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Characterizations for the fractional maximal operator and its commutators in generalized weighted Morrey spaces on Carnot groups

Analysis and Mathematical Physics volume 10, Article number: 15 (2020) Cite this article

Abstract

In this paper, we shall give a characterization for the strong and weak type Spanne type boundedness of the fractional maximal operator \(M_{\alpha }\), \(0\le \alpha <Q\) on Carnot group \({{\mathbb {G}}}\) on generalized weighted Morrey spaces \(M_{p,\varphi }({{\mathbb {G}}},w)\), where Q is the homogeneous dimension of \({{\mathbb {G}}}\). Also we give a characterization for the Spanne type boundedness of the fractional maximal commutator operator \(M_{b,\alpha }\) on generalized weighted Morrey spaces.

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Acknowledgements

The author thanks the referee(s) for careful reading the paper and useful comments. The research of V.S. Guliyev was partially supported by the Grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement Number no. EIF-BGM-4-RFTF-1/2017-21/01/1). The author is also supported by Department of Mathematics Analysis and the Theory of Functions, Peoples’ Friendship University of Russia, Moscow, Russia.

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Authors and Affiliations

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

    V. S. Guliyev

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

    V. S. Guliyev

  3. S.M. Nikolskii Institute of Mathematics, RUDN University, Moscow, Russia

    V. S. Guliyev

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  1. V. S. Guliyev
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Correspondence to V. S. Guliyev.

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Guliyev, V.S. Characterizations for the fractional maximal operator and its commutators in generalized weighted Morrey spaces on Carnot groups. Anal.Math.Phys. 10, 15 (2020). https://doi.org/10.1007/s13324-020-00360-9

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  • DOI: https://doi.org/10.1007/s13324-020-00360-9

Keywords

  • Carnot group
  • Fractional maximal operator
  • Generalized weighted Morrey space
  • Commutator
  • \({\textit{B}MO}\)
  • Homogeneous dimension

Mathematics Subject Classification

  • Primary 42B25
  • 42B35
  • 43A15
  • 43A80