{"title":"一些$\\boldsymbol {L^p}$ -HARDY和$\\boldsymbol {L^p}$ -RELLICH型带余项不等式","authors":"Yongyang Jin, Shoufeng Shen","doi":"10.1017/S1446788721000100","DOIUrl":null,"url":null,"abstract":"Abstract In this paper we obtain some improved \n$L^p$\n -Hardy and \n$L^p$\n -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SOME \\n$\\\\boldsymbol {L^p}$\\n -HARDY AND \\n$\\\\boldsymbol {L^p}$\\n -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS\",\"authors\":\"Yongyang Jin, Shoufeng Shen\",\"doi\":\"10.1017/S1446788721000100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper we obtain some improved \\n$L^p$\\n -Hardy and \\n$L^p$\\n -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/S1446788721000100\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/S1446788721000100","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SOME
$\boldsymbol {L^p}$
-HARDY AND
$\boldsymbol {L^p}$
-RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS
Abstract In this paper we obtain some improved
$L^p$
-Hardy and
$L^p$
-Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.
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