Nontangential and probabilistic boundary behavior of pluriharmonic functions
概率论
2007-05-23 v2 复变函数
摘要
Let be a pluriharmonic function on the unit ball in . I consider the relationship between the set of points on the boundary of the ball at which converges nontangentially and the set of points at which converges along conditioned Brownian paths. For harmonic functions of two variables, the result has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the result to pluriharmonic functions in arbitrary dimensions.
引用
@article{arxiv.math/0511368,
title = {Nontangential and probabilistic boundary behavior of pluriharmonic functions},
author = {Steve Tanner},
journal= {arXiv preprint arXiv:math/0511368},
year = {2007}
}
备注
Published at http://dx.doi.org/10.1214/009117906000000188 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)