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Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces

Burenkov, Victor, Guliev, V. S. and Guliev, G. V. 2007. Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces. Doklady Mathematics 75 (1) , pp. 103-107. 10.1134/S1064562407010292

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Abstract

This paper deals with the boundedness of the Riesz potential in local and global Morrey-type spaces. We obtain an estimate for the Lp norm of the Riesz potential over a ball, which is used to reduce this problem to the boundedness of a Hardy operator in weighted Lp spaces on a half-line on the cone of nonnegative nonincreasing functions. This makes it possible to derive sufficient conditions for the boundedness of the Riesz potential for all admissible parameter values. For local Morrey-type spaces, these sufficient conditions are also necessary under certain relations between the parameters.

Item Type: Article
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 1064-5624
Last Modified: 04 Jun 2017 08:47
URI: http://orca.cf.ac.uk/id/eprint/84910

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