Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2023; 60(5): 1391-1408

Online first article September 12, 2023      Printed September 30, 2023

https://doi.org/10.4134/BKMS.b220724

Copyright © The Korean Mathematical Society.

Commutators of the maximal functions on Banach function spaces

Müjdat Ağcayazı, Pu Zhang

Aydin Adnan Menderes University; Mudanjiang Normal University

Abstract

Let $M$ and $M^{\#}$ be Hardy-Littlewood maximal operator and sharp maximal operator, respectively. In this article, we present necessary and sufficient conditions for the boundedness properties for commutator operators $[M,b]$ and $[M^{\#},b]$ in a general context of Banach function spaces when $b$ belongs to $\operatorname{BMO}(\mathbb{R}^{n})$ spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak--Orlicz spaces are also given.

Keywords: Banach function spaces, commutators, maximal functions, $\B(\mathbb{R}^{n}$)

MSC numbers: Primary 47B47, 42B25, 42B35, 46E30

Supported by: Pu Zhang was supported by National Natural Science Foundation of China (Grant No. 11571160).