id	sid	eid	entity	type
ma-234	1	1	2024	CARDINAL
ma-234	2	1	j. math	PERSON
ma-234	4	1	4 (2024	CARDINAL
ma-234	4	2	16doi	CARDINAL
ma-234	4	3	10.28924	CARDINAL
ma-234	4	4	bourgain-morrey	PRODUCT
ma-234	4	5	diarra laboratoire de mathématiques et applications	ORG
ma-234	4	6	ufr mathématiques et informatique	PERSON
ma-234	4	7	abidjan-cocody	ORG
ma-234	4	8	22	CARDINAL
ma-234	4	9	582	CARDINAL
ma-234	5	1	1 ≤	MONEY
ma-234	5	2	1991	DATE
ma-234	6	1	f(q	GPE
ma-234	6	2	2015	DATE
ma-234	9	1	1 ≤	QUANTITY
ma-234	9	2	1	CARDINAL
ma-234	10	1	1 α	TIME
ma-234	12	1	rd	ORG
ma-234	12	2	rd	ORG
ma-234	13	1	1,∞	CARDINAL
ma-234	13	2	rd	GPE
ma-234	15	1	1	CARDINAL
ma-234	15	2	⊂ rd	GPE
ma-234	15	3	lqloc denotesthe	PERSON
ma-234	15	4	rd	GPE
ma-234	15	5	k of rd	FAC
ma-234	15	6	1 ≤	CARDINAL
ma-234	17	1	1 α	QUANTITY
ma-234	17	2	1	CARDINAL
ma-234	17	3	20	CARDINAL
ma-234	17	4	2024	DATE
ma-234	19	1	bourgain-morrey	PERSON
ma-234	20	1	1	CARDINAL
ma-234	22	1	j. math	PERSON
ma-234	24	1	10.28924	CARDINAL
ma-234	24	2	2where q(x	PERSON
ma-234	25	1	2	DATE
ma-234	25	2	2	CARDINAL
ma-234	25	3	0	CARDINAL
ma-234	26	1	morrey spaces	ORG
ma-234	26	2	1938	DATE
ma-234	26	3	c. morrey	PERSON
ma-234	27	1	11	CARDINAL
ma-234	28	1	1 ≤	QUANTITY
ma-234	28	2	morrey spaces	ORG
ma-234	29	1	mα	ORG
ma-234	29	2	1 ≤	QUANTITY
ma-234	30	1	morrey spaces	ORG
ma-234	30	2	bourgain-morrey	PRODUCT
ma-234	30	3	1 ≤	CARDINAL
ma-234	31	1	2	CARDINAL
ma-234	31	2	1991	DATE
ma-234	34	1	1.1	CARDINAL
ma-234	35	1	1 ≤	QUANTITY
ma-234	35	2	1	CARDINAL
ma-234	36	1	kj	ORG
ma-234	36	2	2	CARDINAL
ma-234	36	3	k =	PERSON
ma-234	36	4	∈	ORG
ma-234	36	5	rd	GPE
ma-234	36	6	∑	ORG
ma-234	36	7	1	CARDINAL
ma-234	36	8	1 ≤	QUANTITY
ma-234	36	9	mα	ORG
ma-234	37	1	⊂mα	PERSON
ma-234	38	1	1 ≤	QUANTITY
ma-234	40	1	1 ≤	QUANTITY
ma-234	40	2	1	CARDINAL
ma-234	41	1	j. math	PERSON
ma-234	43	1	10.28924	CARDINAL
ma-234	43	2	3many	CARDINAL
ma-234	43	3	morrey spaces	GPE
ma-234	43	4	bourgain-morrey	PRODUCT
ma-234	43	5	8	CARDINAL
ma-234	44	1	hatano et al	ORG
ma-234	45	1	8].let	CARDINAL
ma-234	45	2	1	CARDINAL
ma-234	47	1	1.2	CARDINAL
ma-234	48	1	14	CARDINAL
ma-234	48	2	1 α ≤ 1	QUANTITY
ma-234	48	3	1	CARDINAL
ma-234	50	1	1	CARDINAL
ma-234	50	2	‖iγf ‖p ≤ aα	ORG
ma-234	50	3	‖α	GPE
ma-234	50	4	2	CARDINAL
ma-234	50	5	1	CARDINAL
ma-234	50	6	1 1−γ	CARDINAL
ma-234	50	7	∞ ≤	CARDINAL
ma-234	50	8	∈	ORG
ma-234	51	1	3	CARDINAL
ma-234	51	2	1,∞	CARDINAL
ma-234	52	1	1	CARDINAL
ma-234	53	1	first	ORDINAL
ma-234	53	2	bourgain-morrey	PRODUCT
ma-234	54	1	hatano et al.	GPE
ma-234	54	2	bourgain-morrey	PERSON
ma-234	54	3	8	CARDINAL
ma-234	54	4	f(q	GPE
ma-234	54	5	1 ≤	MONEY
ma-234	54	6	2015	DATE
ma-234	55	1	7	CARDINAL
ma-234	56	1	2020	DATE
ma-234	56	2	f(q	GPE
ma-234	56	3	15	CARDINAL
ma-234	56	4	rmp	ORG
ma-234	56	5	1	CARDINAL
ma-234	58	1	1.3	CARDINAL
ma-234	59	1	1 ≤	MONEY
ma-234	60	1	f(q	GPE
ma-234	62	1	1 α	QUANTITY
ma-234	62	2	1	CARDINAL
ma-234	62	3	1 α	QUANTITY
ma-234	62	4	1	CARDINAL
ma-234	62	5	•	CARDINAL
ma-234	62	6	q(x	PERSON
ma-234	62	7	•	CARDINAL
ma-234	63	1	⊂	GPE
ma-234	66	1	j. math	PERSON
ma-234	68	1	10.28924	CARDINAL
ma-234	68	2	4it	ORDINAL
ma-234	68	3	f(q	GPE
ma-234	69	1	f(q	GPE
ma-234	70	1	1 ≤	QUANTITY
ma-234	71	1	⊂	GPE
ma-234	71	2	f(q	GPE
ma-234	71	3	⊂	GPE
ma-234	71	4	f(q	GPE
ma-234	71	5	f(q	GPE
ma-234	71	6	f(q1	ORG
ma-234	72	1	4	CARDINAL
ma-234	72	2	4	CARDINAL
ma-234	72	3	f(q	GPE
ma-234	73	1	morrey spaces	GPE
ma-234	73	2	5	CARDINAL
ma-234	74	1	1	CARDINAL
ma-234	74	2	4	CARDINAL
ma-234	74	3	f(q	GPE
ma-234	75	1	two	CARDINAL
ma-234	76	1	f(q	GPE
ma-234	77	1	second	ORDINAL
ma-234	78	1	f(q	GPE
ma-234	78	2	f(q	GPE
ma-234	80	1	1 ≤	QUANTITY
ma-234	80	2	1	CARDINAL
ma-234	81	1	1 α	TIME
ma-234	82	1	section 2	LAW
ma-234	83	1	section 3	LAW
ma-234	84	1	section 4we	LAW
ma-234	84	2	f(q	GPE
ma-234	85	1	section 5	LAW
ma-234	86	1	section 6contains	LAW
ma-234	87	1	•	CARDINAL
ma-234	88	1	rd	ORG
ma-234	88	2	rd	GPE
ma-234	89	1	•	CARDINAL
ma-234	89	2	φ	ORG
ma-234	89	3	0	CARDINAL
ma-234	89	4	1]d	CARDINAL
ma-234	89	5	∫ rd φ(x)dx = 1.	ORG
ma-234	90	1	integer n ≥ 1	ORG
ma-234	91	1	•	CARDINAL
ma-234	92	1	integer n ≥ 1	ORG
ma-234	92	2	ωn	CARDINAL
ma-234	95	1	j. math	PERSON
ma-234	97	1	10.28924	CARDINAL
ma-234	97	2	52	CARDINAL
ma-234	98	1	1	CARDINAL
ma-234	98	2	supremum	ORG
ma-234	98	3	first	ORDINAL
ma-234	99	1	2.1	CARDINAL
ma-234	100	1	1 α ≤ 1	QUANTITY
ma-234	100	2	1	CARDINAL
ma-234	101	1	mα 1,p	ORG
ma-234	101	2	‖p	DATE
ma-234	101	3	3d(2−γ	CARDINAL
ma-234	102	1	1,p	CARDINAL
ma-234	103	1	5	CARDINAL
ma-234	103	2	2.1	CARDINAL
ma-234	103	3	8	CARDINAL
ma-234	103	4	4.5	CARDINAL
ma-234	104	1	8	CARDINAL
ma-234	104	2	4.4	CARDINAL
ma-234	105	1	2.2	CARDINAL
ma-234	106	1	1 α ≤ 1	QUANTITY
ma-234	106	2	1	CARDINAL
ma-234	106	3	1 α−γ	DATE
ma-234	107	1	0	CARDINAL
ma-234	107	2	mα 1,p	ORG
ma-234	108	1	1,p	CARDINAL
ma-234	109	1	6	CARDINAL
ma-234	109	2	⊂	GPE
ma-234	109	3	⊂	GPE
ma-234	109	4	1,p	CARDINAL
ma-234	109	5	1 ≤	QUANTITY
ma-234	109	6	2.2	CARDINAL
ma-234	109	7	1.2	CARDINAL
ma-234	109	8	bourgain-morrey	PERSON
ma-234	110	1	1	CARDINAL
ma-234	110	2	6	CARDINAL
ma-234	110	3	⊂	GPE
ma-234	110	4	b(γ	PERSON
ma-234	110	5	1 α <	QUANTITY
ma-234	110	6	1	CARDINAL
ma-234	111	1	7	CARDINAL
ma-234	111	2	b(γ	PERSON
ma-234	111	3	1 ≤	MONEY
ma-234	111	4	1 ≤	MONEY
ma-234	111	5	f(q	GPE
ma-234	111	6	b(γ	PERSON
ma-234	111	7	b(γ	PERSON
ma-234	111	8	α)c	GPE
ma-234	111	9	⊂	GPE
ma-234	112	1	⊂	GPE
ma-234	112	2	1 α ≤ 1	QUANTITY
ma-234	112	3	1	CARDINAL
ma-234	112	4	f(q	GPE
ma-234	112	5	f ∈ f(q	ORG
ma-234	112	6	lim y→0	PERSON
ma-234	112	7	− y)‖f(q	PERSON
ma-234	112	8	1 ≤	MONEY
ma-234	113	1	j. math	PERSON
ma-234	115	1	10.28924	CARDINAL
ma-234	116	1	6note	ORG
ma-234	116	2	f(q	GPE
ma-234	116	3	f(q	GPE
ma-234	116	4	7	CARDINAL
ma-234	116	5	1,p ⊂ f(1	PERCENT
ma-234	117	1	1 α <	QUANTITY
ma-234	117	2	1	CARDINAL
ma-234	117	3	9	CARDINAL
ma-234	117	4	9	CARDINAL
ma-234	118	1	2.3	CARDINAL
ma-234	119	1	1 ≤	QUANTITY
ma-234	120	1	1	CARDINAL
ma-234	120	2	2	CARDINAL
ma-234	121	1	10	CARDINAL
ma-234	121	2	f(q	GPE
ma-234	122	1	f(q	GPE
ma-234	123	1	4	CARDINAL
ma-234	123	2	6	CARDINAL
ma-234	123	3	lq	ORG
ma-234	123	4	lp)α	ORG
ma-234	123	5	f(q	GPE
ma-234	125	1	2.4	CARDINAL
ma-234	126	1	1 ≤	QUANTITY
ma-234	128	1	lim n→∞	PERSON
ma-234	129	1	0	CARDINAL
ma-234	129	2	∈	ORG
ma-234	129	3	2.4	CARDINAL
ma-234	129	4	asa	ORG
ma-234	130	1	2.5	CARDINAL
ma-234	131	1	1 ≤	QUANTITY
ma-234	132	1	mα	ORG
ma-234	133	1	lim	PERSON
ma-234	134	1	0	CARDINAL
ma-234	135	1	integer n ≥ 1	ORG
ma-234	137	1	11	CARDINAL
ma-234	137	2	1,∞	CARDINAL
ma-234	137	3	11	CARDINAL
ma-234	139	1	13	CARDINAL
ma-234	139	2	3.2	CARDINAL
ma-234	139	3	11	CARDINAL
ma-234	140	1	j. math	PERSON
ma-234	142	1	10.28924	CARDINAL
ma-234	143	1	7solution	CARDINAL
ma-234	145	1	7	CARDINAL
ma-234	145	2	1	CARDINAL
ma-234	145	3	1	CARDINAL
ma-234	145	4	1	CARDINAL
ma-234	145	5	1,p	CARDINAL
ma-234	146	1	2.2	CARDINAL
ma-234	146	2	2.5 allowsus	QUANTITY
ma-234	146	3	11	CARDINAL
ma-234	147	1	2.6	CARDINAL
ma-234	148	1	1 ≤	QUANTITY
ma-234	148	2	1	CARDINAL
ma-234	149	1	1 α	TIME
ma-234	151	1	rj	PERSON
ma-234	152	1	1≤j≤d	CARDINAL
ma-234	152	2	11	CARDINAL
ma-234	152	3	rj	PERSON
ma-234	152	4	1 ≤ j ≤	QUANTITY
ma-234	153	1	− y |d+1 ϕ(y)dy	PERSON
ma-234	153	2	∈	ORG
ma-234	154	1	3	CARDINAL
ma-234	155	1	3.1	CARDINAL
ma-234	156	1	3.1	CARDINAL
ma-234	158	1	0	CARDINAL
ma-234	158	2	1)d	DATE
ma-234	160	1	∈	ORG
ma-234	161	1	2	CARDINAL
ma-234	161	2	∈	ORG
ma-234	162	1	∈ z	ORG
ma-234	162	2	2	CARDINAL
ma-234	162	3	rd	ORG
ma-234	163	1	3.2	CARDINAL
ma-234	164	1	•	CARDINAL
ma-234	164	2	2	CARDINAL
ma-234	164	3	0	CARDINAL
ma-234	166	1	∈ z	ORG
ma-234	166	2	k ∈ zd	PERSON
ma-234	167	1	•	CARDINAL
ma-234	167	2	3d	CARDINAL
ma-234	168	1	2	CARDINAL
ma-234	168	2	0	CARDINAL
ma-234	168	3	1)d +	DATE
ma-234	170	1	∈ z	ORG
ma-234	170	2	k ∈ zd	PERSON
ma-234	170	3	0	DATE
ma-234	170	4	1/3}d	DATE
ma-234	171	1	3	CARDINAL
ma-234	171	2	3.1	CARDINAL
ma-234	172	1	3.3	CARDINAL
ma-234	173	1	rd	ORG
ma-234	173	2	0	CARDINAL
ma-234	173	3	1/3}d	DATE
ma-234	176	1	j. math	PERSON
ma-234	178	1	10.28924	CARDINAL
ma-234	178	2	8	CARDINAL
ma-234	178	3	3.4	CARDINAL
ma-234	179	1	1 ≤	QUANTITY
ma-234	180	1	1 α	QUANTITY
ma-234	180	2	1	CARDINAL
ma-234	180	3	1	CARDINAL
ma-234	181	1	0	CARDINAL
ma-234	181	2	1/3}d	DATE
ma-234	181	3	p(dt	GPE
ma-234	183	1	3.5	CARDINAL
ma-234	184	1	1 ≤	QUANTITY
ma-234	185	1	d′	PERSON
ma-234	185	2	two	CARDINAL
ma-234	191	1	2	CARDINAL
ma-234	191	2	d′	PERSON
ma-234	192	1	2m}form	DATE
ma-234	192	2	rd	ORG
ma-234	193	1	d′	PERSON
ma-234	193	2	6=	CARDINAL
ma-234	193	3	d′	PERSON
ma-234	193	4	2d elements.a	DATE
ma-234	197	1	x)|qdx 	DATE
ma-234	200	1	1 α	QUANTITY
ma-234	200	2	1	CARDINAL
ma-234	200	3	1	CARDINAL
ma-234	201	1	2 d m	MONEY
ma-234	201	2	1 α	QUANTITY
ma-234	201	3	1	CARDINAL
ma-234	202	1	2	CARDINAL
ma-234	203	1	1 α	QUANTITY
ma-234	203	2	1	CARDINAL
ma-234	203	3	6=∅	CARDINAL
ma-234	205	1	2 d	MONEY
ma-234	205	2	2	CARDINAL
ma-234	205	3	1 α	QUANTITY
ma-234	205	4	1	CARDINAL
ma-234	205	5	∑ q∈dm	PERSON
ma-234	206	1	2	CARDINAL
ma-234	207	1	1 α	QUANTITY
ma-234	207	2	1	CARDINAL
ma-234	208	1	2 d	MONEY
ma-234	209	1	1 α	QUANTITY
ma-234	209	2	1	CARDINAL
ma-234	210	1	1	CARDINAL
ma-234	213	1	j. math	PERSON
ma-234	215	1	10.28924	CARDINAL
ma-234	215	2	9b	CARDINAL
ma-234	215	3	∈	ORG
ma-234	215	4	1 α	QUANTITY
ma-234	215	5	1	CARDINAL
ma-234	215	6	1	CARDINAL
ma-234	215	7	1 α	TIME
ma-234	215	8	1	CARDINAL
ma-234	217	1	x)|qdx  1	DATE
ma-234	217	2	1 α	QUANTITY
ma-234	218	1	1	CARDINAL
ma-234	218	2	1 α	QUANTITY
ma-234	218	3	1	CARDINAL
ma-234	219	1	6=∅	CARDINAL
ma-234	220	1	1 α	QUANTITY
ma-234	220	2	1	CARDINAL
ma-234	222	1	lemma	ORG
ma-234	223	1	3.6	CARDINAL
ma-234	224	1	1 ≤	QUANTITY
ma-234	224	2	0	CARDINAL
ma-234	224	3	1/3}d	DATE
ma-234	225	1	1	CARDINAL
ma-234	226	1	p(dt	GPE
ma-234	227	1	q,∞ ≤ ‖f	FAC
ma-234	227	2	q,∞	ORG
ma-234	228	1	mα q	ORG
ma-234	228	2	bourgain-morrey	PRODUCT
ma-234	230	1	3.7	CARDINAL
ma-234	231	1	8	CARDINAL
ma-234	231	2	1 ≤	QUANTITY
ma-234	231	3	1	CARDINAL
ma-234	231	4	0	CARDINAL
ma-234	233	1	2	CARDINAL
ma-234	234	1	3	CARDINAL
ma-234	235	1	0	CARDINAL
ma-234	236	1	mα	ORG
ma-234	238	1	3.8	CARDINAL
ma-234	239	1	1 ≤	QUANTITY
ma-234	239	2	lim y→0	PERSON
ma-234	240	1	− y)‖α	PERSON
ma-234	242	1	j. math	PERSON
ma-234	244	1	10.28924	CARDINAL
ma-234	244	2	bourgain-morrey	PRODUCT
ma-234	245	1	3.9	CARDINAL
ma-234	246	1	1 ≤	QUANTITY
ma-234	247	1	mα	ORG
ma-234	248	1	lim y→0	PERSON
ma-234	249	1	0	CARDINAL
ma-234	252	1	0	CARDINAL
ma-234	253	1	wesuppose	GPE
ma-234	253	2	2	CARDINAL
ma-234	253	3	3.7	CARDINAL
ma-234	253	4	lim	ORG
ma-234	255	1	0	CARDINAL
ma-234	256	1	1	CARDINAL
ma-234	256	2	3.7	CARDINAL
ma-234	256	3	thereexists	NORP
ma-234	256	4	0	CARDINAL
ma-234	257	1	y ∈ rd	PERSON
ma-234	257	2	n ≥ 1	DATE
ma-234	258	1	2(1	CARDINAL
ma-234	259	1	1	CARDINAL
ma-234	259	2	3	CARDINAL
ma-234	259	3	3.7	CARDINAL
ma-234	266	1	2 +	DATE
ma-234	268	1	3.8	CARDINAL
ma-234	272	1	4	CARDINAL
ma-234	272	2	4.1	CARDINAL
ma-234	273	1	f(q	GPE
ma-234	274	1	2.3	CARDINAL
ma-234	275	1	2.31	CARDINAL
ma-234	275	2	•	CARDINAL
ma-234	276	1	q,∞	PERSON
ma-234	277	1	•	CARDINAL
ma-234	277	2	0	CARDINAL
ma-234	279	1	•	CARDINAL
ma-234	279	2	1 ≤	QUANTITY
ma-234	280	1	rd	GPE
ma-234	282	1	j. math	PERSON
ma-234	284	1	10.28924	CARDINAL
ma-234	284	2	11	CARDINAL
ma-234	284	3	i.	PERSON
ma-234	284	4	0	DATE
ma-234	285	1	1/3}d	CARDINAL
ma-234	285	2	andan element r(i	PERSON
ma-234	285	3	r(i	PERSON
ma-234	285	4	3.3	CARDINAL
ma-234	286	1	|qi	LANGUAGE
ma-234	287	1	1 α	QUANTITY
ma-234	287	2	1	CARDINAL
ma-234	287	3	1	CARDINAL
ma-234	287	4	|qi	NORP
ma-234	287	5	|r(i	ORG
ma-234	287	6	t)|	CARDINAL
ma-234	287	7	1 α	QUANTITY
ma-234	287	8	1	CARDINAL
ma-234	288	1	|r(i	ORG
ma-234	288	2	1 α	QUANTITY
ma-234	288	3	1	CARDINAL
ma-234	288	4	t	GPE
ma-234	289	1	1	CARDINAL
ma-234	289	2	1	CARDINAL
ma-234	290	1	|r(i	ORG
ma-234	290	2	1 α	QUANTITY
ma-234	290	3	1	CARDINAL
ma-234	290	4	t	GPE
ma-234	291	1	1	CARDINAL
ma-234	292	1	0	CARDINAL
ma-234	292	2	1/3}d	DATE
ma-234	293	1	∈	ORG
ma-234	294	1	∃	PERSON
ma-234	294	2	r(i	PERSON
ma-234	296	1	∈	ORG
ma-234	297	1	∈	ORG
ma-234	299	1	|qi	NORP
ma-234	300	1	3d	CARDINAL
ma-234	301	1	|qi |	TIME
ma-234	302	1	1 α	QUANTITY
ma-234	302	2	1	CARDINAL
ma-234	302	3	1	CARDINAL
ma-234	302	4	|qi	LANGUAGE
ma-234	303	1	1 α	QUANTITY
ma-234	303	2	1	CARDINAL
ma-234	303	3	1	CARDINAL
ma-234	303	4	3 d ( 1	CARDINAL
ma-234	303	5	1	CARDINAL
ma-234	303	6	1 α	QUANTITY
ma-234	303	7	1	CARDINAL
ma-234	303	8	1	CARDINAL
ma-234	304	1	1	CARDINAL
ma-234	305	1	3d	CARDINAL
ma-234	305	2	∑	PERSON
ma-234	305	3	r∈rt	CARDINAL
ma-234	305	4	1	CARDINAL
ma-234	306	1	1	CARDINAL
ma-234	307	1	1	CARDINAL
ma-234	308	1	3d	CARDINAL
ma-234	308	2	∑	PERSON
ma-234	308	3	1	CARDINAL
ma-234	308	4	1	CARDINAL
ma-234	308	5	rt ⊂	ORG
ma-234	309	1	|qi	LANGUAGE
ma-234	309	2	1 α	QUANTITY
ma-234	309	3	1	CARDINAL
ma-234	309	4	1	CARDINAL
ma-234	310	1	1 p	MONEY
ma-234	310	2	1	CARDINAL
ma-234	310	3	p(dt	GPE
ma-234	311	1	rd	GPE
ma-234	311	2	1	CARDINAL
ma-234	311	3	p(dt	GPE
ma-234	313	1	j. math	PERSON
ma-234	315	1	10.28924	CARDINAL
ma-234	315	2	12therefore	CARDINAL
ma-234	315	3	3.6	CARDINAL
ma-234	315	4	1	CARDINAL
ma-234	315	5	2	CARDINAL
ma-234	315	6	pand consequently mα	ORG
ma-234	315	7	f(q	GPE
ma-234	315	8	α).2	PERSON
ma-234	316	1	mα	ORG
ma-234	317	1	f(q	GPE
ma-234	317	2	y ∈ rd	PERSON
ma-234	318	1	− y)‖f(q	PERSON
ma-234	318	2	1	CARDINAL
ma-234	318	3	2	CARDINAL
ma-234	319	1	3.9	CARDINAL
ma-234	319	2	lim y→0	PERSON
ma-234	319	3	− y)‖f(q	PERSON
ma-234	319	4	f(q	GPE
ma-234	321	1	4.2	CARDINAL
ma-234	322	1	bourgain-morrey	PRODUCT
ma-234	324	1	4.1	CARDINAL
ma-234	325	1	8	CARDINAL
ma-234	325	2	1 ≤	QUANTITY
ma-234	325	3	0	CARDINAL
ma-234	325	4	∈	ORG
ma-234	325	5	‖g ∗ f	PERSON
ma-234	327	1	3.7	CARDINAL
ma-234	327	2	3.9	CARDINAL
ma-234	327	3	4.1	CARDINAL
ma-234	327	4	2.4	CARDINAL
ma-234	328	1	2.4 •	CARDINAL
ma-234	336	1	∗	CARDINAL
ma-234	337	1	− u n	PERSON
ma-234	339	1	− u n	PERSON
ma-234	341	1	3.9	CARDINAL
ma-234	341	2	lim	PERSON
ma-234	341	3	− u n	PERSON
ma-234	344	1	j. math	PERSON
ma-234	346	1	10.28924	CARDINAL
ma-234	346	2	minkowski	PERSON
ma-234	346	3	1	CARDINAL
ma-234	346	4	3.7	CARDINAL
ma-234	347	1	have∥∥∥f − f	ORG
ma-234	347	2	− u n	PERSON
ma-234	349	1	n ≥ 1	DATE
ma-234	350	1	lim n→∞	PERSON
ma-234	350	2	0	CARDINAL
ma-234	352	1	1	CARDINAL
ma-234	352	2	∈	ORG
ma-234	353	1	∈	ORG
ma-234	354	1	∈	ORG
ma-234	354	2	4.1	CARDINAL
ma-234	355	1	lim n→∞	PERSON
ma-234	356	1	mα	ORG
ma-234	359	1	4.2	CARDINAL
ma-234	360	1	1	CARDINAL
ma-234	360	2	1 ≤	QUANTITY
ma-234	360	3	lim	PERSON
ma-234	360	4	n→∞	PRODUCT
ma-234	360	5	rd	ORG
ma-234	360	6	0	CARDINAL
ma-234	361	1	bourgain-morrey	PRODUCT
ma-234	362	1	4.3	CARDINAL
ma-234	363	1	1 ≤	QUANTITY
ma-234	364	1	mα	ORG
ma-234	364	2	rd	ORG
ma-234	364	3	0	CARDINAL
ma-234	365	1	lim n→∞	FAC
ma-234	365	2	0	CARDINAL
ma-234	368	1	0	CARDINAL
ma-234	369	1	wesuppose	PERSON
ma-234	369	2	1 ≤	QUANTITY
ma-234	369	3	2	CARDINAL
ma-234	369	4	3.7	CARDINAL
ma-234	370	1	lim	ORG
ma-234	370	2	0.let	CARDINAL
ma-234	370	3	0	CARDINAL
ma-234	372	1	2	CARDINAL
ma-234	374	1	j. math	PERSON
ma-234	376	1	10.28924	CARDINAL
ma-234	376	2	3	CARDINAL
ma-234	376	3	3.7	CARDINAL
ma-234	377	1	4.2	CARDINAL
ma-234	377	2	n0	GPE
ma-234	377	3	1	CARDINAL
ma-234	378	1	n0	GPE
ma-234	380	1	n ≥	GPE
ma-234	382	1	1	CARDINAL
ma-234	382	2	3.6	CARDINAL
ma-234	382	3	4.3	CARDINAL
ma-234	383	1	4.4	CARDINAL
ma-234	384	1	1 ≤	QUANTITY
ma-234	388	1	lim	ORG
ma-234	389	1	0	CARDINAL
ma-234	390	1	4.4	CARDINAL
ma-234	391	1	4.5	CARDINAL
ma-234	392	1	1 ≤	QUANTITY
ma-234	393	1	mα	ORG
ma-234	393	2	lim	PERSON
ma-234	394	1	0	CARDINAL
ma-234	395	1	2.5	CARDINAL
ma-234	396	1	2.5for	CARDINAL
ma-234	396	2	integer n ≥ 1	ORG
ma-234	396	3	4.1	CARDINAL
ma-234	401	1	integer n ≥ 1	ORG
ma-234	404	1	− f χq(0,n	PERSON
ma-234	407	1	2.4	CARDINAL
ma-234	407	2	4.5	CARDINAL
ma-234	407	3	lim	PERSON
ma-234	408	1	0	CARDINAL
ma-234	411	1	j. math	PERSON
ma-234	413	1	10.28924	CARDINAL
ma-234	413	2	155	CARDINAL
ma-234	413	3	2.1	CARDINAL
ma-234	413	4	2.2	CARDINAL
ma-234	415	1	|q|γ−1	PRODUCT
ma-234	416	1	∈	ORG
ma-234	417	1	lemma	ORG
ma-234	417	2	3.3	CARDINAL
ma-234	418	1	5.1	CARDINAL
ma-234	419	1	1	CARDINAL
ma-234	420	1	max	PERSON
ma-234	420	2	md	GPE
ma-234	422	1	l1 loc × rd	ORG
ma-234	422	2	rd	ORG
ma-234	423	1	byproposition 3.3	LAW
ma-234	423	2	0	CARDINAL
ma-234	423	3	1/3}d	DATE
ma-234	424	1	|q|γ−1	LANGUAGE
ma-234	424	2	q)d(γ−1	NORP
ma-234	425	1	1 3	CARDINAL
ma-234	428	1	max	PERSON
ma-234	428	2	md	GPE
ma-234	430	1	see point 2	CARDINAL
ma-234	430	2	3.7	CARDINAL
ma-234	430	3	8].here	CARDINAL
ma-234	430	4	5.3	CARDINAL
ma-234	431	1	5.2	CARDINAL
ma-234	432	1	1 ≤	QUANTITY
ma-234	434	1	↑	PRODUCT
ma-234	435	1	lim	PERSON
ma-234	435	2	0	CARDINAL
ma-234	436	1	integer n ≥ 1	ORG
ma-234	439	1	6=	DATE
ma-234	442	1	j. math	PERSON
ma-234	444	1	10.28924	CARDINAL
ma-234	444	2	16it	ORDINAL
ma-234	444	3	↑	PRODUCT
ma-234	445	1	4.4	CARDINAL
ma-234	445	2	lim n→∞	FAC
ma-234	445	3	0	CARDINAL
ma-234	447	1	5.2	CARDINAL
ma-234	448	1	5.3	CARDINAL
ma-234	449	1	1 α ≤ 1	QUANTITY
ma-234	449	2	1	CARDINAL
ma-234	450	1	mα 1,p	ORG
ma-234	450	2	2	CARDINAL
ma-234	450	3	1,p	CARDINAL
ma-234	452	1	1	CARDINAL
ma-234	452	2	0	CARDINAL
ma-234	453	1	1.let	CARDINAL
ma-234	453	2	rd	ORG
ma-234	453	3	|q|γ−1	PRODUCT
ma-234	454	1	1 α	QUANTITY
ma-234	454	2	1	CARDINAL
ma-234	454	3	−1	DATE
ma-234	454	4	1	CARDINAL
ma-234	454	5	1	CARDINAL
ma-234	455	1	lim	PERSON
ma-234	455	2	|q|γ−1	PRODUCT
ma-234	455	3	∈	ORG
ma-234	455	4	|q|γ−1	PRODUCT
ma-234	455	5	1	CARDINAL
ma-234	455	6	1	CARDINAL
ma-234	456	1	max	PERSON
ma-234	456	2	1	CARDINAL
ma-234	457	1	0	CARDINAL
ma-234	461	1	j. math	PERSON
ma-234	463	1	10.28924	CARDINAL
ma-234	465	1	∈	PRODUCT
ma-234	466	1	∈	ORG
ma-234	466	2	q.	PERSON
ma-234	467	1	⋃	PERSON
ma-234	467	2	q.	PERSON
ma-234	467	3	∗	CARDINAL
ma-234	467	4	∆j the	ORG
ma-234	468	1	that ⋃ q∈∆j	ORG
ma-234	468	2	⋃	WORK_OF_ART
ma-234	468	3	∀ q′	GPE
ma-234	468	4	∈	ORG
ma-234	468	5	∆j	PRODUCT
ma-234	468	6	|q|γ−1	PRODUCT
ma-234	469	1	2 |q|γ−1	CARDINAL
ma-234	469	2	∫	ORG
ma-234	470	1	2p	CARDINAL
ma-234	470	2	2p	CARDINAL
ma-234	470	3	1	CARDINAL
ma-234	470	4	−1	DATE
ma-234	471	1	∫	ORG
ma-234	471	2	∑ q∈∆j ∫	ORG
ma-234	472	1	1	CARDINAL
ma-234	472	2	−1	DATE
ma-234	473	1	⋃	PRODUCT
ma-234	474	1	∀ j ′	ORG
ma-234	474	2	j ′′ ∈ n	PERSON
ma-234	474	3	j ′ 6=	LAW
ma-234	474	4	j ′′,ej ′ ∩ ej	LAW
ma-234	474	5	′′	ORG
ma-234	474	6	∫ rd	ORG
ma-234	475	1	∑ j≥0 ∫	ORG
ma-234	475	2	2	CARDINAL
ma-234	475	3	∑	ORG
ma-234	475	4	1	CARDINAL
ma-234	475	5	−1	DATE
ma-234	475	6	1	CARDINAL
ma-234	478	1	j. math	PERSON
ma-234	480	1	10.28924	CARDINAL
ma-234	481	1	j ′	LAW
ma-234	481	2	j ′′	PERSON
ma-234	481	3	two	CARDINAL
ma-234	481	4	′′	ORG
ma-234	481	5	0	CARDINAL
ma-234	482	1	q′′	GPE
ma-234	484	1	qk	ORG
ma-234	484	2	qk	PERSON
ma-234	484	3	qk	ORG
ma-234	484	4	qk	PERSON
ma-234	484	5	∈ ∆j ′′	PERSON
ma-234	484	6	k ∈ zd	PERSON
ma-234	484	7	∈ z.therefore∑ j≥0 ∑ q∈∆j	ORG
ma-234	484	8	1	CARDINAL
ma-234	484	9	−1	DATE
ma-234	484	10	∑ k∈zd	PERSON
ma-234	484	11	qk	ORG
ma-234	484	12	⋃	PRODUCT
ma-234	484	13	∆j [ |qk	PERSON
ma-234	485	1	2	CARDINAL
ma-234	485	2	1,p	CARDINAL
ma-234	486	1	2	CARDINAL
ma-234	486	2	5.2	CARDINAL
ma-234	486	3	↑	PRODUCT
ma-234	486	4	lim	PERSON
ma-234	486	5	0	CARDINAL
ma-234	487	1	1	CARDINAL
ma-234	487	2	∥∥mdγ fn∥∥p ≤ 2 ‖fn‖mα 1,p ≤ 2 ‖f	ORG
ma-234	487	3	1,p	CARDINAL
ma-234	487	4	∥∥mdγ fn∥∥p)n≥1 ↑ ∥∥mdγ	ORG
ma-234	488	1	‖mdγ f	ORG
ma-234	488	2	2	CARDINAL
ma-234	488	3	1,p	CARDINAL
ma-234	489	1	2.1	CARDINAL
ma-234	489	2	5.1	CARDINAL
ma-234	489	3	5.3	CARDINAL
ma-234	489	4	3.6	CARDINAL
ma-234	490	1	2.1let	CARDINAL
ma-234	490	2	1,p	ORDINAL
ma-234	491	1	5.1	CARDINAL
ma-234	491	2	5.3	CARDINAL
ma-234	492	1	max	PERSON
ma-234	492	2	md	GPE
ma-234	492	3	2	CARDINAL
ma-234	492	4	1,p(dt	CARDINAL
ma-234	493	1	3.6	CARDINAL
ma-234	494	1	0	CARDINAL
ma-234	494	2	1/3}d	DATE
ma-234	495	1	2 d	MONEY
ma-234	495	2	3d(2−γ	CARDINAL
ma-234	495	3	1,p	DATE
ma-234	497	1	j. math	PERSON
ma-234	499	1	10.28924	CARDINAL
ma-234	500	1	2.1	CARDINAL
ma-234	500	2	2.2	CARDINAL
ma-234	501	1	2.2let	CARDINAL
ma-234	501	2	1,p	ORDINAL
ma-234	502	1	12	CARDINAL
ma-234	502	2	1	CARDINAL
ma-234	503	1	2.1	CARDINAL
ma-234	504	1	6	CARDINAL
ma-234	504	2	2.2	CARDINAL
ma-234	504	3	2.5	CARDINAL
ma-234	504	4	2.6	CARDINAL
ma-234	505	1	6.1	CARDINAL
ma-234	506	1	1 ≤	QUANTITY
ma-234	506	2	1	CARDINAL
ma-234	507	1	1 α	TIME
ma-234	508	1	1	CARDINAL
ma-234	508	2	1 ≤ j ≤	QUANTITY
ma-234	508	3	= rj	PERSON
ma-234	508	4	2	CARDINAL
ma-234	509	1	1≤j≤d	CARDINAL
ma-234	509	2	11	CARDINAL
ma-234	511	1	1 ≤	QUANTITY
ma-234	511	2	⊂	GPE
ma-234	511	3	1,p	ORDINAL
ma-234	511	4	1	CARDINAL
ma-234	511	5	2.2	CARDINAL
ma-234	512	1	rj	PERSON
ma-234	512	2	1 ≤	QUANTITY
ma-234	514	1	fj	NORP
ma-234	514	2	= rj	PERSON
ma-234	515	1	1 ≤ j ≤	QUANTITY
ma-234	515	2	rj	PERSON
ma-234	515	3	d−1 lr	PERSON
ma-234	516	1	2	CARDINAL
ma-234	516	2	∈	ORG
ma-234	518	1	∂jψj	DATE
ma-234	518	2	14	CARDINAL
ma-234	518	3	17	CARDINAL
ma-234	518	4	1	CARDINAL
ma-234	519	1	∈	ORG
ma-234	519	2	1≤j≤d	CARDINAL
ma-234	519	3	∈	ORG
ma-234	519	4	d−1 lr	PERSON
ma-234	519	5	1 ≤	QUANTITY
ma-234	519	6	2.5	CARDINAL
ma-234	519	7	mα 1,p	ORG
ma-234	520	1	•	CARDINAL
ma-234	520	2	1 ≤	QUANTITY
ma-234	521	1	rj	PERSON
ma-234	524	1	j. math	PERSON
ma-234	526	1	10.28924	CARDINAL
ma-234	530	1	n→∞	CARDINAL
ma-234	531	1	lim n→∞ ∫ rd	ORG
ma-234	532	1	∂jfnj	PERSON
ma-234	532	2	ϕ(x)dx = lim	PERSON
ma-234	532	3	lim	ORG
ma-234	532	4	n→∞ ∫ rd	PERCENT
ma-234	532	5	= ∫ rd f (x)ϕ(x)dx.	ORG
ma-234	536	1	ibrahim	PERSON
ma-234	537	1	1	CARDINAL
ma-234	537	2	c. bennett	PERSON
ma-234	537	3	r.c.	PERSON
ma-234	537	4	new york	GPE
ma-234	537	5	1988).[2	CARDINAL
ma-234	537	6	j. bourgain	PERSON
ma-234	537	7	1989-90	DATE
ma-234	537	8	berlin	GPE
ma-234	537	9	1469	DATE
ma-234	537	10	1991	DATE
ma-234	537	11	179	CARDINAL
ma-234	537	12	d. cruz-uribe	PERSON
ma-234	537	13	two	CARDINAL
ma-234	537	14	universidad de málaga	ORG
ma-234	537	15	spain	GPE
ma-234	537	16	2017	CARDINAL
ma-234	538	1	25–85	CARDINAL
ma-234	539	1	10.1142/9789813147645_0002.[4	CARDINAL
ma-234	539	2	n. diarra	PERSON
ma-234	539	3	i. fofana	PERSON
ma-234	539	4	morrey spaces and	ORG
ma-234	540	1	14	CARDINAL
ma-234	540	2	2023	CARDINAL
ma-234	541	1	n. diarra	PERSON
ma-234	541	2	i. fofana	PERSON
ma-234	541	3	morrey spaces	ORG
ma-234	541	4	khayyam j. math.(2024).[6	PERSON
ma-234	541	5	m. dosso	PERSON
ma-234	541	6	i. fofana	PERSON
ma-234	541	7	m. sanogo	PERSON
ma-234	541	8	ann	PERSON
ma-234	543	1	108	CARDINAL
ma-234	543	2	2013	DATE
ma-234	543	3	133–153	CARDINAL
ma-234	544	1	https://doi.org/10.4064/ap108-2-2.[7] i. fofana	ORG
ma-234	544	2	faléa	GPE
ma-234	544	3	b.a.	GPE
ma-234	544	4	kpata	ORG
ma-234	545	1	26	CARDINAL
ma-234	545	2	2015	DATE
ma-234	546	1	717–739	CARDINAL
ma-234	547	1	n. hatano	PERSON
ma-234	547	2	t. nogayama	GPE
ma-234	547	3	d.i. hakim	PERSON
ma-234	547	4	bourgain	PERSON
ma-234	547	5	j. funct	PERSON
ma-234	549	1	284	CARDINAL
ma-234	549	2	2023	CARDINAL
ma-234	549	3	109720	DATE
ma-234	550	1	s. masaki	PERSON
ma-234	550	2	j. segata	PERSON
ma-234	550	3	generalized korteweg	PERSON
ma-234	550	4	ann	PERSON
ma-234	550	5	inst	PERSON
ma-234	551	1	h. poincaré	PERSON
ma-234	552	1	35	DATE
ma-234	552	2	2018	DATE
ma-234	552	3	283–326	CARDINAL
ma-234	554	1	anihpc.2017.04.003.[10] s. masaki	PERSON
ma-234	554	2	j. segata	PERSON
ma-234	554	3	2020	DATE
ma-234	554	4	11–25	DATE
ma-234	556	1	amer	PERSON
ma-234	558	1	43(1938	CARDINAL
ma-234	559	1	126–166	CARDINAL
ma-234	562	1	j. math	PERSON
ma-234	564	1	10.28924	CARDINAL
ma-234	564	2	21	CARDINAL
ma-234	565	1	12	CARDINAL
ma-234	565	2	r. wheeden	PERSON
ma-234	566	1	amer	PERSON
ma-234	568	1	192(1974	CARDINAL
ma-234	568	2	261–274	CARDINAL
ma-234	569	1	https://doi.org/10.1090/s0002-9947-1974-0340523-6.[13] n.c	ORG
ma-234	569	2	phuc	PERSON
ma-234	569	3	m. torrès	PERSON
ma-234	569	4	indiana	GPE
ma-234	569	5	univ	NORP
ma-234	571	1	j.	PERSON
ma-234	571	2	57	DATE
ma-234	572	1	e.m. stein	PERSON
ma-234	572	2	princeton university press	ORG
ma-234	572	3	princeton	ORG
ma-234	572	4	new jersey	GPE
ma-234	572	5	1970).[15	CARDINAL
ma-234	572	6	j. tao	PERSON
ma-234	572	7	d. yang	PERSON
ma-234	572	8	w. yuan	PERSON
ma-234	572	9	morrey spaces	ORG
ma-234	572	10	j. math	PERSON
ma-234	573	1	2021	CARDINAL
ma-234	573	2	20	DATE
ma-234	577	1	2	CARDINAL
ma-234	577	2	3	CARDINAL
ma-234	577	3	3.1	CARDINAL
ma-234	578	1	3.2	CARDINAL
ma-234	579	1	mq	ORG
ma-234	579	2	4	CARDINAL
ma-234	579	3	4.1	CARDINAL
ma-234	580	1	mq	ORG
ma-234	580	2	f(q	GPE
ma-234	580	3	4.2	CARDINAL
ma-234	581	1	mq	ORG
ma-234	581	2	5	CARDINAL
ma-234	581	3	mq	ORG
ma-234	581	4	6	CARDINAL