Small Cap Square Function Estimates

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

引用次数: 0

Abstract

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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小盘股平方函数估计值

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。

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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

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