Weighted Hardy and potential operators in the generalized Morrey spaces

We study the weighted p -> q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces L-p.phi(R-n, w) defined by an almost increasing function phi(r) and radial type weight w(vertical bar x vertical bar). We obtain sufficient conditions, in terms of some integral...

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Bibliographic Details
Main Author: Persson, Lars-Erik (author)
Other Authors: Samko, Natasha (author)
Format: article
Language:eng
Published: 2018
Subjects:
Singular integral-operators
Fractional integrals
Maximal operator
Sufficient conditions
Variable exponent
Riesz-potentials
Boundedness
Online Access:http://hdl.handle.net/10400.1/11731
Country:Portugal
Oai:oai:sapientia.ualg.pt:10400.1/11731
Description
Summary:We study the weighted p -> q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces L-p.phi(R-n, w) defined by an almost increasing function phi(r) and radial type weight w(vertical bar x vertical bar). We obtain sufficient conditions, in terms of some integral inequalities imposed on phi and w, for such a p -> q-boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p -> q-boundedness of the Riesz potential operator. (c) 2010 Elsevier Inc. All rights reserved.

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