Obtaining upper bounds of heat kernels from lower bounds |
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| Authors: | Alexander Grigor′yan Jiaxin Hu Ka‐Sing Lau |
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| Institution: | 1. Universit?t Bielefeld, Fakult?t f?r Mathematik, 33507 Bielefeld, Germany;2. Tsinghua University, Department of Mathematical Sciences, 100084 Beijing, People's Rep of China;3. Chinese University of Hong Kong, Department of Mathematics, Shatin, N.T., Hong Kong |
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| Abstract: | We show that a near‐diagonal lower bound of the heat kernel of a Dirichlet form on a metric measure space with a regular measure implies an on‐diagonal upper bound. If in addition the Dirichlet form is local and regular, then we obtain a full off‐diagonal upper bound of the heat kernel provided the Dirichlet heat kernel on any ball satisfies a near‐diagonal lower estimate. This reveals a new phenomenon in the relationship between the lower and upper bounds of the heat kernel. © 2007 Wiley Periodicals, Inc. |
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