反对称函数上的Hardy不等式和Sobolev不等式

IF 1.1 2区数学 Q1 MATHEMATICS Bulletin of Mathematical Sciences Pub Date : 2023-06-13 DOI:10.1142/s1664360723500108

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

{"title":"反对称函数上的Hardy不等式和Sobolev不等式","authors":"T. Hoffmann-Ostenhof, A. Laptev, Ilya A. Shcherbakov","doi":"10.1142/s1664360723500108","DOIUrl":null,"url":null,"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.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hardy and Sobolev Inequalities on Antisymmetric Functions\",\"authors\":\"T. Hoffmann-Ostenhof, A. Laptev, Ilya A. Shcherbakov\",\"doi\":\"10.1142/s1664360723500108\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":9348,\"journal\":{\"name\":\"Bulletin of Mathematical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of Mathematical Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1664360723500108\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1664360723500108","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

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。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Hardy and Sobolev Inequalities on Antisymmetric Functions

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.