小盘股平方函数估计值

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-11 DOI:10.1007/s00041-024-10095-x

Shengwen Gan

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引用次数: 0

摘要

我们引入并证明了单位抛物线和截顶光锥的小帽平方函数估计值。更准确地说，我们研究了$$\begin{aligned}形式的不等式\Vert f\Vert _p\le C_{\alpha ,p}(R) \Big \Vert \Big (\sum _{\gamma \in \Gamma _\alpha (R^{-1})}|f_\gamma |^2\Big )^{1/2}\Big \Vert _p、\end{aligned}$$其中 $\Gamma _\alpha (R^{-1})$ 是宽度为 $R^{-\alpha }$ 的小帽子的集合。我们找到了常数 $C_{\alpha ,p}(R)$ 的尖锐上界和下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Small Cap Square Function Estimates

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Small Cap Square Function Estimates

We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form

$$\begin{aligned} \Vert f\Vert _p\le C_{\alpha ,p}(R) \Big \Vert \Big (\sum _{\gamma \in \Gamma _\alpha (R^{-1})}|f_\gamma |^2\Big )^{1/2}\Big \Vert _p, \end{aligned}$$

where $\Gamma _\alpha (R^{-1})$ is the set of small caps of width $R^{-\alpha }$. We find sharp upper and lower bounds of the constant $C_{\alpha ,p}(R)$.

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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.