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Weighted Hardy Operators in Complementary Morrey Spaces

Abstract

We study the weighted -boundedness of the multidimensional weighted Hardy-type operators and with radial type weight , in the generalized complementary Morrey spaces defined by an almost increasing function . We prove a theorem which provides conditions, in terms of some integral inequalities imposed on and , for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the function and the weight are power functions. We also prove that the spaces over bounded domains Ω are embedded between weighted Lebesgue space with the weight and such a space with the weight , perturbed by a logarithmic factor. Both the embeddings are sharp.

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Category

Academic article

Language

English

Author(s)

  • Dag Lukkassen
  • Lars-Erik Persson
  • Stefan Samko

Affiliation

  • SINTEF Narvik
  • Luleå University of Technology
  • University of Algarve
  • UiT The Arctic University of Norway

Year

2012

Published in

Journal of Function Spaces and Applications

ISSN

0972-6802

Volume

2012

View this publication at Norwegian Research Information Repository