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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

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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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