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On Generalized Spherical Fractional Integration Operators in Weighted Generalized Hölder Spaces on the Unit Sphere

  • Natasha Samko
  • Boris Vakulov
Part of the Operator Theory: Advances and Applications book series (OT, volume 181)

Abstract

For spherical convolution operators with a given power type asymptotic of their Fourier-Laplace multiplier we prove a statement on the boundedness within the framework of weighted generalized Hölder spaces on the unit sphere. The result obtained explicitly shows how spherical convolution operators under consideration improve the behavior of the continuity modulus of functions.

Keywords

spherical convolution operators spherical potentials indices of almost monotonic functions Boyd-type indices continuity modulus generalized Hölder spaces 

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References

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Natasha Samko
    • 1
  • Boris Vakulov
    • 2
  1. 1.FCT Post DocUniversidade do AlgarvePortugal
  2. 2.Rostov State UniversityRussia

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