Hardy inequalities for antisymmetric functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-29 DOI:10.1016/j.na.2024.113619

Shubham Gupta

引用次数: 0

Abstract

We study Hardy inequalities for antisymmetric functions in three different settings: Euclidean space, torus and the integer lattice. In particular, we show that under the antisymmetric condition the sharp constant in Hardy inequality increases substantially and grows as $d^{4}$ as $d \to \infty$ in all cases. As a side product, we prove Hardy inequality on a domain whose boundary forms a corner at the point of singularity $x = 0$ .

查看原文本刊更多论文

反对称函数的哈代不等式

我们在三种不同的环境中研究了反不对称函数的哈代不等式：欧几里得空间、环和整数网格。我们特别指出，在反对称条件下，Hardy 不等式中的尖锐常数会大幅增加，并且在所有情况下都一样增长。作为附带结果，我们证明了边界在奇点处形成一个角的域上的哈代不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.