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Comparison inequalities for heat semigroups and heat kernels on metric measure spaces |
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| Authors: | Alexander Grigor'yan Ka-Sing Lau |
| Institution: | a Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany b Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China c Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong |
| Abstract: | We prove a certain inequality for a subsolution of the heat equation associated with a regular Dirichlet form. As a consequence of this inequality, we obtain various interesting comparison inequalities for heat semigroups and heat kernels, which can be used for obtaining pointwise estimates of heat kernels. As an example of application, we present a new method of deducing sub-Gaussian upper bounds of the heat kernel from on-diagonal bounds and tail estimates. |
| Keywords: | Dirichlet form Heat semigroup Heat kernel Maximum principle |
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