Fractional maximal function and its commutators on Orlicz spaces

TL;DR

This paper establishes conditions for the boundedness of fractional maximal operators and their commutators on Orlicz spaces, providing new characterizations of Lipschitz spaces.

Contribution

It offers necessary and sufficient conditions for boundedness and introduces new characterizations of Lipschitz spaces via commutators on Orlicz spaces.

Findings

Boundedness conditions for fractional maximal operator on Orlicz spaces

Boundedness of fractional maximal commutator and nonlinear commutator on Orlicz spaces

New characterizations of Lipschitz spaces

Abstract

In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $M_{b,\alpha}$ and nonlinear commutator of fractional maximal operator $[b,M_{\alpha}]$ on Orlicz spaces, when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.