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
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.
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