Weighted Hardy and potential operators in the generalized Morrey spaces

Persson, Lars-Erik; Samko, Natasha

http://hdl.handle.net/10400.1/11731

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Authors

Persson, Lars-Erik

Samko, Natasha

Abstract(s)

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.