Gagliardo-Nirenberg 和 Sobolev 不等式的新证明：热半群方法

Proceedings of the American Mathematical Society, Series B Pub Date : 2024-07-11 DOI:10.1090/bproc/211

Tohru Ozawa, Taiki Takeuchi

{"title":"Gagliardo-Nirenberg 和 Sobolev 不等式的新证明：热半群方法","authors":"Tohru Ozawa, Taiki Takeuchi","doi":"10.1090/bproc/211","DOIUrl":null,"url":null,"abstract":"We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the \n\n \n \n L\n p\n \n L^p\n \n\n-\n\n \n \n L\n q\n \n L^q\n \n\n estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"113 16","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A new proof of the Gagliardo–Nirenberg and Sobolev inequalities: Heat semigroup approach\",\"authors\":\"Tohru Ozawa, Taiki Takeuchi\",\"doi\":\"10.1090/bproc/211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the \\n\\n \\n \\n L\\n p\\n \\n L^p\\n \\n\\n-\\n\\n \\n \\n L\\n q\\n \\n L^q\\n \\n\\n estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.\",\"PeriodicalId\":106316,\"journal\":{\"name\":\"Proceedings of the American Mathematical Society, Series B\",\"volume\":\"113 16\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the American Mathematical Society, Series B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/bproc/211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们给出了基于热半群的 Gagliardo-Nirenberg 和 Sobolev 不等式的新证明。关于 Gagliardo-Nirenberg 不等式，我们仅依靠热半群的 L p L^p - L q L^q 估计值简化了之前的证明。对于索博廖夫不等式，我们考虑使用热半群和哈代不等式的另一种方法。

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

A new proof of the Gagliardo–Nirenberg and Sobolev inequalities: Heat semigroup approach

We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the L p L^p - L q L^q estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.

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

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

发文量