General gauge and conditional gauge theorems

• 成果类型: Article
• 署名作者: Chen, ZQ; Song, RM
• 署名单位: University of Washington; University of Washington Seattle; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 1313-1339
• 关键词: symmetric stable processes; intrinsic ultracontractivity; schrodinger operator; MARKOV-PROCESSES; elliptic-equations; brownian-motion; green-function; domains; perturbation; excursions

摘要

General gauge and conditional gauge theorems are established for a large class of (not necessarily symmetric) strong Markov processes, including Brownian motions with singular drifts and symmetric stable processes. Furthermore, new classes of functions are introduced under which the general gauge and conditional gauge theorems hold. These classes are larger than the classical Kato class when the process is Brownian motion in a bounded C domain.