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Pre-Compactness of Sets and Compactness of Commutators for Riesz Potential in Global Morrey-Type Spaces

Author

Listed:
  • Nurzhan Bokayev

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

  • Victor Burenkov

    (V.A. Steklov Mathematical Institute, Russian Academy of Sciences, 42 Gubkin St, 117966 Moscow, Russia
    V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya St, 117997 Moscow, Russia
    These authors contributed equally to this work.)

  • Dauren Matin

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

  • Aidos Adilkhanov

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

Abstract

In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces G M p θ w ( · ) . Our main result is the compactness of the commutators of the Riesz potential b , I α in global Morrey-type spaces from G M p 1 θ 1 w 1 ( · ) to G M p 2 θ 2 w 2 ( · ) . We also present new sufficient conditions for the commutator b , I α to be bounded from G M p 1 θ 1 w 1 ( · ) to G M p 2 θ 2 w 2 ( · ) . In the proof of the theorem regarding the compactness of the commutator for the Riesz potential, we primarily utilize the boundedness condition for the commutator for the Riesz potential b , I α in global Morrey-type spaces G M p θ w ( · ) , and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces G M p θ w ( · ) .

Suggested Citation

  • Nurzhan Bokayev & Victor Burenkov & Dauren Matin & Aidos Adilkhanov, 2024. "Pre-Compactness of Sets and Compactness of Commutators for Riesz Potential in Global Morrey-Type Spaces," Mathematics, MDPI, vol. 12(22), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3533-:d:1519318
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    1. 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.
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