超抛物型极大函数的L2界估计

doi:10.7523/j.ucas.2026.019

中国科学院大学学报

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超抛物型极大函数的L²界估计

聂旭东¹, 燕敦验², 杨雅晴²

1.石家庄铁道大学数理系,石家庄 050043;
2.中国科学院大学数学科学学院,北京, 100049

收稿日期:2026-02-04 修回日期:2026-04-10 发布日期:2026-04-21

On the L²-bounds for hyper-parabolic maximal function^*

NIE xudong¹, YAN Dunyan^2,†, YANG Yaqing²

1 Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
2 School of Mathematics Science, University of Chinese Academy of Scinces, Beijing 10049, China

Received:2026-02-04 Revised:2026-04-10 Published:2026-04-21
Contact: ^†E-mail：ydunyan@mails.ucas.ac.cn
Supported by:
^*National Key R&D Program of China （2023YFC3007303）and National Natural Science Foundation of China（12271501）

摘要/Abstract

摘要： 本文估计了超抛物面极大函数
$ \sup _{t>0} \frac{1}{\left|S^{n}\right|}\left|\int_{S^{n}} f(\bar{x}-t \bar{y}) d \sigma(\bar{y})\right|$
的$ L^{2}$界。我们证明了该极大函数的 $ L^{2}$ 界可由 $ Cn^{\frac{3}{4}}$ 控制,其中常数C与维数 n 无关。

关键词: 极大函数, 维数无关性, 傅里叶乘子

Abstract: We estimate the $ L^{2}$-bounds for the maximal function over hyper-surface
$ \sup _{t>0} \frac{1}{\left|S^{n}\right|}\left|\int_{S^{n}} f(\bar{x}-t \bar{y}) d \sigma(\bar{y})\right|.$
We prove the $ L^{2}$-bounds of the maximal function can be controlled by $ Cn^{\frac{3}{4}}$, where C is independent of n.

Key words: maximal function, dimension-free estimate, Fourier multiplier

中图分类号:

O174.2

聂旭东, 燕敦验, 杨雅晴. 超抛物型极大函数的L²界估计[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2026.019.

NIE xudong, YAN Dunyan, YANG Yaqing. On the L²-bounds for hyper-parabolic maximal function^*[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2026.019.

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超抛物型极大函数的L²界估计

On the L²-bounds for hyper-parabolic maximal function^*

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