CHARACTERIZATIONS FOR THE GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON MORREY SPACES

被引：36

作者：

Eridani ^{[1
]}

Gunawan, Hendra ^{[2
]}

Nakai, Eiichi ^{[3
]}

Sawano, Yoshihiro ^{[4
]}

机构：

[1] Airlangga Univ, Dept Math, Surabaya 60115, Indonesia

[2] Bandung Inst Technol, Dept Math, Bandung 40132, Indonesia

[3] Ibaraki Univ, Dept Math, Mito, Ibaraki 3108512, Japan

[4] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Hachioji, Tokyo 1920397, Japan

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2014年 / 17卷 / 02期

基金：

日本学术振兴会;

关键词：

Fractional integrals; bounded operators; Morrey spaces; SUFFICIENT CONDITIONS; SOBOLEV EMBEDDINGS; RIESZ-POTENTIALS; BOUNDEDNESS; COMMUTATORS;

D O I：

10.7153/mia-17-56

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present some characterizations for the boundedness of the generalized fractional integral operators on Morrey spaces. The characterizations follow from two key estimates, one for the norm of some functions in Morrey spaces, and another for the values of the corresponding fractional integrals. We prove three theorems about necessary and sufficient conditions. We show that these theorems are independent by giving some examples. We also obtain counterparts for the weak generalized Morrey spaces.

引用

页码：761 / 777

页数：17

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