[	[	X
ejpam-5282	125	2	3	3	X
ejpam-5282	125	3	]	]	X
ejpam-5282	125	4	e.	e.	PROPN
ejpam-5282	125	5	f.	f.	PROPN
ejpam-5282	125	6	beckenbach	beckenbach	PROPN
ejpam-5282	125	7	.	.	PUNCT
ejpam-5282	126	1	on	on	ADP
ejpam-5282	126	2	a	a	DET
ejpam-5282	126	3	theorem	theorem	NOUN
ejpam-5282	126	4	of	of	ADP
ejpam-5282	126	5	fejér	fejér	NOUN
ejpam-5282	126	6	and	and	CCONJ
ejpam-5282	126	7	riesz	riesz	NOUN
ejpam-5282	126	8	.	.	PUNCT
ejpam-5282	127	1	j.	j.	PROPN
ejpam-5282	127	2	london	london	PROPN
ejpam-5282	127	3	math	math	PROPN
ejpam-5282	127	4	.	.	PUNCT
ejpam-5282	128	1	soc	soc	PROPN
ejpam-5282	128	2	.	.	PROPN
ejpam-5282	128	3	,	,	PUNCT
ejpam-5282	128	4	13:82–86	13:82–86	NUM
ejpam-5282	128	5	,	,	PUNCT
ejpam-5282	128	6	1938	1938	NUM
ejpam-5282	128	7	.	.	PUNCT
ejpam-5282	129	1	[	[	X
ejpam-5282	129	2	4	4	X
ejpam-5282	129	3	]	]	PUNCT
ejpam-5282	129	4	m.	m.	PROPN
ejpam-5282	129	5	stein	stein	PROPN
ejpam-5282	129	6	c.	c.	PROPN
ejpam-5282	129	7	efferman	efferman	PROPN
ejpam-5282	129	8	.	.	PUNCT
ejpam-5282	130	1	hp	hp	ADJ
ejpam-5282	130	2	spaces	space	NOUN
ejpam-5282	130	3	of	of	ADP
ejpam-5282	130	4	several	several	ADJ
ejpam-5282	130	5	variables	variable	NOUN
ejpam-5282	130	6	.	.	PUNCT
ejpam-5282	131	1	acta	acta	PROPN
ejpam-5282	131	2	math	math	PROPN
ejpam-5282	131	3	.	.	PUNCT
ejpam-5282	131	4	,	,	PUNCT
ejpam-5282	131	5	129:137–193	129:137–193	NUM
ejpam-5282	131	6	,	,	PUNCT
ejpam-5282	131	7	1972	1972	NUM
ejpam-5282	131	8	.	.	PUNCT
ejpam-5282	132	1	[	[	X
ejpam-5282	132	2	5	5	X
ejpam-5282	132	3	]	]	PUNCT
ejpam-5282	132	4	t.	t.	PROPN
ejpam-5282	132	5	tao	tao	PROPN
ejpam-5282	132	6	s.	s.	PROPN
ejpam-5282	132	7	wainger	wainger	PROPN
ejpam-5282	132	8	c.	c.	PROPN
ejpam-5282	132	9	efferman	efferman	PROPN
ejpam-5282	132	10	,	,	PUNCT
ejpam-5282	132	11	a.	a.	NOUN
ejpam-5282	132	12	lonescu	lonescu	PROPN
ejpam-5282	132	13	.	.	PUNCT
ejpam-5282	133	1	analysis	analysis	NOUN
ejpam-5282	133	2	and	and	CCONJ
ejpam-5282	133	3	its	its	PRON
ejpam-5282	133	4	applications	application	NOUN
ejpam-5282	133	5	:	:	PUNCT
ejpam-5282	133	6	the	the	DET
ejpam-5282	133	7	mathematical	mathematical	ADJ
ejpam-5282	133	8	work	work	NOUN
ejpam-5282	133	9	of	of	ADP
ejpam-5282	133	10	elias	elias	PROPN
ejpam-5282	133	11	stein	stein	PROPN
ejpam-5282	133	12	.	.	PUNCT
ejpam-5282	134	1	bull	bull	PROPN
ejpam-5282	134	2	.	.	PUNCT
ejpam-5282	135	1	amer	amer	PROPN
ejpam-5282	135	2	.	.	PUNCT
ejpam-5282	135	3	math	math	PROPN
ejpam-5282	135	4	.	.	PUNCT
ejpam-5282	136	1	soc	soc	PROPN
ejpam-5282	136	2	.	.	PUNCT
ejpam-5282	137	1	new	new	ADJ
ejpam-5282	137	2	ser	ser	PROPN
ejpam-5282	137	3	.	.	PROPN
ejpam-5282	137	4	,	,	PUNCT
ejpam-5282	137	5	57:523–594	57:523–594	PROPN
ejpam-5282	137	6	,	,	PUNCT
ejpam-5282	137	7	2020	2020	NUM
ejpam-5282	137	8	.	.	PUNCT
ejpam-5282	138	1	[	[	X
ejpam-5282	138	2	6	6	NUM
ejpam-5282	138	3	]	]	PUNCT
ejpam-5282	138	4	e.bajrami	e.bajrami	PROPN
ejpam-5282	138	5	d.	d.	PROPN
ejpam-5282	138	6	kalaj	kalaj	PROPN
ejpam-5282	138	7	.	.	PUNCT
ejpam-5282	139	1	on	on	ADP
ejpam-5282	139	2	some	some	DET
ejpam-5282	139	3	riesz	riesz	NOUN
ejpam-5282	139	4	and	and	CCONJ
ejpam-5282	139	5	carleman	carleman	ADJ
ejpam-5282	139	6	type	type	NOUN
ejpam-5282	139	7	inequalities	inequality	NOUN
ejpam-5282	139	8	for	for	ADP
ejpam-5282	139	9	harmonic	harmonic	ADJ
ejpam-5282	139	10	functions	function	NOUN
ejpam-5282	139	11	in	in	ADP
ejpam-5282	139	12	the	the	DET
ejpam-5282	139	13	unit	unit	NOUN
ejpam-5282	139	14	disk	disk	NOUN
ejpam-5282	139	15	.	.	PUNCT
ejpam-5282	140	1	comput	comput	NOUN
ejpam-5282	140	2	.	.	PUNCT
ejpam-5282	141	1	methods	method	NOUN
ejpam-5282	141	2	funct	funct	VERB
ejpam-5282	141	3	.	.	PUNCT
ejpam-5282	142	1	theory	theory	NOUN
ejpam-5282	142	2	,	,	PUNCT
ejpam-5282	142	3	18:295–305	18:295–305	PROPN
ejpam-5282	142	4	,	,	PUNCT
ejpam-5282	142	5	2018	2018	NUM
ejpam-5282	142	6	.	.	PUNCT
ejpam-5282	143	1	[	[	X
ejpam-5282	143	2	7	7	X
ejpam-5282	143	3	]	]	X
ejpam-5282	143	4	p.	p.	NOUN
ejpam-5282	143	5	l.	l.	PROPN
ejpam-5282	143	6	duren	duren	PROPN
ejpam-5282	143	7	.	.	PUNCT
ejpam-5282	143	8	theory	theory	NOUN
ejpam-5282	143	9	of	of	ADP
ejpam-5282	143	10	hp	hp	ADJ
ejpam-5282	143	11	spaces	space	NOUN
ejpam-5282	143	12	.	.	PUNCT
ejpam-5282	144	1	pure	pure	ADJ
ejpam-5282	144	2	and	and	CCONJ
ejpam-5282	144	3	applied	applied	ADJ
ejpam-5282	144	4	mathematics	mathematic	NOUN
ejpam-5282	144	5	,	,	PUNCT
ejpam-5282	144	6	38	38	NUM
ejpam-5282	144	7	:	:	PUNCT
ejpam-5282	144	8	xii+25	xii+25	PROPN
ejpam-5282	144	9	,	,	PUNCT
ejpam-5282	144	10	1970	1970	NUM
ejpam-5282	144	11	.	.	PUNCT
ejpam-5282	145	1	[	[	X
ejpam-5282	145	2	8	8	X
ejpam-5282	145	3	]	]	PUNCT
ejpam-5282	145	4	j.	j.	PROPN
ejpam-5282	145	5	b.	b.	PROPN
ejpam-5282	145	6	garnett	garnett	PROPN
ejpam-5282	145	7	.	.	PUNCT
ejpam-5282	146	1	bounded	bound	VERB
ejpam-5282	146	2	analytic	analytic	ADJ
ejpam-5282	146	3	functions	function	NOUN
ejpam-5282	146	4	.	.	PUNCT
ejpam-5282	147	1	springer	springer	NOUN
ejpam-5282	147	2	,	,	PUNCT
ejpam-5282	147	3	new	new	PROPN
ejpam-5282	147	4	york	york	PROPN
ejpam-5282	147	5	,	,	PUNCT
ejpam-5282	147	6	2007	2007	NUM
ejpam-5282	147	7	.	.	PUNCT
ejpam-5282	148	1	[	[	X
ejpam-5282	148	2	9	9	NUM
ejpam-5282	148	3	]	]	X
ejpam-5282	148	4	d.	d.	PROPN
ejpam-5282	148	5	kalaj	kalaj	PROPN
ejpam-5282	148	6	.	.	PUNCT
ejpam-5282	149	1	on	on	ADP
ejpam-5282	149	2	riesz	riesz	PROPN
ejpam-5282	149	3	type	type	NOUN
ejpam-5282	149	4	inequalities	inequality	NOUN
ejpam-5282	149	5	for	for	ADP
ejpam-5282	149	6	harmonic	harmonic	ADJ
ejpam-5282	149	7	mappings	mapping	NOUN
ejpam-5282	149	8	in	in	ADP
ejpam-5282	149	9	the	the	DET
ejpam-5282	149	10	unit	unit	NOUN
ejpam-5282	149	11	disk	disk	NOUN
ejpam-5282	149	12	.	.	PUNCT
ejpam-5282	150	1	trans	trans	PROPN
ejpam-5282	150	2	.	.	PUNCT
ejpam-5282	151	1	amer	amer	PROPN
ejpam-5282	151	2	.	.	PUNCT
ejpam-5282	151	3	math	math	PROPN
ejpam-5282	151	4	.	.	PUNCT
ejpam-5282	152	1	soc	soc	PROPN
ejpam-5282	152	2	.	.	PUNCT
ejpam-5282	152	3	,	,	PUNCT
ejpam-5282	152	4	372(6):4031–4051	372(6):4031–4051	NUM
ejpam-5282	152	5	,	,	PUNCT
ejpam-5282	152	6	2019	2019	NUM
ejpam-5282	152	7	.	.	PUNCT
ejpam-5282	153	1	[	[	X
ejpam-5282	153	2	10	10	NUM
ejpam-5282	153	3	]	]	PUNCT
ejpam-5282	153	4	p.	p.	NOUN
ejpam-5282	153	5	melentijević.	melentijević.	PROPN
ejpam-5282	153	6	hollenbeck	hollenbeck	NOUN
ejpam-5282	153	7	-	-	PUNCT
ejpam-5282	153	8	verbitsky	verbitsky	NOUN
ejpam-5282	153	9	conjecture	conjecture	NOUN
ejpam-5282	153	10	on	on	ADP
ejpam-5282	153	11	best	good	ADJ
ejpam-5282	153	12	constant	constant	ADJ
ejpam-5282	153	13	inequalities	inequality	NOUN
ejpam-5282	153	14	for	for	ADP
ejpam-5282	153	15	analytic	analytic	ADJ
ejpam-5282	153	16	and	and	CCONJ
ejpam-5282	153	17	co	co	ADJ
ejpam-5282	153	18	-	-	ADJ
ejpam-5282	153	19	analytic	analytic	ADJ
ejpam-5282	153	20	projections	projection	NOUN
ejpam-5282	153	21	.	.	PUNCT
ejpam-5282	154	1	arxiv:2203.14364v1	arxiv:2203.14364v1	ADJ
ejpam-5282	154	2	.	.	PUNCT
ejpam-5282	155	1	[	[	X
ejpam-5282	155	2	11	11	NUM
ejpam-5282	155	3	]	]	PUNCT
ejpam-5282	155	4	w.	w.	PROPN
ejpam-5282	155	5	ramey	ramey	PROPN
ejpam-5282	155	6	s.	s.	PROPN
ejpam-5282	155	7	axler	axler	PROPN
ejpam-5282	155	8	,	,	PUNCT
ejpam-5282	155	9	p.	p.	PROPN
ejpam-5282	155	10	bourdon	bourdon	PROPN
ejpam-5282	155	11	.	.	PUNCT
ejpam-5282	156	1	harmonic	harmonic	ADJ
ejpam-5282	156	2	function	function	NOUN
ejpam-5282	156	3	theory	theory	NOUN
ejpam-5282	156	4	.	.	PUNCT
ejpam-5282	157	1	springer	springer	PROPN
ejpam-5282	157	2	verlag	verlag	PROPN
ejpam-5282	157	3	,	,	PUNCT
ejpam-5282	157	4	new	new	PROPN
ejpam-5282	157	5	york	york	PROPN
ejpam-5282	157	6	,	,	PUNCT
ejpam-5282	157	7	1992	1992	NUM
ejpam-5282	157	8	.	.	PUNCT
ejpam-5282	158	1	[	[	X
ejpam-5282	158	2	12	12	NUM
ejpam-5282	158	3	]	]	X
ejpam-5282	158	4	i.	i.	PROPN
ejpam-5282	158	5	e.	e.	PROPN
ejpam-5282	158	6	verbitsky	verbitsky	PROPN
ejpam-5282	158	7	.	.	PUNCT
ejpam-5282	159	1	estimate	estimate	NOUN
ejpam-5282	159	2	of	of	ADP
ejpam-5282	159	3	the	the	DET
ejpam-5282	159	4	norm	norm	NOUN
ejpam-5282	159	5	of	of	ADP
ejpam-5282	159	6	a	a	DET
ejpam-5282	159	7	function	function	NOUN
ejpam-5282	159	8	in	in	ADP
ejpam-5282	159	9	hardy	hardy	ADJ
ejpam-5282	159	10	space	space	NOUN
ejpam-5282	159	11	in	in	ADP
ejpam-5282	159	12	terms	term	NOUN
ejpam-5282	159	13	of	of	ADP
ejpam-5282	159	14	a	a	DET
ejpam-5282	159	15	norms	norm	NOUN
ejpam-5282	159	16	of	of	ADP
ejpam-5282	159	17	its	its	PRON
ejpam-5282	159	18	real	real	ADJ
ejpam-5282	159	19	and	and	CCONJ
ejpam-5282	159	20	imaginary	imaginary	ADJ
ejpam-5282	159	21	parts	part	NOUN
ejpam-5282	159	22	.	.	PUNCT
ejpam-5282	160	1	linear	linear	PROPN
ejpam-5282	160	2	operators	operator	NOUN
ejpam-5282	160	3	.	.	PUNCT
ejpam-5282	161	1	mat	mat	PROPN
ejpam-5282	161	2	.	.	PROPN
ejpam-5282	161	3	issled	issle	VERB
ejpam-5282	161	4	.	.	PUNCT
ejpam-5282	161	5	,	,	PUNCT
ejpam-5282	161	6	54:16–20	54:16–20	NUM
ejpam-5282	161	7	,	,	PUNCT
ejpam-5282	161	8	164	164	NUM
ejpam-5282	161	9	–	–	PUNCT
ejpam-5282	161	10	165	165	NUM
ejpam-5282	161	11	,	,	PUNCT
ejpam-5282	161	12	1980	1980	NUM
ejpam-5282	161	13	.	.	PUNCT