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arXiv · 2407.03983

Characterization of Lipschitz functions via commutators of maximal operators on slice spaces

Heng Yang·Jiang Zhou
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Abstract

Let $0 \leq \alpha<n$, $M_{\alpha}$ be the fractional maximal operator, $M^{\sharp}$ be the sharp maximal operator and $b$ be the locally integrable function. Denote by $[b, M_{\alpha}]$ and $[b, M^{\sharp}]$ be the commutators of the fractional maximal operator $M_{\alpha}$ and the sharp maximal operator $M^{\sharp}$. In this paper, we show some necessary and sufficient conditions for the boundedness of the commutators $[b, M_{\alpha}]$ and $[b, M^{\sharp}]$ on slice spaces when the function $b$ is the Lipschitz function, by which some new characterizations of the non-negative Lipschitz function are obtained

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Heng Yang, Jiang Zhou. 2024-07-04. Characterization of Lipschitz functions via commutators of maximal operators on slice spaces. https://arxiv.org/abs/2407.03983

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