Heat Kernels and Green Functions on Metric Measure Spaces
Authors:
- Alexander Grigor'YAnAGAlexander Grigor'YAn
- Jiaxin HuJHJiaxin Hu
- 1 June 2014
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 66 (3) , 641-699
Abstract
We prove that, in a setting of local Dirichlet forms on metric measure spaces, a two-sided sub-Gaussian estimate of the heat kernel is equivalent to the conjunction of the volume doubling property, the elliptic Harnack inequality, and a certain estimate of the capacity between concentric balls. The main technical tool is the equivalence between the capacity estimate and the estimate of a mean exit time in a ball that uses two-sided estimates of a Green function in a ball.Keywords
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