Hardy and Sobolev Inequalities on Antisymmetric Functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-13 DOI:10.1142/s1664360723500108

T. Hoffmann-Ostenhof, A. Laptev, Ilya A. Shcherbakov

引用次数: 0

Abstract

We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were considered for the antisymmetric functions in the case of the 1D particles. As a byproduct we obtain some Sobolev and Gagliardo-Nirenberg type inequalities that are applied to the study of spectral properties of Schr\"odinger operators.

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反对称函数上的Hardy不等式和Sobolev不等式

我们得到了反对称函数上的尖锐Hardy不等式，其中多维粒子的反对称被理解。部分地，它是先前发表的论文\cite{HL}的扩展，其中Hardy不等式被认为是一维粒子情况下的反对称函数。作为一个副产品，我们得到了一些Sobolev和Gagliardo-Nirenberg型不等式，这些不等式应用于Schrödinger算符的谱性质的研究。

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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