Obtaining upper bounds of heat kernels from lower bounds | Zendy

Grigor′yan Alexander | Zendy; Hu Jiaxin | Zendy; Lau KaSing | Zendy

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Obtaining upper bounds of heat kernels from lower bounds

Author(s) -

Grigor′yan Alexander,

Hu Jiaxin,

Lau KaSing

Publication year - 2008

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.20215

Subject(s) - heat kernel , mathematics , upper and lower bounds , diagonal , dirichlet distribution , kernel (algebra) , dirichlet form , ball (mathematics) , measure (data warehouse) , metric (unit) , combinatorics , mathematical analysis , geometry , operations management , database , computer science , economics , boundary value problem

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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