ROUNDEDNESS OF GENERALIZED RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES L(1,φ:κ) (G) OVER NON-DOUBLING MEASURE SPACES

被引：1

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：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2019年 / 22卷 / 02期

基金：

日本学术振兴会;

关键词：

Sobolev embeddings; Morrey space; Orlicz space; Riesz potential; fractional integral; non-doubling measure; FRACTIONAL INTEGRAL-OPERATORS; SOBOLEV EMBEDDINGS; BOUNDEDNESS;

D O I：

10.7153/mia-2019-22-41

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our aim in this paper is to deal with the boundedness of generalized Riesz potentials I(rho, mu, tau)f of functions in Morrey spaces L-(1,L-phi:kappa)(G) over non-doubling measure spaces, as an extension of [4, 6, 9, 12, 19]. The local integrability is assumed to be minimal, so that the results can not be obtained by the Hardy-Littlewood maximal operator. What is new in this paper is that phi depends on x is an element of X and that the underlying measure mu is not doubling.

引用

页码：577 / 599

页数：23

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