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Characterization of the boundedness of fractional maximal operator and its commutators in Orlicz and generalized Orlicz–Morrey spaces on spaces of homogeneous type

Analysis and Mathematical Physics volume 11, Article number: 63 (2021) Cite this article

Abstract

In this paper, we establish the necessary and sufficient conditions for the boundedness of fractional maximal operator \(M_{\alpha }\) and the fractional maximal commutators \(M_{b,\alpha }\) in Orlicz \(L^{\Phi }(X)\) and generalized Orlicz–Morrey spaces \(\mathcal {M}^{\Phi ,\varphi }(X)\) on spaces of homogeneous type \(X=(X,d,\mu )\) in the sense of Coifman-Weiss.

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Acknowledgements

We thank the referee for careful reading the paper and useful comments. The research of V. Guliyev was partially supported by grant of Cooperation Program 2532 TUBITAK–RFBR (RUSSIAN foundation for basic research) (Agreement number no. 119N455), by Grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1-M-08) and by the RUDN University Strategic Academic Leadership Program.

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Authors and Affiliations

  1. Department of Mathematics, Ahi Evran University, Kirsehir, Turkey

    Fatih Deringoz & Kendal Dorak

  2. Department of Mathematics, Dumlupinar University, Kutahya, Turkey

    Vagif S. Guliyev

  3. Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

    Vagif S. Guliyev

  4. Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

    Vagif S. Guliyev

Authors
  1. Fatih Deringoz
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  2. Kendal Dorak
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  3. Vagif S. Guliyev
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Correspondence to Fatih Deringoz.

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Deringoz, F., Dorak, K. & Guliyev, V.S. Characterization of the boundedness of fractional maximal operator and its commutators in Orlicz and generalized Orlicz–Morrey spaces on spaces of homogeneous type. Anal.Math.Phys. 11, 63 (2021). https://doi.org/10.1007/s13324-021-00497-1

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  • DOI: https://doi.org/10.1007/s13324-021-00497-1

Keywords

  • Orlicz space
  • Generalized Orlicz–Morrey space
  • Fractional maximal operator
  • Commutator
  • Spaces of homogeneous type

Mathematics subject classification

  • 42B20
  • 42B25
  • 42B35