$$L^2$$ Estimates for a Nikodym Maximal Function Associated to Space Curves

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-02 DOI:10.1007/s00041-023-10062-y

Aswin Govindan Sheri

引用次数: 0

Abstract

For $p \in [2,\infty )$, we consider the $L^p \rightarrow L^p$ boundedness of a Nikodym maximal function associated to a one-parameter family of tubes in ${\mathbb {R}}^{d+1}$ whose directions are determined by a non-degenerate curve $\gamma $ in ${\mathbb {R}}^d$. These operators arise in the analysis of maximal averages over space curves. The main theorem generalises the known results for $d = 2$ and $d = 3$ to general dimensions. The key ingredient is an induction scheme motivated by recent work of Ko-Lee-Oh.

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与空间曲线相关的尼科迪姆最大函数的 $L^2$$ 估计数

对于(p in [2,infty))，我们考虑的是${\mathbb {R}}^{d+1}$ 中与一参数管族相关的尼科迪姆最大函数的有界性，该管族的方向由${\mathbb {R}}^{d+1}$ 中的非退化曲线$\gamma $决定。这些算子出现在空间曲线最大平均的分析中。主要定理将已知的 $d = 2$ 和 $d = 3$ 结果推广到了一般维度。其中的关键因素是柯李欧（Ko-Lee-Oh）最近研究的归纳方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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