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October, 2015 Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces
Alexander GRIGOR'YAN, Jiaxin HU, Ka-Sing LAU
J. Math. Soc. Japan 67(4): 1485-1549 (October, 2015). DOI: 10.2969/jmsj/06741485

Abstract

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 Poincaré 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.

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Alexander GRIGOR'YAN. Jiaxin HU. Ka-Sing LAU. "Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces." J. Math. Soc. Japan 67 (4) 1485 - 1549, October, 2015. https://doi.org/10.2969/jmsj/06741485

Information

Published: October, 2015
First available in Project Euclid: 27 October 2015

zbMATH: 1331.35152
MathSciNet: MR3417504
Digital Object Identifier: 10.2969/jmsj/06741485

Subjects:
Primary: 35K08
Secondary: 28A80, 31B05, 35J08, 46E35, 47D07

Rights: Copyright © 2015 Mathematical Society of Japan

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Vol.67 • No. 4 • October, 2015
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