Generalized fractional integral operators on generalized Orlicz-Morrey spaces of the second kind over non-doubling metric measure spaces

被引：2

作者：

Sawano, Yoshihiro ^{[1
]}

Shimomura, Tetsu ^{[2
]}

机构：

[1] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Minami Ohsawa 1-1, Hachioji, Tokyo 1920397, Japan

[2] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2018年 / 25卷 / 02期

基金：

日本学术振兴会;

关键词：

Sobolev's inequality; Morrey space; Riesz potential; non-doubling measure; CALDERON-ZYGMUND OPERATORS; RIESZ-POTENTIALS;

D O I：

10.1515/gmj-2018-0018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we aim to deal with the boundedness and the weak-type boundedness for the generalized fractional integral operators on generalized Orlicz-Morrey spaces of the second kind over non-doubling metric measure spaces, as an extension of [Y. Sawano and T. Shimomura, Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces, Z. Anal. Anwend. 36 (2017), no. 2, 159-190], [Y. Sawano and T. Shimomura, Generalized fractional integral operators over non-doubling metric measure spaces, Integral Transforms Spec. Funct. 28 (2017), no. 7, 534-546] and [I. Sihwaningrum, H. Gunawan and E. Nakai, Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces, Math. Nachr., to appear].

引用

页码：303 / 311

页数：9

共 24 条

[1] [Anonymous], 2002, MATH APPL
[2] Deringoz F, 2014, OPER THEORY ADV APPL, V242, P139
[3] DiFazio G, 1996, B UNIONE MAT ITAL, V10A, P409
[4] Non-smooth Atomic Decompositions for Generalized Orlicz-Morrey Spaces of the Third Kind
Guliyev, Vagif S.
Hasanov, Sabir G.
Sawano, Yoshihiro
Noi, Takahiro
[J]. ACTA APPLICANDAE MATHEMATICAE, 2016, 145 (01) : 133 - 174
[5] Hakim D. I., 2013, MATH AETERNA, V3, P161
[6] Morrey-Type Spaces on Gauss Measure Spaces and Boundedness of Singular Integrals
Liu, Liguang
Sawano, Yoshihiro
Yang, Dachun
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2014, 24 (02) : 1007 - 1051
[7] Mizuta Y, 2009, OSAKA J MATH, V46, P255
[8] Generalized fractional integrals on generalized Morrey spaces
Nakai, Eiichi
[J]. MATHEMATISCHE NACHRICHTEN, 2014, 287 (2-3) : 339 - 351
[9] Orlicz-Morrey spaces and the Hardy-Littlewood maximal function
Nakai, Eiichi
[J]. STUDIA MATHEMATICA, 2008, 188 (03) : 193 - 221
[10] Nazarov F, 1997, INT MATH RES NOTICES, V1997, P703

← 1 2 3 →