Abstract
In this survey, we describe joint work in collaboration with A. Stokolos, O. Svensson and T. Weiss. We consider the following question: How sharp is the Stolz approach region condition for the almost everywhere convergence of bounded harmonic functions? The issue was first settled in the rotation invariant case in the unit disc by Littlewood in 1927 and later examined, under less stringent conditions, by Aikawa in 1991. We show that our results are, in a precise sense, sharp.
Information
Published: 1 January 2006
First available in Project Euclid: 16 December 2018
zbMATH: 1127.31001
MathSciNet: MR2277827
Digital Object Identifier: 10.2969/aspm/04410117
Subjects:
Primary:
31A20
Secondary:
03E15
,
31B25
,
32A40
Keywords:
Almost everywhere convergence
,
boundary behaviour
,
Harmonic functions
,
Holomorphic functions
,
independence proofs
,
inner functions
,
Lebesgue points
,
nontangentially accessible domains
,
pseudoconvex domains
,
sharp approach regions
,
tangential approach
,
unit disc
Rights: Copyright © 2006 Mathematical Society of Japan
