Opuscula Math. 42, no. 4 (2022), 583-604
https://doi.org/10.7494/OpMath.2022.42.4.583

 
Opuscula Mathematica

Fractional operators and their commutators on generalized Orlicz spaces

Arttu Karppinen

Abstract. In this paper we examine boundedness of fractional maximal operator. The main focus is on commutators and maximal commutators on generalized Orlicz spaces (also known as Musielak-Orlicz spaces) for fractional maximal functions and Riesz potentials. We prove their boundedness between generalized Orlicz spaces and give a characterization for functions of bounded mean oscillation.

Keywords: maximal operator, commutator, fractional operator, generalized Orlicz, Musielak-Orlicz.

Mathematics Subject Classification: 46E30, 42B35, .

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  • Arttu Karppinen
  • University of Warsaw, Institute of Applied Mathematics and Mechanics, Warsaw, Poland
  • Communicated by P.A. Cojuhari.
  • Received: 2022-05-04.
  • Accepted: 2022-05-23.
  • Published online: 2022-06-30.
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Cite this article as:
Arttu Karppinen, Fractional operators and their commutators on generalized Orlicz spaces, Opuscula Math. 42, no. 4 (2022), 583-604, https://doi.org/10.7494/OpMath.2022.42.4.583

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