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arXiv · 2110.13493

The sharp constant for truncated Hardy-Littlewood maximal inequality

Jia Wu·Shao Liu·Mingquan Wei·Dunyan Yan
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Abstract

This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator $M^b_a$ and the strong truncated Hardy-Littlewood maximal operator $\tilde{M}^{\boldsymbol{b}}_{\boldsymbol{a}}$, respectively. We first present the $L^1$-norm of $M^b_a$, and then the $L^1$-norm of $\tilde{M}^{\boldsymbol{b}}_{\boldsymbol{a}}$ is given. Our study may have some enlightening significance for the research on sharp constant for the classical Hardy-Littlewood maximal inequality.

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Jia Wu, Shao Liu, Mingquan Wei, Dunyan Yan. 2021-10-26. The sharp constant for truncated Hardy-Littlewood maximal inequality. https://arxiv.org/abs/2110.13493

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