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Potential Analysis

, Volume 35, Issue 1, pp 67–87 | Cite as

Boundedness of the Riesz Potential in Local Morrey-Type Spaces

  • Victor I. Burenkov
  • Amiran Gogatishvili
  • Vagif S. Guliyev
  • Rza Ch. Mustafayev
Article

Abstract

The problem of boundedness of the Riesz potential in local Morrey-type spaces is reduced to the problem of boundedness of the Hardy operator in weighted L p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for boundedness for all admissible values of the parameters, which, for a certain range of the parameters wider than known before, coincide with the necessary ones.

Keywords

Riesz potential Local and global Morrey-type spaces Hardy operator on the cone of monotonic functions 

Mathematics Subject Classifications (2010)

Primary 42B20 42B25 42B35 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Victor I. Burenkov
    • 1
  • Amiran Gogatishvili
    • 2
  • Vagif S. Guliyev
    • 3
    • 4
  • Rza Ch. Mustafayev
    • 4
  1. 1.Dipartimento di matematica pura ed applicataPadova UniversityPadovaItaly
  2. 2.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPrague 1Czech Republic
  3. 3.Department of MathematicsAhi Evran UniversityKirsehirTurkey
  4. 4.Institute of Mathematics and MechanicsAcademy of Sciences of AzerbaijanBakuAzerbaijan

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