id	sid	eid	entity	type
ejpam-6667	1	1	european journal	ORG
ejpam-6667	1	2	2025	DATE
ejpam-6667	1	3	18	CARDINAL
ejpam-6667	1	4	4	CARDINAL
ejpam-6667	1	5	6667	CARDINAL
ejpam-6667	1	6	new york	GPE
ejpam-6667	1	7	muhammad asim1	PERSON
ejpam-6667	1	8	suwais2	PERSON
ejpam-6667	1	9	nabil mlaiki3,∗ 1	ORG
ejpam-6667	1	10	nusash, national university of technology	ORG
ejpam-6667	1	11	islamabad	GPE
ejpam-6667	1	12	44000	CARDINAL
ejpam-6667	1	13	pakistan 2	ORG
ejpam-6667	1	14	arab	NORP
ejpam-6667	1	15	saudi arabia	GPE
ejpam-6667	1	16	3	CARDINAL
ejpam-6667	1	17	prince sultan university	ORG
ejpam-6667	1	18	saudi arabia	GPE
ejpam-6667	4	1	2020	DATE
ejpam-6667	4	2	42b35	CARDINAL
ejpam-6667	4	3	47g10	CARDINAL
ejpam-6667	4	4	1	CARDINAL
ejpam-6667	5	1	1	CARDINAL
ejpam-6667	6	1	1	CARDINAL
ejpam-6667	6	2	0	CARDINAL
ejpam-6667	6	3	faris	PERSON
ejpam-6667	6	4	2	CARDINAL
ejpam-6667	6	5	1	CARDINAL
ejpam-6667	6	6	0	CARDINAL
ejpam-6667	6	7	∈	ORG
ejpam-6667	8	1	h∗	ORG
ejpam-6667	8	2	|y|α−nf(y)dy	ORG
ejpam-6667	10	1	m. asim	PERSON
ejpam-6667	10	2	khaled.suwais@arabou.edu.sa	PERSON
ejpam-6667	10	3	k. suwais	PERSON
ejpam-6667	10	4	nmlaiki@psu.edu.sa	PERSON
ejpam-6667	10	5	n. mlaiki	PERSON
ejpam-6667	11	1	1	CARDINAL
ejpam-6667	11	2	2025	CARDINAL
ejpam-6667	12	1	m. asim	PERSON
ejpam-6667	12	2	k. suwais	PERSON
ejpam-6667	12	3	n. mlaiki	PERSON
ejpam-6667	13	1	j. pure	PERSON
ejpam-6667	13	2	18	CARDINAL
ejpam-6667	13	3	4	CARDINAL
ejpam-6667	13	4	2025	CARDINAL
ejpam-6667	13	5	6667 2	DATE
ejpam-6667	13	6	20	CARDINAL
ejpam-6667	13	7	1	CARDINAL
ejpam-6667	13	8	supremum	ORG
ejpam-6667	14	1	∈	ORG
ejpam-6667	15	1	h∗ α	PERSON
ejpam-6667	15	2	3	CARDINAL
ejpam-6667	16	1	h∗ α	PERSON
ejpam-6667	19	1	electrorheological fluids	ORG
ejpam-6667	20	1	4	CARDINAL
ejpam-6667	23	1	k̇α	LOC
ejpam-6667	23	2	8–13	CARDINAL
ejpam-6667	24	1	14–29	CARDINAL
ejpam-6667	25	1	littlewood	ORG
ejpam-6667	27	1	30	CARDINAL
ejpam-6667	28	1	31–38	CARDINAL
ejpam-6667	31	1	0	CARDINAL
ejpam-6667	33	1	section 3	LAW
ejpam-6667	33	2	m. asim	PERSON
ejpam-6667	33	3	k. suwais	PERSON
ejpam-6667	33	4	n. mlaiki	PERSON
ejpam-6667	34	1	j. pure	PERSON
ejpam-6667	34	2	18	CARDINAL
ejpam-6667	34	3	4	CARDINAL
ejpam-6667	34	4	2025	CARDINAL
ejpam-6667	34	5	6667 3	DATE
ejpam-6667	34	6	20	CARDINAL
ejpam-6667	35	1	section 4.1	LAW
ejpam-6667	36	1	section 4.2	LAW
ejpam-6667	38	1	≈	CARDINAL
ejpam-6667	38	2	greater than zero	CARDINAL
ejpam-6667	38	3	c1g ≤ h ≤	ORG
ejpam-6667	38	4	2j	CARDINAL
ejpam-6667	39	1	≤ 2j	CARDINAL
ejpam-6667	39	2	j ∈ z	WORK_OF_ART
ejpam-6667	40	1	2	CARDINAL
ejpam-6667	40	2	4	CARDINAL
ejpam-6667	41	1	1,+∞	DATE
ejpam-6667	42	1	the norm ∥g∥lp	DATE
ejpam-6667	44	1	≤ 1	CARDINAL
ejpam-6667	45	1	inf p(x	PERSON
ejpam-6667	46	1	1	CARDINAL
ejpam-6667	46	2	sup p(x	PERSON
ejpam-6667	48	1	1	CARDINAL
ejpam-6667	49	1	1	CARDINAL
ejpam-6667	49	2	2	CARDINAL
ejpam-6667	49	3	littlewood	ORG
ejpam-6667	50	1	1	CARDINAL
ejpam-6667	53	1	∈	ORG
ejpam-6667	54	1	m. asim	PERSON
ejpam-6667	54	2	k. suwais	PERSON
ejpam-6667	54	3	n. mlaiki	PERSON
ejpam-6667	55	1	j. pure	PERSON
ejpam-6667	55	2	18	CARDINAL
ejpam-6667	55	3	4	CARDINAL
ejpam-6667	55	4	2025	CARDINAL
ejpam-6667	55	5	6667 4	DATE
ejpam-6667	55	6	20	CARDINAL
ejpam-6667	55	7	∈	ORG
ejpam-6667	57	1	1	CARDINAL
ejpam-6667	58	1	∥f∥lp(·)(w	ORG
ejpam-6667	58	2	1	CARDINAL
ejpam-6667	59	1	1	CARDINAL
ejpam-6667	61	1	1	CARDINAL
ejpam-6667	62	1	1	CARDINAL
ejpam-6667	62	2	weight w	PERSON
ejpam-6667	64	1	2	CARDINAL
ejpam-6667	65	1	∈	ORG
ejpam-6667	66	1	1	CARDINAL
ejpam-6667	67	1	1	CARDINAL
ejpam-6667	70	1	1	CARDINAL
ejpam-6667	70	2	1	CARDINAL
ejpam-6667	70	3	−1	DATE
ejpam-6667	71	1	16	CARDINAL
ejpam-6667	72	1	3	CARDINAL
ejpam-6667	73	1	∈	ORG
ejpam-6667	73	2	1 p1	QUANTITY
ejpam-6667	73	3	1 p2	QUANTITY
ejpam-6667	75	1	rn ∥w−1χb∥ 1	DATE
ejpam-6667	78	1	4	CARDINAL
ejpam-6667	79	1	∈	ORG
ejpam-6667	81	1	loc	PERSON
ejpam-6667	83	1	5	CARDINAL
ejpam-6667	84	1	λ−	FAC
ejpam-6667	86	1	loc	PERSON
ejpam-6667	88	1	m. asim	PERSON
ejpam-6667	88	2	k. suwais	PERSON
ejpam-6667	88	3	n. mlaiki	PERSON
ejpam-6667	89	1	j. pure	PERSON
ejpam-6667	89	2	18	CARDINAL
ejpam-6667	89	3	4	CARDINAL
ejpam-6667	89	4	2025	CARDINAL
ejpam-6667	89	5	6667 5	DATE
ejpam-6667	90	1	1	CARDINAL
ejpam-6667	91	1	16	CARDINAL
ejpam-6667	91	2	∈	ORG
ejpam-6667	91	3	ap1	PRODUCT
ejpam-6667	92	1	⊂	GPE
ejpam-6667	93	1	2	CARDINAL
ejpam-6667	94	1	16	CARDINAL
ejpam-6667	94	2	∈	ORG
ejpam-6667	94	3	1 p1	QUANTITY
ejpam-6667	94	4	1 p2	QUANTITY
ejpam-6667	96	1	w ∈	ORG
ejpam-6667	97	1	⇔ wp2	PERSON
ejpam-6667	97	2	1+ p2	QUANTITY
ejpam-6667	98	1	′ 1	DATE
ejpam-6667	99	1	3	CARDINAL
ejpam-6667	100	1	45	CARDINAL
ejpam-6667	101	1	1	CARDINAL
ejpam-6667	106	1	2	CARDINAL
ejpam-6667	107	1	g ∈ y ′	PERSON
ejpam-6667	108	1	4	CARDINAL
ejpam-6667	109	1	45	CARDINAL
ejpam-6667	110	1	1 ≤ 1 |b|	QUANTITY
ejpam-6667	111	1	5	CARDINAL
ejpam-6667	112	1	46	CARDINAL
ejpam-6667	112	2	3	CARDINAL
ejpam-6667	112	3	1 |b| ∥χb∥y∥χb∥y′	TIME
ejpam-6667	112	4	4	CARDINAL
ejpam-6667	113	1	∈	ORG
ejpam-6667	113	2	|b|	ORG
ejpam-6667	113	3	y(rn	ORG
ejpam-6667	113	4	w	GPE
ejpam-6667	114	1	∈	ORG
ejpam-6667	116	1	6	CARDINAL
ejpam-6667	117	1	47	CARDINAL
ejpam-6667	117	2	1	CARDINAL
ejpam-6667	117	3	y(rn	ORG
ejpam-6667	117	4	w	GPE
ejpam-6667	118	1	2	CARDINAL
ejpam-6667	118	2	y(rn	ORG
ejpam-6667	118	3	w	GPE
ejpam-6667	119	1	m. asim	PERSON
ejpam-6667	119	2	k. suwais	PERSON
ejpam-6667	119	3	n. mlaiki	PERSON
ejpam-6667	120	1	j. pure	PERSON
ejpam-6667	120	2	18	CARDINAL
ejpam-6667	120	3	4	CARDINAL
ejpam-6667	120	4	2025	CARDINAL
ejpam-6667	120	5	6667 6	DATE
ejpam-6667	120	6	20	CARDINAL
ejpam-6667	120	7	1	CARDINAL
ejpam-6667	121	1	∈	ORG
ejpam-6667	122	1	y(rn	ORG
ejpam-6667	122	2	w	GPE
ejpam-6667	123	1	w−q ′	DATE
ejpam-6667	123	2	1	CARDINAL
ejpam-6667	123	3	lq(·)(rn	ORG
ejpam-6667	123	4	w	GPE
ejpam-6667	124	1	2.	CARDINAL
ejpam-6667	124	2	w−1	GPE
ejpam-6667	125	1	w−q ′	DATE
ejpam-6667	126	1	6	CARDINAL
ejpam-6667	128	1	lq(·)(rn	ORG
ejpam-6667	128	2	w−1	GPE
ejpam-6667	130	1	w−q ′	DATE
ejpam-6667	131	1	1 p1	QUANTITY
ejpam-6667	133	1	∈ p ∩lh(rn	ORG
ejpam-6667	134	1	1+ p2	QUANTITY
ejpam-6667	135	1	′ 1	DATE
ejpam-6667	136	1	2	CARDINAL
ejpam-6667	137	1	7	CARDINAL
ejpam-6667	138	1	48	CARDINAL
ejpam-6667	139	1	w ∈	ORG
ejpam-6667	139	2	w(b	PERSON
ejpam-6667	141	1	1	CARDINAL
ejpam-6667	141	2	b. lemma 8	PERSON
ejpam-6667	142	1	48	CARDINAL
ejpam-6667	142	2	∈	ORG
ejpam-6667	143	1	wp2	PERSON
ejpam-6667	143	2	∈	ORG
ejpam-6667	143	3	ap1	PRODUCT
ejpam-6667	143	4	′ 2	DATE
ejpam-6667	143	5	′ 1	DATE
ejpam-6667	143	6	′ 1	DATE
ejpam-6667	144	1	′ 2(·)(w−p	DATE
ejpam-6667	146	1	0	CARDINAL
ejpam-6667	146	2	1	CARDINAL
ejpam-6667	151	1	2(·))′ ≲	PERCENT
ejpam-6667	151	2	5	CARDINAL
ejpam-6667	153	1	6	CARDINAL
ejpam-6667	153	2	9	CARDINAL
ejpam-6667	154	1	16	CARDINAL
ejpam-6667	154	2	∈	ORG
ejpam-6667	155	1	1	CARDINAL
ejpam-6667	156	1	1 p1	CARDINAL
ejpam-6667	160	1	10	CARDINAL
ejpam-6667	161	1	49	CARDINAL
ejpam-6667	161	2	littlewood	ORG
ejpam-6667	161	3	∥χb∥y ∥χe∥y ≲ |b|	ORG
ejpam-6667	162	1	m. asim	PERSON
ejpam-6667	162	2	k. suwais	PERSON
ejpam-6667	162	3	n. mlaiki	PERSON
ejpam-6667	163	1	j. pure	PERSON
ejpam-6667	163	2	18	CARDINAL
ejpam-6667	163	3	4	CARDINAL
ejpam-6667	163	4	2025	CARDINAL
ejpam-6667	163	5	6667 7	DATE
ejpam-6667	163	6	11	CARDINAL
ejpam-6667	164	1	wq1	PERSON
ejpam-6667	164	2	∈	ORG
ejpam-6667	164	3	∈	ORG
ejpam-6667	164	4	1 q2(x	TIME
ejpam-6667	167	1	lq1(·)(wq1(·)))′	ORG
ejpam-6667	169	1	9	CARDINAL
ejpam-6667	171	1	c2−kα∥χbk	PERSON
ejpam-6667	172	1	lq1(·)(wq1(·)))′	ORG
ejpam-6667	173	1	7	CARDINAL
ejpam-6667	173	2	4.1	CARDINAL
ejpam-6667	174	1	1	CARDINAL
ejpam-6667	175	1	∈	ORG
ejpam-6667	176	1	1 q2(x	TIME
ejpam-6667	178	1	wq1	PERSON
ejpam-6667	178	2	∈	ORG
ejpam-6667	178	3	0	CARDINAL
ejpam-6667	179	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	179	2	wq1	PERSON
ejpam-6667	180	1	1	CARDINAL
ejpam-6667	180	2	3	CARDINAL
ejpam-6667	180	3	≤ 1	CARDINAL
ejpam-6667	185	1	m. asim	PERSON
ejpam-6667	185	2	k. suwais	PERSON
ejpam-6667	185	3	n. mlaiki	PERSON
ejpam-6667	186	1	j. pure	PERSON
ejpam-6667	186	2	18	CARDINAL
ejpam-6667	186	3	4	CARDINAL
ejpam-6667	186	4	2025	CARDINAL
ejpam-6667	186	5	6667 8	DATE
ejpam-6667	186	6	20	CARDINAL
ejpam-6667	186	7	5	CARDINAL
ejpam-6667	187	1	j=−∞ ∥χj∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥−1	PERSON
ejpam-6667	187	2	lq2(·))(wq2(·)))′ ≤	DATE
ejpam-6667	187	3	j=−∞ ∥fj∥lq1(·)(wq1	PERSON
ejpam-6667	188	1	∥χj∥(lq1(·)(wq1(·)))′	ORG
ejpam-6667	188	2	lq2(·)(wq2(·)))′	ORG
ejpam-6667	189	1	8	CARDINAL
ejpam-6667	189	2	6	CARDINAL
ejpam-6667	191	1	2nδ2(j−k)∥χk∥(lq1(·)(wq1(·)))′∥fj∥lq1(·)(wq1(·))∥χk∥−1	CARDINAL
ejpam-6667	191	2	lq2(·)(wq2(·)))′	ORG
ejpam-6667	192	1	8)	CARDINAL
ejpam-6667	192	2	7	CARDINAL
ejpam-6667	192	3	5	CARDINAL
ejpam-6667	194	1	2nδ2(j−k)2k(n−α)∥fj∥lq1(·)(wq1(·))∥χk∥−1	CARDINAL
ejpam-6667	195	1	j=−∞ 2nδ2(j−k)∥fj∥lq1(·)(wq1	PERSON
ejpam-6667	195	2	2−kn∥χk∥lq2(·)(wq2(·))∥χk∥(lq2(·)(wq2(·)))′	CARDINAL
ejpam-6667	195	3	j=−∞ 2nδ2(j−k)∥fj∥lq1(·)(wq1	PERSON
ejpam-6667	196	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	196	2	wq1	PERSON
ejpam-6667	197	1	2nδ2(j−k)w(bj	CARDINAL
ejpam-6667	199	1	∥χj∥lq1(·)(wq1	CARDINAL
ejpam-6667	200	1	≈ w(b	PERSON
ejpam-6667	200	2	1	CARDINAL
ejpam-6667	201	1	≈ w(b	PERSON
ejpam-6667	201	2	1	CARDINAL
ejpam-6667	204	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	204	2	wq1	PERSON
ejpam-6667	205	1	2nδ2(j−k)w(bj	CARDINAL
ejpam-6667	206	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	206	2	wq1	PERSON
ejpam-6667	207	1	2nδ2(j−k)w(bk	CARDINAL
ejpam-6667	207	2	w(bj	PERSON
ejpam-6667	207	3	w(bk)λ2	PERSON
ejpam-6667	210	1	m. asim	PERSON
ejpam-6667	210	2	k. suwais	PERSON
ejpam-6667	210	3	n. mlaiki	PERSON
ejpam-6667	211	1	j. pure	PERSON
ejpam-6667	211	2	18	CARDINAL
ejpam-6667	211	3	4	CARDINAL
ejpam-6667	211	4	2025	CARDINAL
ejpam-6667	211	5	6667 9	DATE
ejpam-6667	211	6	20	CARDINAL
ejpam-6667	211	7	8	CARDINAL
ejpam-6667	212	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	212	2	wq1	PERSON
ejpam-6667	214	1	2nδ2(j−k)|bk|λ2	CARDINAL
ejpam-6667	216	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	218	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	218	2	wq1	PERSON
ejpam-6667	219	1	2n(j−k)(δ2+δ1+δλ2	CARDINAL
ejpam-6667	220	1	0	CARDINAL
ejpam-6667	221	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	221	2	wq1	PERSON
ejpam-6667	221	3	2	CARDINAL
ejpam-6667	221	4	1	CARDINAL
ejpam-6667	222	1	wq1	PERSON
ejpam-6667	222	2	∈	ORG
ejpam-6667	223	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	223	2	wq1	PERSON
ejpam-6667	224	1	2	CARDINAL
ejpam-6667	230	1	∥χj∥(lq1(·)(wq1(·)))′	ORG
ejpam-6667	231	1	2	CARDINAL
ejpam-6667	231	2	10	DATE
ejpam-6667	231	3	6	DATE
ejpam-6667	237	1	m. asim	PERSON
ejpam-6667	237	2	k. suwais	PERSON
ejpam-6667	237	3	n. mlaiki	PERSON
ejpam-6667	238	1	j. pure	PERSON
ejpam-6667	238	2	18	CARDINAL
ejpam-6667	238	3	4	CARDINAL
ejpam-6667	238	4	2025	CARDINAL
ejpam-6667	238	5	6667 10	DATE
ejpam-6667	239	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	239	2	wq1	PERSON
ejpam-6667	240	1	∞∑	PERSON
ejpam-6667	241	1	c∥f∥ḃq1(·),λ1	ORG
ejpam-6667	241	2	wq1	PERSON
ejpam-6667	242	1	4.2	CARDINAL
ejpam-6667	243	1	3	CARDINAL
ejpam-6667	244	1	∈	ORG
ejpam-6667	245	1	1	CARDINAL
ejpam-6667	245	2	+ 1	DATE
ejpam-6667	247	1	∈	ORG
ejpam-6667	249	1	3	CARDINAL
ejpam-6667	250	1	+ 1	DATE
ejpam-6667	250	2	bb)f(v)|dv	GPE
ejpam-6667	251	1	first	ORDINAL
ejpam-6667	251	2	1 s(x	QUANTITY
ejpam-6667	251	3	1	CARDINAL
ejpam-6667	253	1	1	CARDINAL
ejpam-6667	253	2	1 s(x	QUANTITY
ejpam-6667	254	1	+ 1 p(x	DATE
ejpam-6667	255	1	1	CARDINAL
ejpam-6667	258	1	1 p2	QUANTITY
ejpam-6667	258	2	1 s	CARDINAL
ejpam-6667	261	1	∥a1∥lp2(·)(wp2	ORG
ejpam-6667	262	1	m. asim	PERSON
ejpam-6667	262	2	k. suwais	PERSON
ejpam-6667	262	3	n. mlaiki	PERSON
ejpam-6667	263	1	j. pure	PERSON
ejpam-6667	263	2	18	CARDINAL
ejpam-6667	263	3	4	CARDINAL
ejpam-6667	263	4	2025	CARDINAL
ejpam-6667	263	5	6667 11	DATE
ejpam-6667	263	6	20 ∥χb∥lp2(·)(wp2	QUANTITY
ejpam-6667	264	1	≈ w(b	PERSON
ejpam-6667	264	2	1	CARDINAL
ejpam-6667	265	1	≈ w(b	PERSON
ejpam-6667	265	2	1	CARDINAL
ejpam-6667	265	3	1	CARDINAL
ejpam-6667	266	1	≈	CARDINAL
ejpam-6667	266	2	1 ∥a1∥lp2(·)(wp2	PERCENT
ejpam-6667	267	1	1	CARDINAL
ejpam-6667	267	2	bb)f(v)|dv	GPE
ejpam-6667	270	1	1	CARDINAL
ejpam-6667	270	2	2lb\2l−1b	CARDINAL
ejpam-6667	270	3	bb)f(v)|dv	GPE
ejpam-6667	270	4	1	CARDINAL
ejpam-6667	271	1	2lb\2l−1b	CARDINAL
ejpam-6667	271	2	b2lb)f(v)|dv	ORG
ejpam-6667	272	1	1	CARDINAL
ejpam-6667	272	2	2lb\2l−1b	CARDINAL
ejpam-6667	273	1	b2lb)f(v)|dv	ORG
ejpam-6667	277	1	2lb\2l−1b	CARDINAL
ejpam-6667	277	2	b2lb)f(v)|dv	ORG
ejpam-6667	280	1	1	CARDINAL
ejpam-6667	286	1	0∑	CARDINAL
ejpam-6667	289	1	1	CARDINAL
ejpam-6667	290	1	≈ w(2lb	QUANTITY
ejpam-6667	290	2	1	CARDINAL
ejpam-6667	290	3	1	CARDINAL
ejpam-6667	291	1	≈	CARDINAL
ejpam-6667	292	1	0∑	CARDINAL
ejpam-6667	293	1	n −1χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	ORG
ejpam-6667	294	1	1(·)(wp1(·)))′	CARDINAL
ejpam-6667	295	1	m. asim	PERSON
ejpam-6667	295	2	k. suwais	PERSON
ejpam-6667	295	3	n. mlaiki	PERSON
ejpam-6667	296	1	j. pure	PERSON
ejpam-6667	296	2	18	CARDINAL
ejpam-6667	296	3	4	CARDINAL
ejpam-6667	296	4	2025	CARDINAL
ejpam-6667	296	5	6667 12	DATE
ejpam-6667	296	6	20	CARDINAL
ejpam-6667	296	7	5	CARDINAL
ejpam-6667	296	8	0∑	CARDINAL
ejpam-6667	297	1	n −1χ2kb\2k−1b(x)∥b∥cbmop(·),λ(wp(·))∥f∥ḃp1(·),λ1	ORG
ejpam-6667	300	1	0∑ k=−∞	ORG
ejpam-6667	304	1	0∑ k=−∞	ORG
ejpam-6667	306	1	0∑ k=−∞	ORG
ejpam-6667	307	1	1 p2	QUANTITY
ejpam-6667	307	2	1	CARDINAL
ejpam-6667	308	1	0∑ k=−∞ |2|k(λ2	ORG
ejpam-6667	309	1	2lb\2l−1b	CARDINAL
ejpam-6667	310	1	l 1	DATE
ejpam-6667	311	1	l 1 |2ib| ∥(b− b2i+1b)χ2i+1b∥lp(·)(wp(·))∥χ2i+1b∥(lp(·)(wp1(·)))′	DATE
ejpam-6667	311	2	5	CARDINAL
ejpam-6667	311	3	|(bb − b2lb)| ≤ c	ORG
ejpam-6667	312	1	l 1	DATE
ejpam-6667	314	1	9	CARDINAL
ejpam-6667	314	2	m. asim	PERSON
ejpam-6667	314	3	k. suwais	PERSON
ejpam-6667	314	4	n. mlaiki	PERSON
ejpam-6667	315	1	j. pure	PERSON
ejpam-6667	315	2	18	CARDINAL
ejpam-6667	315	3	4	CARDINAL
ejpam-6667	315	4	2025	CARDINAL
ejpam-6667	315	5	6667 13	DATE
ejpam-6667	315	6	20 a22	QUANTITY
ejpam-6667	317	1	∥fχ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp1(·)(wp1(·)))′ ≤ c∥b∥cbmop(·),λ(wp	FAC
ejpam-6667	319	1	χ2kb\2k−1b(x)|2kb|	PERSON
ejpam-6667	321	1	χ2kb\2k−1b(x)|2kb|	PERSON
ejpam-6667	323	1	χ2kb\2k−1b(x)|2kb|	PERSON
ejpam-6667	327	1	χ2kb\2k−1b(x)|2kb|	PERSON
ejpam-6667	329	1	∥a22∥lp2(·)(wp2	PERSON
ejpam-6667	335	1	+ α	DATE
ejpam-6667	335	2	1	CARDINAL
ejpam-6667	337	1	0∑ k=−∞	PERSON
ejpam-6667	338	1	|b|λ2w(b	PERSON
ejpam-6667	338	2	1	CARDINAL
ejpam-6667	338	3	hα]f∥lp2(·)(wp2	GPE
ejpam-6667	342	1	4	CARDINAL
ejpam-6667	343	1	3	CARDINAL
ejpam-6667	346	1	m. asim	PERSON
ejpam-6667	346	2	k. suwais	PERSON
ejpam-6667	346	3	n. mlaiki	PERSON
ejpam-6667	347	1	j. pure	PERSON
ejpam-6667	347	2	18	CARDINAL
ejpam-6667	347	3	4	CARDINAL
ejpam-6667	347	4	2025	CARDINAL
ejpam-6667	347	5	6667 14	DATE
ejpam-6667	347	6	20	CARDINAL
ejpam-6667	347	7	4 |[b	CARDINAL
ejpam-6667	347	8	α]f(x	CARDINAL
ejpam-6667	347	9	dv	ORG
ejpam-6667	348	1	dv	ORG
ejpam-6667	349	1	dv	ORG
ejpam-6667	351	1	1 p2	QUANTITY
ejpam-6667	351	2	1 s	CARDINAL
ejpam-6667	354	1	2	CARDINAL
ejpam-6667	354	2	dv	ORG
ejpam-6667	355	1	2lb\2l−1b	CARDINAL
ejpam-6667	356	1	2lb\2l−1b	CARDINAL
ejpam-6667	356	2	b2lb)f(v)|dv + 0∑ k=−∞	ORG
ejpam-6667	356	3	2lb\2l−1b	CARDINAL
ejpam-6667	356	4	2lb\2l−1b	CARDINAL
ejpam-6667	356	5	b2lb)f(v)|dv	ORG
ejpam-6667	356	6	m. asim	PERSON
ejpam-6667	356	7	k. suwais	PERSON
ejpam-6667	356	8	n. mlaiki	PERSON
ejpam-6667	357	1	j. pure	PERSON
ejpam-6667	357	2	18	CARDINAL
ejpam-6667	357	3	4	CARDINAL
ejpam-6667	357	4	2025	CARDINAL
ejpam-6667	357	5	6667 15	DATE
ejpam-6667	357	6	20	CARDINAL
ejpam-6667	357	7	1	CARDINAL
ejpam-6667	359	1	1	CARDINAL
ejpam-6667	360	1	d21	ORG
ejpam-6667	364	1	0∑ k=−∞	ORG
ejpam-6667	367	1	lb|λ1∥χ2lb∥lp1(·)(wp1(·))∥χ2lb∥(lp(·)(wp(·)))′	GPE
ejpam-6667	373	1	|2(k+1)b|λ2w(2	CARDINAL
ejpam-6667	373	2	kb	ORG
ejpam-6667	373	3	1	CARDINAL
ejpam-6667	374	1	1	CARDINAL
ejpam-6667	374	2	0∑ k=−∞	PERSON
ejpam-6667	375	1	2lb\2l−1b	CARDINAL
ejpam-6667	375	2	b2lb)f(v)|dv	ORG
ejpam-6667	376	1	m. asim	PERSON
ejpam-6667	376	2	k. suwais	PERSON
ejpam-6667	376	3	n. mlaiki	PERSON
ejpam-6667	377	1	j. pure	PERSON
ejpam-6667	377	2	18	CARDINAL
ejpam-6667	377	3	4	CARDINAL
ejpam-6667	377	4	2025	CARDINAL
ejpam-6667	377	5	6667 16	DATE
ejpam-6667	377	6	20	CARDINAL
ejpam-6667	377	7	9	CARDINAL
ejpam-6667	379	1	n −1|2l+1b|λ|l| ∥fχ2lb∥lp1(·)(wp1	ORG
ejpam-6667	383	1	+ 1| ≤	MONEY
ejpam-6667	386	1	+ 1||2k+1b|λ2χ2kb\2k−1b(x	DATE
ejpam-6667	393	1	+ 1||2k+1b|λ2w(2	PERCENT
ejpam-6667	393	2	kb	ORG
ejpam-6667	393	3	1	CARDINAL
ejpam-6667	397	1	|b|λ2w(b	PERSON
ejpam-6667	397	2	1	CARDINAL
ejpam-6667	398	1	d2, d21	GPE
ejpam-6667	398	2	d22	ORG
ejpam-6667	402	1	5	CARDINAL
ejpam-6667	402	2	m. asim	PERSON
ejpam-6667	402	3	k. suwais	PERSON
ejpam-6667	402	4	n. mlaiki	PERSON
ejpam-6667	403	1	j. pure	PERSON
ejpam-6667	403	2	18	CARDINAL
ejpam-6667	403	3	4	CARDINAL
ejpam-6667	403	4	2025	CARDINAL
ejpam-6667	403	5	6667 17	DATE
ejpam-6667	403	6	20	CARDINAL
ejpam-6667	405	1	khaled suwais	PERSON
ejpam-6667	405	2	arab	NORP
ejpam-6667	406	1	n. mlaiki	PERSON
ejpam-6667	406	2	prince sultan university	ORG
ejpam-6667	407	1	m.a.	GPE
ejpam-6667	407	2	s.h.	PERSON
ejpam-6667	407	3	n.m.	GPE
ejpam-6667	409	1	1	CARDINAL
ejpam-6667	409	2	g. h.	PERSON
ejpam-6667	410	1	hilbert	ORG
ejpam-6667	411	1	mathematische zeitschrift	PERSON
ejpam-6667	411	2	1920	DATE
ejpam-6667	412	1	2	CARDINAL
ejpam-6667	412	2	w. g. faris	PERSON
ejpam-6667	414	1	duke mathematical journal	ORG
ejpam-6667	414	2	43:365–373	CARDINAL
ejpam-6667	414	3	1976	DATE
ejpam-6667	415	1	3	CARDINAL
ejpam-6667	415	2	z. fu	PERSON
ejpam-6667	415	3	z. liu	PERSON
ejpam-6667	415	4	s. lu	PERSON
ejpam-6667	415	5	h. wang	PERSON
ejpam-6667	417	1	china	GPE
ejpam-6667	417	2	50:1418–1426, 2007	DATE
ejpam-6667	418	1	4	CARDINAL
ejpam-6667	418	2	j. rákosńık	PERSON
ejpam-6667	419	1	p(x	PERSON
ejpam-6667	420	1	czechoslovak mathematical journal	ORG
ejpam-6667	420	2	41(4):592–618, 1991	DATE
ejpam-6667	421	1	5	CARDINAL
ejpam-6667	421	2	s. samko	PERSON
ejpam-6667	423	1	2003	DATE
ejpam-6667	424	1	6	CARDINAL
ejpam-6667	424	2	stefan samko	PERSON
ejpam-6667	426	1	10:1–18, 2007	DATE
ejpam-6667	427	1	7	CARDINAL
ejpam-6667	427	2	p. hästö	PERSON
ejpam-6667	427	3	m. koskenoja	PERSON
ejpam-6667	429	1	georgian mathematical journal	ORG
ejpam-6667	429	2	12:431–442, 2005	DATE
ejpam-6667	430	1	8	CARDINAL
ejpam-6667	430	2	j. l. wu	PERSON
ejpam-6667	430	3	q. g. liu	PERSON
ejpam-6667	432	1	30:201–206	CARDINAL
ejpam-6667	432	2	2014	DATE
ejpam-6667	433	1	9	CARDINAL
ejpam-6667	433	2	a. hussain	PERSON
ejpam-6667	433	3	m. asim	PERSON
ejpam-6667	434	1	herz-morrey	FAC
ejpam-6667	435	1	article id 9705250	LAW
ejpam-6667	435	2	8	CARDINAL
ejpam-6667	435	3	2021	CARDINAL
ejpam-6667	436	1	10	CARDINAL
ejpam-6667	436	2	m. asim	PERSON
ejpam-6667	436	3	a. hussain	PERSON
ejpam-6667	438	1	article id 2739	LAW
ejpam-6667	438	2	13	CARDINAL
ejpam-6667	438	3	2021	CARDINAL
ejpam-6667	439	1	m. asim	PERSON
ejpam-6667	439	2	k. suwais	PERSON
ejpam-6667	439	3	n. mlaiki	PERSON
ejpam-6667	440	1	j. pure	PERSON
ejpam-6667	440	2	18	CARDINAL
ejpam-6667	440	3	4	CARDINAL
ejpam-6667	440	4	2025	CARDINAL
ejpam-6667	440	5	6667 18	DATE
ejpam-6667	440	6	11	CARDINAL
ejpam-6667	440	7	m. asim	PERSON
ejpam-6667	440	8	i. ayoob	PERSON
ejpam-6667	440	9	a. hussain	PERSON
ejpam-6667	440	10	n. mlaiki	PERSON
ejpam-6667	442	1	2024:11	DATE
ejpam-6667	442	2	2024	DATE
ejpam-6667	443	1	12	CARDINAL
ejpam-6667	443	2	a. hussain	PERSON
ejpam-6667	443	3	m. asim	PERSON
ejpam-6667	443	4	f. jarad	PERSON
ejpam-6667	445	1	article id 5855068	LAW
ejpam-6667	445	2	13	CARDINAL
ejpam-6667	445	3	2022	CARDINAL
ejpam-6667	446	1	13	CARDINAL
ejpam-6667	446	2	m. izuki	PERSON
ejpam-6667	447	1	del circolo matematico di palermo	PERSON
ejpam-6667	447	2	59:199–213	CARDINAL
ejpam-6667	447	3	2010	DATE
ejpam-6667	448	1	14	CARDINAL
ejpam-6667	448	2	m. izuki	PERSON
ejpam-6667	448	3	k. tachizawa	PERSON
ejpam-6667	450	1	67:353–363, 2008	DATE
ejpam-6667	451	1	15	CARDINAL
ejpam-6667	451	2	s. lu	PERSON
ejpam-6667	451	3	k. yabuta	PERSON
ejpam-6667	451	4	k. yang	PERSON
ejpam-6667	453	1	kodai mathematical journal	ORG
ejpam-6667	453	2	23:391–410	CARDINAL
ejpam-6667	453	3	2000	DATE
ejpam-6667	454	1	16	CARDINAL
ejpam-6667	454	2	m. izuki	PERSON
ejpam-6667	454	3	t. noi	ORG
ejpam-6667	456	1	2016:199	CARDINAL
ejpam-6667	456	2	2016	DATE
ejpam-6667	457	1	17	CARDINAL
ejpam-6667	457	2	a. almeida	PERSON
ejpam-6667	457	3	d. drihem	PERSON
ejpam-6667	459	1	2012	DATE
ejpam-6667	460	1	18	CARDINAL
ejpam-6667	460	2	j. xu	PERSON
ejpam-6667	461	1	besov	PERSON
ejpam-6667	462	1	2012	DATE
ejpam-6667	462	2	article id 384593	LAW
ejpam-6667	462	3	27	CARDINAL
ejpam-6667	462	4	2012	DATE
ejpam-6667	463	1	19	CARDINAL
ejpam-6667	463	2	f.	PERSON
ejpam-6667	465	1	19:145–165	CARDINAL
ejpam-6667	465	2	2016	DATE
ejpam-6667	466	1	20	CARDINAL
ejpam-6667	466	2	m. izuki	PERSON
ejpam-6667	468	1	east journal	ORG
ejpam-6667	468	2	15:87–109	CARDINAL
ejpam-6667	468	3	2009	DATE
ejpam-6667	469	1	21	CARDINAL
ejpam-6667	469	2	m. izuki	PERSON
ejpam-6667	470	1	del circolo matematico di palermo	PERSON
ejpam-6667	470	2	2	CARDINAL
ejpam-6667	470	3	59:199–213	CARDINAL
ejpam-6667	470	4	2010	DATE
ejpam-6667	471	1	22	CARDINAL
ejpam-6667	471	2	m. izuki	PERSON
ejpam-6667	473	1	del circolo matematico di palermo	PERSON
ejpam-6667	473	2	2	CARDINAL
ejpam-6667	473	3	59:461–472	CARDINAL
ejpam-6667	473	4	2010	DATE
ejpam-6667	474	1	23	CARDINAL
ejpam-6667	474	2	m. izuki	PERSON
ejpam-6667	474	3	herz-morrey	FAC
ejpam-6667	475	1	hiroshima mathematical journal	ORG
ejpam-6667	475	2	40:343–355	CARDINAL
ejpam-6667	475	3	2010	DATE
ejpam-6667	476	1	24	CARDINAL
ejpam-6667	476	2	m. izuki	PERSON
ejpam-6667	477	1	glasnik matematicki	PERSON
ejpam-6667	477	2	45:475–503, 2010	DATE
ejpam-6667	478	1	25	CARDINAL
ejpam-6667	478	2	m. izuki	PERSON
ejpam-6667	478	3	t. noi	ORG
ejpam-6667	479	1	besov	GPE
ejpam-6667	480	1	del circolo matematico di palermo	PERSON
ejpam-6667	480	2	2	CARDINAL
ejpam-6667	480	3	63:221–245	CARDINAL
ejpam-6667	480	4	2014	DATE
ejpam-6667	481	1	26	CARDINAL
ejpam-6667	481	2	m. izuki	PERSON
ejpam-6667	481	3	t. noi	ORG
ejpam-6667	483	1	mediterranean journal	ORG
ejpam-6667	483	2	13:2981–3013	DATE
ejpam-6667	483	3	2016	DATE
ejpam-6667	484	1	27	CARDINAL
ejpam-6667	484	2	y. zhu	PERSON
ejpam-6667	485	1	multilinear	ORG
ejpam-6667	486	1	acta mathematica sinica	PERSON
ejpam-6667	486	2	english	LANGUAGE
ejpam-6667	486	3	30:1180–1194, 2014	DATE
ejpam-6667	487	1	28	CARDINAL
ejpam-6667	487	2	h. wang	PERSON
ejpam-6667	489	1	czechoslovak mathematical journal	ORG
ejpam-6667	489	2	66(141):251–269	DATE
ejpam-6667	489	3	2016	DATE
ejpam-6667	490	1	m. asim	PERSON
ejpam-6667	490	2	k. suwais	PERSON
ejpam-6667	490	3	n. mlaiki	PERSON
ejpam-6667	491	1	j. pure	PERSON
ejpam-6667	491	2	18	CARDINAL
ejpam-6667	491	3	4	CARDINAL
ejpam-6667	491	4	2025	CARDINAL
ejpam-6667	491	5	6667 19	DATE
ejpam-6667	491	6	29	CARDINAL
ejpam-6667	491	7	h. wang	PERSON
ejpam-6667	491	8	j. wang	PERSON
ejpam-6667	491	9	z. fu.	PERSON
ejpam-6667	492	1	morrey	PERSON
ejpam-6667	493	1	article id 1908794	LAW
ejpam-6667	493	2	11	CARDINAL
ejpam-6667	493	3	2017	CARDINAL
ejpam-6667	494	1	30	CARDINAL
ejpam-6667	494	2	z. fu	PERSON
ejpam-6667	494	3	s. lu	PERSON
ejpam-6667	494	4	h. wang	PERSON
ejpam-6667	494	5	l. wang	PERSON
ejpam-6667	496	1	annales academiae scientiarum	ORG
ejpam-6667	496	2	mathematica	PERSON
ejpam-6667	496	3	44:505–522	CARDINAL
ejpam-6667	496	4	2019	DATE
ejpam-6667	497	1	31	CARDINAL
ejpam-6667	497	2	z. si	PERSON
ejpam-6667	498	1	acta mathematica sinica	PERSON
ejpam-6667	498	2	english	LANGUAGE
ejpam-6667	498	3	26:2093–2108	CARDINAL
ejpam-6667	498	4	2010	DATE
ejpam-6667	499	1	32	CARDINAL
ejpam-6667	499	2	t. ohno	GPE
ejpam-6667	499	3	t. shimomura	ORG
ejpam-6667	501	1	hokkaido mathematical journal	ORG
ejpam-6667	501	2	44:185–201	CARDINAL
ejpam-6667	501	3	2015	DATE
ejpam-6667	502	1	33	CARDINAL
ejpam-6667	502	2	d. cruz-uribe	PERSON
ejpam-6667	502	3	a. fiorenza	PERSON
ejpam-6667	502	4	j. m. martell	PERSON
ejpam-6667	502	5	c. pérez	PERSON
ejpam-6667	504	1	annales academiae scientiarum	ORG
ejpam-6667	504	2	mathematica	PERSON
ejpam-6667	504	3	31:239–264, 2006	DATE
ejpam-6667	505	1	34	CARDINAL
ejpam-6667	505	2	m. sultan	PERSON
ejpam-6667	505	3	b. sultan	PERSON
ejpam-6667	505	4	a. aloqaily	PERSON
ejpam-6667	505	5	n. mlaiki	PERSON
ejpam-6667	507	1	2023	CARDINAL
ejpam-6667	508	1	35	CARDINAL
ejpam-6667	508	2	b. sultan	PERSON
ejpam-6667	508	3	f. azmi	PERSON
ejpam-6667	508	4	m. sultan	PERSON
ejpam-6667	508	5	m. mehmood	PERSON
ejpam-6667	508	6	n. mlaiki	PERSON
ejpam-6667	510	1	11(11):583	CARDINAL
ejpam-6667	510	2	2022	CARDINAL
ejpam-6667	511	1	36	CARDINAL
ejpam-6667	511	2	muhammad asim	PERSON
ejpam-6667	511	3	ghada alnemer	PERSON
ejpam-6667	513	1	10(5):10431–10451	CARDINAL
ejpam-6667	513	2	2025	DATE
ejpam-6667	514	1	37	CARDINAL
ejpam-6667	514	2	b. sultan	PERSON
ejpam-6667	514	3	m. sultan	PERSON
ejpam-6667	514	4	m. mehmood	PERSON
ejpam-6667	514	5	f. azmi	PERSON
ejpam-6667	514	6	m. a.	PERSON
ejpam-6667	514	7	n. mlaiki	PERSON
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ejpam-6667	517	1	38	CARDINAL
ejpam-6667	517	2	b. sultan	PERSON
ejpam-6667	517	3	f. m. azmi	PERSON
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ejpam-6667	517	5	t. mahmood	PERSON
ejpam-6667	517	6	n. mlaiki	PERSON
ejpam-6667	517	7	n. souayah	PERSON
ejpam-6667	518	1	herz-morrey	PERSON
ejpam-6667	519	1	2022	CARDINAL
ejpam-6667	520	1	39	CARDINAL
ejpam-6667	520	2	d. cruz-uribe	PERSON
ejpam-6667	520	3	a. fiorenza	PERSON
ejpam-6667	523	1	heidelberg	GPE
ejpam-6667	523	2	2013	DATE
ejpam-6667	524	1	40	CARDINAL
ejpam-6667	524	2	p. hästö	PERSON
ejpam-6667	524	3	m. r̊užička	PERSON
ejpam-6667	525	1	lebesgue	ORG
ejpam-6667	525	2	2017	CARDINAL
ejpam-6667	526	1	heidelberg	GPE
ejpam-6667	526	2	2011	DATE
ejpam-6667	527	1	41	CARDINAL
ejpam-6667	527	2	m. izuki	PERSON
ejpam-6667	527	3	e. nakai	PERSON
ejpam-6667	529	1	sci	PERSON
ejpam-6667	530	1	jpn	PERSON
ejpam-6667	531	1	77(2):187–315	GPE
ejpam-6667	531	2	2014	DATE
ejpam-6667	532	1	42	CARDINAL
ejpam-6667	532	2	d. c. uribe	PERSON
ejpam-6667	532	3	a. fiorenza	PERSON
ejpam-6667	534	1	acad	ORG
ejpam-6667	535	1	sci	ORG
ejpam-6667	535	2	fenn	PERSON
ejpam-6667	535	3	28:223–238,	DATE
ejpam-6667	535	4	2003	DATE
ejpam-6667	536	1	43	CARDINAL
ejpam-6667	537	1	generalized lebesgue spaces	ORG
ejpam-6667	538	1	2004	DATE
ejpam-6667	539	1	44	CARDINAL
ejpam-6667	540	1	generalized lebesgue spaces	ORG
ejpam-6667	541	1	bulletin des sciences mathématiques	ORG
ejpam-6667	541	2	129:657–700, 2005	DATE
ejpam-6667	542	1	45	CARDINAL
ejpam-6667	542	2	c. bennett	PERSON
ejpam-6667	542	3	r. sharpley	PERSON
ejpam-6667	544	1	academic press	ORG
ejpam-6667	544	2	boston	GPE
ejpam-6667	544	3	1988	DATE
ejpam-6667	545	1	m. asim	PERSON
ejpam-6667	545	2	k. suwais	PERSON
ejpam-6667	545	3	n. mlaiki	PERSON
ejpam-6667	546	1	j. pure	PERSON
ejpam-6667	546	2	18	CARDINAL
ejpam-6667	546	3	4	CARDINAL
ejpam-6667	546	4	2025	CARDINAL
ejpam-6667	546	5	6667 20	DATE
ejpam-6667	546	6	46	CARDINAL
ejpam-6667	546	7	m. izuki	PERSON
ejpam-6667	548	1	sci	ORG
ejpam-6667	549	1	jpn	PERSON
ejpam-6667	549	2	2(1):27–41, 2013	DATE
ejpam-6667	550	1	47	CARDINAL
ejpam-6667	550	2	a. y. karlovich	PERSON
ejpam-6667	550	3	i. spitkovsky	PERSON
ejpam-6667	552	1	236	CARDINAL
ejpam-6667	552	2	275–291	CARDINAL
ejpam-6667	552	3	birkhäuser, basel	ORG
ejpam-6667	552	4	2014	DATE
ejpam-6667	553	1	48	CARDINAL
ejpam-6667	553	2	m. izuki	PERSON
ejpam-6667	553	3	t. noi	ORG
ejpam-6667	554	1	two	CARDINAL
ejpam-6667	554	2	bulletin	PERSON
ejpam-6667	554	3	malaysian	NORP
ejpam-6667	554	4	43:169–200	CARDINAL
ejpam-6667	554	5	2020	DATE
ejpam-6667	555	1	49	CARDINAL
ejpam-6667	555	2	m. izuki	PERSON
ejpam-6667	555	3	t. noi	ORG
ejpam-6667	557	1	11(3):799–816	CARDINAL
ejpam-6667	557	2	2017	DATE