Weighted Hardy and potential operators in the generalized Morrey spaces |
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Authors: | Lars-Erik Persson |
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Affiliation: | a Luleå University of Technology, Sweden b Universidade do Algarve, Portugal |
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Abstract: | We study the weighted p→q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces Lp,φ(Rn,w) defined by an almost increasing function φ(r) and radial type weight w(|x|). We obtain sufficient conditions, in terms of some integral inequalities imposed on φ 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. |
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Keywords: | Morrey space Weighted Hardy operator Weighted Hardy inequalities Bary-Stechkin classes Matuszewska-Orlicz indices |
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