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COMMUTATORS OF THE MAXIMAL FUNCTIONS ON BANACH FUNCTION SPACES

Mujdat Agcayazi|Pu Zhang
대한수학회 (The Korean Mathematical Society)|2023.09|대한수학회보 (Bulletin of the KMS)|제60권 제5호|pp. 1391-1408|DOI 10.4134/BKMS.b220724

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키워드

maximal functionsBanach function spacescommutatorsBMO(Rn)
주제분류수학

초록

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 $\B(\mathbb{R}^{n})$ spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak--Orlicz spaces are also given.

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 $\B(\mathbb{R}^{n})$ spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak--Orlicz spaces are also given.

참고문헌 (42)

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