Journal of Function Spaces

Journal of Function Spaces / 2006 / Article

Open Access

Volume 4 |Article ID 610535 | https://doi.org/10.1155/2006/610535

Alexandre Almeida, Stefan Samko, "Characterization of Riesz and Bessel potentials on variable Lebesgue spaces", Journal of Function Spaces, vol. 4, Article ID 610535, 32 pages, 2006. https://doi.org/10.1155/2006/610535

Characterization of Riesz and Bessel potentials on variable Lebesgue spaces

Academic Editor: Vakhtang Kokilashvili
Received01 Mar 2005

Abstract

Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we describe a relation between the spaces of Riesz or Bessel potentials and the variable Sobolev spaces.

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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