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Characterization of the Range of One-dimensional Fractional Integration in the Space with Variable Exponent

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Operator Algebras, Operator Theory and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 181))

Abstract

Within the frameworks of weighted Lebesgue spaces with variable exponent, we give a characterization of the range of the one-dimensional Riemann-Liouville fractional integral operator in terms of convergence of the corresponding hypersingular integrals. We also show that this range coincides with the weighted Sobolev-type space L α, p(·)[(a, b)ϱ].

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Author information

Authors and Affiliations

  1. University of Algarve, Portugal

    Humberto Rafeiro & Stefan Samko

Authors
  1. Humberto Rafeiro
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  2. Stefan Samko
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, U.T.L., Avenida Rovisco Pais, 1049-001, Lisboa, Portugal

    Maria Amélia Bastos , Amarino Brites Lebre  & Frank-Olme Speck ,  & 

  2. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Rafeiro, H., Samko, S. (2008). Characterization of the Range of One-dimensional Fractional Integration in the Space with Variable Exponent. In: Bastos, M.A., Lebre, A.B., Speck, FO., Gohberg, I. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 181. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8684-9_20

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