Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces

被引：84
|
作者：
Burenkov, Victor I. [1 ]
Guliyev, Vagif S. [2 ]
机构：
[1] Cardiff Univ, Cardiff Sch Math, Cardiff CF24 4AG, S Glam, Wales
[2] Baku State Univ, Inst Math & Mech, Azerbaijan Acad Sci, AZ-1141 Baku, Azerbaijan
来源：
POTENTIAL ANALYSIS | 2009年 / 30卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
Riesz potential; Fractional maximal operator; Local Morrey-type spaces; Hardy operator on the cone of monotonic functions; Weak Morrey-type spaces; Weighted estimates; MAXIMAL OPERATOR;
D O I：
10.1007/s11118-008-9113-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The problem of the boundedness of the Riesz potential I (alpha) , 0 < alpha < n, in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted L (p) -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for the boundedness in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, these sufficient conditions coincide with the necessary ones.
引用
收藏
页码：211 / 249
页数：39
相关论文
共 50 条
  • [31] NECESSARY AND SUFFICIENT CONDITIONS FOR BOUNDEDNESS OF THE HARDY-TYPE OPERATOR FROM A WEIGHTED LEBESGUE SPACE TO A MORREY-TYPE SPACE
    Burenkov, V. I.
    Oinarov, R.
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2013, 16 (01): : 1 - 19
  • [32] ON BOUNDEDNESS OF THE HARDY OPERATOR IN MORREY-TYPE SPACES
    Burenkov, V. I.
    Jain, P.
    Tararykova, T. V.
    [J]. EURASIAN MATHEMATICAL JOURNAL, 2011, 2 (01): : 52 - 80
  • [33] Necessary and sufficient conditions for boundedness of multilinear fractional integrals with rough kernels on Morrey type spaces
    Shi, Yanlong
    Si, Zengyan
    Tao, Xiangxing
    Shi, Yafeng
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, : 1 - 19
  • [34] Necessary and sufficient conditions for boundedness of multilinear fractional integrals with rough kernels on Morrey type spaces
    Yanlong Shi
    Zengyan Si
    Xiangxing Tao
    Yafeng Shi
    [J]. Journal of Inequalities and Applications, 2016
  • [35] The boundedness of fractional integral operators in local and global mixed Morrey-type spaces
    Zhang, Houkun
    Zhou, Jiang
    [J]. POSITIVITY, 2022, 26 (01)
  • [36] BOUNDEDNESS OF THE ANISOTROPIC FRACTIONAL MAXIMAL OPERATOR IN ANISOTROPIC LOCAL MORREY-TYPE SPACES
    Akbulut, A.
    Ekincioglu, I.
    Serbetci, A.
    Tararykova, T.
    [J]. EURASIAN MATHEMATICAL JOURNAL, 2011, 2 (02): : 5 - 30
  • [37] The boundedness of fractional integral operators in local and global mixed Morrey-type spaces
    Houkun Zhang
    Jiang Zhou
    [J]. Positivity, 2022, 26
  • [38] Decompositions of local Morrey-type spaces
    Guliyev, Vagif S.
    Hasanov, Sabir G.
    Sawano, Yoshihiro
    [J]. POSITIVITY, 2017, 21 (03) : 1223 - 1252
  • [39] BOUNDEDNESS OF THE GENERALIZED RIEMANN-LIOUVILLE OPERATOR IN LOCAL MORREY-TYPE SPACES
    Senouci, M. A.
    [J]. EURASIAN MATHEMATICAL JOURNAL, 2023, 14 (04): : 63 - 68
  • [40] DUAL SPACES OF LOCAL MORREY-TYPE SPACES
    Gogatishvili, Amiran
    Mustafayev, Rza
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2011, 61 (03) : 609 - 622
12345