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Obtaining upper bounds of heat kernels from lower bounds

✍ Scribed by Alexander Grigor′yan; Jiaxin Hu; Ka-Sing Lau

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
188 KB
Volume
61
Category
Article
ISSN
0010-3640

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✦ Synopsis

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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