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Vekua’s Generalized Singular Integral on Carleson Curves in Weighted Variable Lebesgue Spaces

  • Vakhtang Kokilashvili
  • Stefan Samko
Part of the Operator Theory: Advances and Applications book series (OT, volume 181)

Abstract

For a Carleson curve Γ we establish the boundedness, in weighted Lebesgue spaces L p(·)(Γ, ϱ) with variable exponent p(·), of the generalized singular integral operator which arises in the theory of I.N.Vekua generalized analytic functions. The obtained result is an extension of the known results even in the case of constant p. We also show that Vekua’s generalized singular integral exists a.e. for fL 1(Γ) on an arbitrary rectifiable curve.

Keywords

singular integrals generalized analytic functions weighted Lebesgue spaces variable exponent Carleson curve Zygmund conditions Bary-Stechkin class 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Vakhtang Kokilashvili
    • 1
  • Stefan Samko
    • 2
  1. 1.Black Sea University and A. Razmadze Mathematical InstituteTbilisiGeorgia
  2. 2.University of AlgarvePortugal

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