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

页码：211 / 249

页数：39

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