Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-17

The sharp constant for truncated Hardy-Littlewood maximal inequality

Jia Wu, Mingquan Wei, Dunyan Yan, Shao Liu

Received June 23, 2024. Published online January 24, 2025.

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

Keywords: sharp constant; truncated maximal operator; strong maximal operator

Classification MSC: 42B25

DOI: 10.21136/CMJ.2025.0259-24

PDF available at: Springer Institute of Mathematics CAS

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Affiliations: Jia Wu, University of Chinese Academy of Sciences, No. 19 A Yuquan Road, Shijingshan District, Beijing, 100049, P. R. China, e-mail: wujia19@mails.ucas.ac.cn; Mingquan Wei, Xinyang Normal University, No.237 Nanhu Road, Xinyang, P. R. China, e-mail: Weimingquan11@mails.ucas.ac.cn; Dunyan Yan, Shao Liu (corresponding author), University of Chinese Academy of Sciences, No. 19 A Yuquan Road, Shijingshan District, Beijing, 100049, P. R. China, e-mail: Yanydunyan@ucas.ac.cn, liushao19@mails.ucas.ac.cn

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