{"title":"约束下\\({\\mathbb{S}^n}\\)上改进的Hardy-Littlewood-Sobolev不等式","authors":"Yun Yun Hu, Jing Bo Dou","doi":"10.1007/s10114-023-2630-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we establish an improved Hardy–Littlewood–Sobolev inequality on <span>\\({\\mathbb{S}^n}\\)</span> under higher-order moments constraint. Moreover, by constructing precise test functions, using improved Hardy–Littlewood–Sobolev inequality on <span>\\({\\mathbb{S}^n}\\)</span>, we show such inequality is almost optimal in critical case. As an application, we give a simpler proof of the existence of the maximizer for conformal Hardy–Littlewood–Sobolev inequality.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-023-2630-8.pdf","citationCount":"0","resultStr":"{\"title\":\"Improved Hardy–Littlewood–Sobolev Inequality on \\\\({\\\\mathbb{S}^n}\\\\) under Constraints\",\"authors\":\"Yun Yun Hu, Jing Bo Dou\",\"doi\":\"10.1007/s10114-023-2630-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we establish an improved Hardy–Littlewood–Sobolev inequality on <span>\\\\({\\\\mathbb{S}^n}\\\\)</span> under higher-order moments constraint. Moreover, by constructing precise test functions, using improved Hardy–Littlewood–Sobolev inequality on <span>\\\\({\\\\mathbb{S}^n}\\\\)</span>, we show such inequality is almost optimal in critical case. As an application, we give a simpler proof of the existence of the maximizer for conformal Hardy–Littlewood–Sobolev inequality.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10114-023-2630-8.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-023-2630-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-023-2630-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Improved Hardy–Littlewood–Sobolev Inequality on \({\mathbb{S}^n}\) under Constraints
In this paper, we establish an improved Hardy–Littlewood–Sobolev inequality on \({\mathbb{S}^n}\) under higher-order moments constraint. Moreover, by constructing precise test functions, using improved Hardy–Littlewood–Sobolev inequality on \({\mathbb{S}^n}\), we show such inequality is almost optimal in critical case. As an application, we give a simpler proof of the existence of the maximizer for conformal Hardy–Littlewood–Sobolev inequality.
期刊介绍:
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.