Fractional operators and their commutators on generalized Orlicz spaces

TL;DR

This paper investigates the boundedness of fractional maximal operators and their commutators on generalized Orlicz spaces, providing new characterizations and extending results to double phase spaces.

Contribution

It introduces new boundedness results for fractional operators and commutators on generalized Orlicz spaces, including a characterization of BMO functions, with novel insights into double phase spaces.

Findings

Boundedness of fractional maximal operators established

Characterization of functions of bounded mean oscillation provided

Results extend to double phase spaces

Abstract

In this paper we examine boundedness of fractional maximal operator. The main focus is on commutators and maximal commutators on generalized 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. To best of our knowledge, these results are also new in the special case of double phase spaces.