{"title":"拓扑Hausdorff维数与poincarcarr不等式","authors":"C. A. DiMarco","doi":"10.17398/2605-5686.37.2.211","DOIUrl":null,"url":null,"abstract":"A relationship between Poincaré inequalities and the topological Hausdorff dimension is exposed—a lower bound on the dimension of Ahlfors regular spaces satisfying a weak (1, p)-Poincaré inequality is given.","PeriodicalId":33668,"journal":{"name":"Extracta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological Hausdorff dimension and Poincaré inequality\",\"authors\":\"C. A. DiMarco\",\"doi\":\"10.17398/2605-5686.37.2.211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A relationship between Poincaré inequalities and the topological Hausdorff dimension is exposed—a lower bound on the dimension of Ahlfors regular spaces satisfying a weak (1, p)-Poincaré inequality is given.\",\"PeriodicalId\":33668,\"journal\":{\"name\":\"Extracta Mathematicae\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Extracta Mathematicae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17398/2605-5686.37.2.211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Extracta Mathematicae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17398/2605-5686.37.2.211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Topological Hausdorff dimension and Poincaré inequality
A relationship between Poincaré inequalities and the topological Hausdorff dimension is exposed—a lower bound on the dimension of Ahlfors regular spaces satisfying a weak (1, p)-Poincaré inequality is given.