{"title":"Hardy空间上的双层势算子","authors":"Y. Komori-Furuya","doi":"10.1007/s10476-023-0202-x","DOIUrl":null,"url":null,"abstract":"<div><p>Many studies have been done for one-dimensional Cauchy integral operator. We consider <i>n</i>-dimensional Cauchy integral operator for hypersurface, or we say, the double layer potential operator, and obtain the boundedness from <i>H</i><sup><i>p</i></sup>(<i>R</i><sup><i>n</i></sup>) to <i>h</i><sup><i>p</i></sup>(<i>R</i><sup><i>n</i></sup>) (local Hardy space). For the proof we introduce Clifford valued Hardy spaces.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Double Layer Potential Operator on Hardy Spaces\",\"authors\":\"Y. Komori-Furuya\",\"doi\":\"10.1007/s10476-023-0202-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Many studies have been done for one-dimensional Cauchy integral operator. We consider <i>n</i>-dimensional Cauchy integral operator for hypersurface, or we say, the double layer potential operator, and obtain the boundedness from <i>H</i><sup><i>p</i></sup>(<i>R</i><sup><i>n</i></sup>) to <i>h</i><sup><i>p</i></sup>(<i>R</i><sup><i>n</i></sup>) (local Hardy space). For the proof we introduce Clifford valued Hardy spaces.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-02-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-023-0202-x\",\"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://link.springer.com/article/10.1007/s10476-023-0202-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Double Layer Potential Operator on Hardy Spaces
Many studies have been done for one-dimensional Cauchy integral operator. We consider n-dimensional Cauchy integral operator for hypersurface, or we say, the double layer potential operator, and obtain the boundedness from Hp(Rn) to hp(Rn) (local Hardy space). For the proof we introduce Clifford valued Hardy spaces.
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