SHARP HEAT KERNEL ESTIMATES FOR RELATIVISTIC STABLE PROCESSES IN OPEN SETS

被引：48

作者：

Chen, Zhen-Qing ^{[1
]}

Kim, Panki ^{[2
]}

Song, Renming ^{[3
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

ANNALS OF PROBABILITY | 2012年 / 40卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Symmetric alpha-stable process; relativistic stable process; heat kernel; transition density; Green function; exit time; Levy system; parabolic Harnack inequality; BOUNDARY HARNACK PRINCIPLE; SYMMETRIC JUMP-PROCESSES; METRIC MEASURE-SPACES; GREEN-FUNCTIONS; FRACTIONAL LAPLACIAN; SCHRODINGER-OPERATORS; SUBORDINATE PROCESSES; STABILITY; DOMAINS; THEOREM;

D O I：

10.1214/10-AOP611

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators m - (m(2/alpha) - Delta)(alpha/2)] in C-1,C-1 open sets. Here m > 0 and alpha is an element of (0, 2). The estimates are uniform in m is an element of (0, M] for each fixed M > 0. Letting m down arrow 0, we recover the Dirichlet heat kernel estimates for Delta(alpha/2) := -(-Delta)(alpha/2) in C-1,C-1 open sets obtained in [14]. Sharp two-sided estimates are also obtained for Green functions of relativistic stable processes in bounded C-1,C-1 open sets.

引用

页码：213 / 244

页数：32

共 43 条

[1] Boundary Harnack principle for p-harmonic functions in smooth Euclidean domains [J].