BOUNDARY HARNACK PRINCIPLE FOR NONLOCAL OPERATORS ON METRIC MEASURE SPACES

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Wang, Jie-Ming
• 署名单位: University of Washington; University of Washington Seattle; Beijing Institute of Technology; Beijing Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1734
• 发表日期: 2025
• 页码: 1287-1330
• 关键词: green-function; MARKOV-PROCESSES; nonnegative solutions; harmonic-functions; potential-theory; INEQUALITY; BEHAVIOR; divergence; laplacian; domains

摘要

In this paper a necessary and sufficient condition is obtained for the scale invariant boundary Harnack principle (BHP in abbreviation) for a large class of Hunt processes on metric measure spaces that are in weak duality with another Hunt process. We then apply it to a class of discontinuous subordinate Brownian motions with Gaussian components in Wdfor which the L & eacute;vy density of the subordinators satisfies some mild comparability condition. We show that the scale invariant BHP holds for these subordinate Brownian motions in any Lipschitz domain that satisfies the interior cone condition with common angle 0 E (cos-1(1/root d), pi) but fails in any truncated circular cone with angle 0 <= cos-1(1/root d), a Lipschitz domain whose Lipschitz constant is larger than or equal to 1/root d-1.