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Moscow Mathematical Journal

Volume 14, Issue 3, July–September 2014  pp. 505–563.

Upper Bounds of Heat Kernels on Doubling Spaces

Authors:  A. Grigor'yan (1) and J. Hu (2)
Author institution:(1) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
(2) Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China


In this paper we give various equivalent characterizations of upper estimates of heat kernels of regular, conservative and local Dirichlet forms on doubling spaces, from both the analytic and probabilistic points of view. The first part of this paper uses purely analytic argument, while the second part focuses on the probabilistic aspects, where the exit time plays an important role.

2010 Mathematics Subject Classification. Primary: 47D07, Secondary: 28A80, 46E35.

Keywords: Dirichlet form, doubling measure, heat kernel, maximum principle, exit time.

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