Endpoint Sobolev Regularity of Multilinear Maximal Operators

被引：0

作者：

Liu, Feng ^{[1
]}

Zhang, Xiao ^{[2
]}

Zhang, Huiyun ^{[3
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Coll Elect & Informat Engn, Qingdao 266590, Shandong, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Elect & Informat Engn, Qingdao 266590, Shandong, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2023年 / 27卷 / 05期

基金：

中国国家自然科学基金;

关键词：

multilinear maximal operators; Sobolev spaces; boundedness; continuity; CONTINUITY;

D O I：

10.11650/tjm/230703

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish some new endpoint regularity properties of multilinear maximal operators and their fractional variants, both in the centered and uncentered cases. The main results we obtain not only answer a question of Liu, Wu, Xue and Yabuta, but also provide some new endpoint Sobolev boundedness and continuity results for multilinear fractional maximal operators. More importantly, we present a new approach to deal with the endpoint Sobolev continuity for the above operators.

引用

页码：889 / 912

页数：24

共 50 条

[1] Endpoint regularity of discrete multilinear maximal and minimal operators
Li, Jing
Liu, Feng
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2023, 34 (11)
[2] Sobolev Regularity of Multilinear Fractional Maximal Operators on Infinite Connected Graphs
Liu, Suying
Liu, Feng
[J]. MATHEMATICS, 2021, 9 (22)
[3] Endpoint Sobolev Regularity of the Fractional Maximal Commutators
Ting Chen
Feng Liu
[J]. Journal of Fourier Analysis and Applications, 2022, 28
[4] Endpoint Sobolev Regularity of the Fractional Maximal Commutators
Chen, Ting
Liu, Feng
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2022, 28 (05)
[5] ENDPOINT ESTIMATES FOR MULTILINEAR FRACTIONAL MAXIMAL OPERATORS
He, Suixin
Zhang, Jing
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 57 (02) : 383 - 391
[6] ON THE ENDPOINT REGULARITY OF DISCRETE MAXIMAL OPERATORS
Carneiro, Emanuel
Hughes, Kevin
[J]. MATHEMATICAL RESEARCH LETTERS, 2012, 19 (06) : 1245 - 1262
[7] Regularity and continuity of the multilinear strong maximal operators
Liu, Feng
Xue, Qingying
Yabuta, Kozo
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2020, 138 : 204 - 241
[8] Regularity and continuity of commutators of multilinear maximal operators
Liu, Feng
Xue, Qingying
Zhang, Pu
[J]. NEW YORK JOURNAL OF MATHEMATICS, 2021, 27 : 1524 - 1553
[9] Endpoint Sobolev and BV continuity for maximal operators
Carneiro, Emanuel }
Madrid, Jose
Pierce, Lillian B.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 273 (10) : 3262 - 3294
[10] Endpoint Sobolev boundedness and continuity of multilinear fractional maximal functions
Liu, Feng
Wu, Huoxiong
Xue, Qingying
Yabuta, Kozo
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2022, 179

← 1 2 3 4 5 →