Holomorphic diffusions and boundary behavior of harmonic functions
成果类型：
Article
署名作者：
Chen, ZQ; Durrett, R; Ma, G
署名单位：
Cornell University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1997
页码：
1103-1134
关键词：
摘要：
We study a family of differential operators (L-alpha, alpha greater than or equal to 0) in the unit bah D of C-n with n greater than or equal to 2 that generalize the classical Laplacian, alpha = 0, and the conformal Laplacian, alpha = 1/2 (that is, the Laplace-Beltrami operator for Bergman metric in D). Using the diffusion processes associated with these (degenerate) differential operators, the boundary behavior of L-alpha-harmonic functions is studied in a unified way for 0 less than or equal to alpha less than or equal to 1/2. More specifically, we show that a bounded L-alpha-harmonic function in D has boundary limits in approaching regions at almost every boundary point and the boundary approaching region increases from the Stolz cone to the Koranyi admissible region as or runs from 0 to 1/2. A local version for this Fatou-type result is also established.