Nontangential and probabilistic boundary behavior of pluriharmonic functions

• 成果类型: Article
• 署名作者: Tanner, Steve
• 署名单位: Eastern Oregon University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000188
• 发表日期: 2006
• 页码: 1623-1634
• 关键词: harmonic-functions

摘要

Let u be a pluriharmonic function on the unit ball in C-n. I consider the relationship between the set of points L-u on the boundary of the ball at which u converges nontangentially and the set of points L-u at which u converges along conditioned Brownian paths. For harmonic functions u of two variables, the result L-u (a.e.)= L-u has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the L-u (a.e.)= result to pluriharmonic functions in arbitrary dimensions.