SHARP HEAT KERNEL ESTIMATES FOR RELATIVISTIC STABLE PROCESSES IN OPEN SETS

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Kim, Panki; Song, Renming
• 署名单位: University of Washington; University of Washington Seattle; Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP611
• 发表日期: 2012
• 页码: 213-244
• 关键词: boundary harnack principle; symmetric jump-processes; metric measure-spaces; green-functions; fractional laplacian; SCHRODINGER-OPERATORS; subordinate processes; STABILITY; domains; THEOREM

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.