Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces
Publication in refereed journal

香港中文大學研究人員

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摘要We give necessary and sufficient conditions for sub-Gaussian estimates of the heat kernel of a strongly local regular Dirichlet form on a metric measure space. The conditions for two-sided estimates are given in terms of the generalized capacity inequality and the Poincare inequality. The main difficulty lies in obtaining the elliptic Harnack inequality under these assumptions. The conditions for upper bound alone are given in terms of the generalized capacity inequality and the Faber-Krahn inequality.
著者Grigor'yan A, Hu JX, Lau KS
期刊名稱JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
出版年份2015
月份10
日期1
卷號67
期次4
出版社MATH SOC JAPAN
頁次1485 - 1549
國際標準期刊號0025-5645
語言英式英語
關鍵詞cutoff Sobolev inequality; generalized capacity; Harnack inequality; heat kernel; Poincare inequality
Web of Science 學科類別Mathematics

上次更新時間 2021-28-02 於 01:33