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VOL. 44 | 2006 On the sharpness of certain approach regions
Fausto Di Biase

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki


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.


Published: 1 January 2006
First available in Project Euclid: 16 December 2018

zbMATH: 1127.31001
MathSciNet: MR2277827

Digital Object Identifier: 10.2969/aspm/04410117

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


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