ON THE COMPACTNESS OF COMMUTATORS OF HARDY OPERATORS

被引：47
|
作者：
Shi, Shaoguang [1 ]
Fu, Zunwei [2 ,3 ]
Lu, Shanzhen [4 ]
机构：
[1] Linyi Univ, Sch Sci, Dept Math, Linyi, Shandong, Peoples R China
[2] Linyi Univ, Dept Math, Linyi, Shandong, Peoples R China
[3] Qufu Normal Univ, Sch Math Sci, Qufu, Shandong, Peoples R China
[4] Beijing Normal Univ, Sch Math Sci, Beijing, Peoples R China
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2020年 / 307卷 / 01期
关键词：
Hardy operator; commutator; compactness; BMO; INTEGRAL-OPERATORS; DIRICHLET PROBLEM; SPACES; INEQUALITIES; BOUNDEDNESS; TRANSFORMS; EQUATIONS;
D O I：
10.2140/pjm.2020.307.239
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We focus on the need for the compactness characterizations of the commutators of Hardy operators. More precisely, we prove that the commutators of Hardy operators, including the fractional Hardy operator, are compact operators on L-p(R-n) (1 < p < infinity) spaces if and only if the symbol functions of the commutators belong to CVMO(R-n) spaces (the central BMO (R-n) closure of C-c(infinity)(R-n)).
引用
收藏
页码：239 / 256
页数：18
相关论文
共 50 条
  • [1] Compactness of commutators of Hardy operators on Heisenberg group
    Xu, Jin
    Zhao, Jiman
    ADVANCES IN OPERATOR THEORY, 2024, 9 (04)
  • [2] Commutators of Hardy operators
    Long, SC
    Wang, J
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 274 (02) : 626 - 644
  • [3] Hardy operators and the commutators on Hardy spaces
    Niu, Zhuang
    Guo, Shasha
    Li, Wenming
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020, 2020 (01)
  • [4] Hardy operators and the commutators on Hardy spaces
    Zhuang Niu
    Shasha Guo
    Wenming Li
    Journal of Inequalities and Applications, 2020
  • [5] Commutators of generalized Hardy operators
    Fu, Zunwei
    Lu, Shanzhen
    MATHEMATISCHE NACHRICHTEN, 2009, 282 (06) : 832 - 845
  • [6] A note on commutators of Hardy operators
    Zhao, Fayou
    MATHEMATISCHE NACHRICHTEN, 2012, 285 (10) : 1294 - 1298
  • [7] On the Compactness of Commutators of Hardy–Littlewood Maximal Operator
    D.-H. Wang
    J. Zhou
    Z.-D. Teng
    Analysis Mathematica, 2019, 45 : 599 - 619
  • [8] Weighted multilinear Hardy operators and commutators
    Fu, Zun Wei
    Gong, Shu Li
    Lu, Shan Zhen
    Yuan, Wen
    FORUM MATHEMATICUM, 2015, 27 (05) : 2825 - 2851
  • [9] ON THE COMPACTNESS OF COMMUTATORS OF HARDY-LITTLEWOOD MAXIMAL OPERATOR
    Wang, D. -H.
    Zhou, J.
    Teng, Z. -D.
    ANALYSIS MATHEMATICA, 2019, 45 (03) : 599 - 619
  • [10] Compactness of the Commutators of Fractional Hardy Operator with Rough Kernel
    Shi, Shaoguang
    Fu, Zunwei
    ANALYSIS IN THEORY AND APPLICATIONS, 2021, 37 (03): : 347 - 361
12345