Characterization of Riesz and Bessel potentials on variable Lebesgue spaces. Issue 2 (2006)

• Record Type: Journal Article
• Authors: Almeida Almeida, Alexandre Alexandre; Samko Samko, Stefan Stefan
• Other Names: Kokilashvili Kokilashvili Vakhtang Vakhtang Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 4:Issue 2(2006)
• Page Start: 113
• Page End: 144
• Publication Date: 2006
• Subjects: Lebesgue space with variable exponent -- hypersingular integral -- Riesz potential -- Bessel potential; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2006/610535
• Languages: English
• ISSNs: 0972-6802

Abstract

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.