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

被引：86
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.
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收藏
页码：211 / 249
页数：39
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