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A characterization for fractional integral and its commutators in Orlicz and generalized Orlicz–Morrey spaces on spaces of homogeneous type

  • Vagif S. Guliyev
  • Fatih DeringozEmail author
Article
  • 26 Downloads

Abstract

In this paper, we investigate the boundedness of maximal operator and its commutators in generalized Orlicz–Morrey spaces on the spaces of homogeneous type. As an application of this boundedness, we give necessary and sufficient condition for the boundedness of fractional integral and its commutators in these spaces. We also discuss criteria for the boundedness of these operators in Orlicz spaces.

Keywords

Orlicz space Generalized Orlicz–Morrey space Maximal operator Fractional integral Commutator Spaces of homogeneous type 

Mathematics Subject Classification

42B20 42B25 42B35 

Notes

Acknowledgements

The research of V.S. Guliyev was partially supported by the grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement No. EIF-BGM-4-RFTF-1/2017-21/01/1) and by the Ministry of Education and Science of the Russian Federation (the Agreement number No. 02.a03.21.0008). The research of F. Deringoz was partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A4.18.019).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

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Authors and Affiliations

  1. 1.S.M. Nikolskii Institute of MathematicsRUDN UniversityMoscowRussia
  2. 2.Department of MathematicsDumlupinar UniversityKutahyaTurkey
  3. 3.Institute of Mathematics and MechanicsBakuAzerbaijan
  4. 4.Department of MathematicsAhi Evran UniversityKirsehirTurkey

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