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Compactness of Commutators for Riesz Potential on Generalized Morrey Spaces

Author

Listed:
  • Nurzhan Bokayev

    (Department of Fundamental Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
    These authors contributed equally to this work.)

  • Dauren Matin

    (Higher Mathematics Department, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
    These authors contributed equally to this work.)

  • Talgat Akhazhanov

    (Higher Mathematics Department, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan)

  • Aidos Adilkhanov

    (Department of Fundamental Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan)

Abstract

In this paper, we give the sufficient conditions for the compactness of sets in generalized Morrey spaces M p w ( · ) . This result is an analogue of the well-known Fréchet–Kolmogorov theorem on the compactness of a set in Lebesgue spaces L p , p > 0 . As an application, we prove the compactness of the commutator of the Riesz potential [ b , I α ] in generalized Morrey spaces, where b ∈ V M O ( V M O ( R n ) denote the B M O -closure of C 0 ∞ ( R n ) ). We prove auxiliary statements regarding the connection between the norm of average functions and the norm of the difference of functions in the generalized Morrey spaces. Such results are also of independent interest.

Suggested Citation

  • Nurzhan Bokayev & Dauren Matin & Talgat Akhazhanov & Aidos Adilkhanov, 2024. "Compactness of Commutators for Riesz Potential on Generalized Morrey Spaces," Mathematics, MDPI, vol. 12(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:304-:d:1321012
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