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Journal of Function Spaces and Applications
Volume 4 (2006), Issue 2, Pages 113-144
http://dx.doi.org/10.1155/2006/610535

Characterization of Riesz and Bessel potentials on variable Lebesgue spaces

1Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal
2Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal

Received 1 March 2005

Academic Editor: Vakhtang Kokilashvili

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.

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.