Open Access
July 2006 Nontangential and probabilistic boundary behavior of pluriharmonic functions
Steve Tanner
Ann. Probab. 34(4): 1623-1634 (July 2006). DOI: 10.1214/009117906000000188


Let u be a pluriharmonic function on the unit ball in ℂn. I consider the relationship between the set of points Lu on the boundary of the ball at which u converges nontangentially and the set of points ℒu at which u converges along conditioned Brownian paths. For harmonic functions u of two variables, the result $L_{u}\stackrel{\mathrm{a.e.}}{=}\mathscr{L}_{u}$ has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the $L_{u}\stackrel{\mathrm{a.e.}}{=}\mathscr{L}_{u}$ result to pluriharmonic functions in arbitrary dimensions.


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Steve Tanner. "Nontangential and probabilistic boundary behavior of pluriharmonic functions." Ann. Probab. 34 (4) 1623 - 1634, July 2006.


Published: July 2006
First available in Project Euclid: 19 September 2006

zbMATH: 1116.60040
MathSciNet: MR2257659
Digital Object Identifier: 10.1214/009117906000000188

Primary: 32A40 , 60J45
Secondary: 60J65

Keywords: conditional process , hitting probability , Nontangential convergence , pluriharmonic function , potential

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 4 • July 2006
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