Comparison inequalities for heat semigroups and heat kernels on metric measure spaces

被引：27

作者：

Grigor'yan, Alexander ^{[2
]}

Hu, Jiaxin ^{[1
]}

Lau, Ka-Sing ^{[3
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[3] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 10期

关键词：

Dirichlet form; Heat semigroup; Heat kernel; Maximum principle; BROWNIAN-MOTION;

D O I：

10.1016/j.jfa.2010.07.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a certain inequality for a subsolution of the heat equation associated with a regular Dirichlet form. As a consequence of this inequality, we obtain various interesting comparison inequalities for heat semigroups and heat kernels, which can be used for obtaining pointwise estimates of heat kernels. As an example of application, we present a new method of deducing sub-Gaussian upper bounds of the heat kernel from on-diagonal bounds and tail estimates. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2613 / 2641

页数：29

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