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

  • Humberto Rafeiro
  • Stefan Samko
Part of the Operator Theory: Advances and Applications book series (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].

Keywords

Fractional integrals Riesz potentials Bessel potentials variable exponent spaces Marchaud fractional derivative 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Humberto Rafeiro
    • 1
  • Stefan Samko
    • 1
  1. 1.University of AlgarvePortugal

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