Sharp Hardy’s Inequality for Orthogonal Expansions in $$H^p$$ Spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-12-19 DOI:10.1007/s00041-023-10060-0

Paweł Plewa

引用次数: 0

Abstract

Hardy’s inequality on $H^p$ spaces, $p\in (0,1]$, in the context of orthogonal expansions is investigated for general bases on a wide class of domains in $\mathbb {R}^d$ with Lebesgue measure. The obtained result is applied to various Hermite, Laguerre, and Jacobi expansions. For that purpose some delicate estimates of the higher order derivatives for the underlying functions and of the associated heat or Poison kernels are proved. Moreover, sharpness of studied Hardy’s inequalities is justified by a construction of an explicit counterexample, which is adjusted to all considered settings.

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$$H^p$$ 空间中正交展开的夏普-哈代不等式

哈代不等式是在（H^p\）空间、（p\in (0,1]\）正交展开的背景下，针对具有勒贝格度量的（\mathbb {R}^d\）中广泛的一类域上的一般基础进行研究的。得到的结果被应用于各种赫米特、拉盖尔和雅可比展开。为此，证明了对底层函数的高阶导数以及相关热核或泊松核的一些微妙估计。此外，通过构建一个明确的反例，证明了所研究的哈代不等式的尖锐性，该反例适用于所有考虑的情况。

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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