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

被引：0
|
作者：
Victor I. Burenkov
Vagif S. Guliyev
机构：
[1] Cardiff University,Cardiff School of Mathematics
[2] Baku State University,Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan
来源：
Potential Analysis | 2009年 / 30卷
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; Primary 42B20; 42B25; 42B35;
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摘要：
The problem of the boundedness of the Riesz potential Iα, 0 < α < n, in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted Lp-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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