ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS

被引：36

作者：

Grigor'yan, Alexander ^{[1
]}

Hu, Jiaxin ^{[2
,3
]}

Lau, Ka-Sing ^{[4
]}

机构：

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

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

[3] Tsinghua Univ, Ctr Math Sci, Beijing 100084, Peoples R China

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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 366卷 / 12期

关键词：

Heat kernel; non-local Dirichlet form; effective resistance; SYMMETRIC JUMP-PROCESSES; METRIC MEASURE-SPACES; BROWNIAN-MOTION; UPPER-BOUNDS; HARMONIC-ANALYSIS; RESISTANCE FORMS; FRACTALS; GRAPHS; INEQUALITIES; MANIFOLDS;

D O I：

10.1090/S0002-9947-2014-06034-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we present new heat kernel upper bounds for a certain class of non-local regular Dirichlet forms on metric measure spaces, including fractal spaces. We use a new purely analytic method where one of the main tools is the parabolic maximum principle. We deduce an off-diagonal upper bound of the heat kernel from the on-diagonal one under the volume regularity hypothesis, restriction of the jump kernel and the survival hypothesis. As an application, we obtain two-sided estimates of heat kernels for non-local regular Dirichlet forms with finite effective resistance, including settings with the walk dimension greater than 2.

引用

页码：6397 / 6441

页数：45

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