{"title":"热核的非对角下限估计和荷尔德正则性","authors":"Alexander Grigor’yan, Eryan Hu, Jiaxin Hu","doi":"10.4310/ajm.2023.v27.n5.a3","DOIUrl":null,"url":null,"abstract":"We study the heat kernel of a regular symmetric Dirichlet form on a metric space with doubling measure, in particular, a connection between the properties of the jump measure and the long time behaviour of the heat kernel. Under appropriate optimal hypotheses, we obtain the Hölder regularity and lower estimates of the heat kernel.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Off-diagonal lower estimates and Hölder regularity of the heat kernel\",\"authors\":\"Alexander Grigor’yan, Eryan Hu, Jiaxin Hu\",\"doi\":\"10.4310/ajm.2023.v27.n5.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the heat kernel of a regular symmetric Dirichlet form on a metric space with doubling measure, in particular, a connection between the properties of the jump measure and the long time behaviour of the heat kernel. Under appropriate optimal hypotheses, we obtain the Hölder regularity and lower estimates of the heat kernel.\",\"PeriodicalId\":55452,\"journal\":{\"name\":\"Asian Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-07-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/ajm.2023.v27.n5.a3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ajm.2023.v27.n5.a3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Off-diagonal lower estimates and Hölder regularity of the heat kernel
We study the heat kernel of a regular symmetric Dirichlet form on a metric space with doubling measure, in particular, a connection between the properties of the jump measure and the long time behaviour of the heat kernel. Under appropriate optimal hypotheses, we obtain the Hölder regularity and lower estimates of the heat kernel.