Two-sided heat kernel estimates for censored stable-like processes

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Kim, Panki; Song, Renming
• 署名单位: Seoul National University (SNU); Seoul National University (SNU); University of Washington; University of Washington Seattle; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0193-3
• 发表日期: 2010
• 页码: 361-399
• 关键词: dirichlet laplacians; fractional laplacian; ultracontractivity; bounds

摘要

In this paper, we study the precise behavior of the transition density functions of censored (resurrected) alpha-stable-like processes in C-1,C-1 open sets in R-d, where d >= 1 and alpha is an element of (1, 2). We first show that the semigroup of the censored alpha-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored alpha-stable-like processes in C-1,C-1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored alpha-stable-like processes in bounded C-1,C-1 open sets.