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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Harmonic functions having no tangential limits


Author: Hiroaki Aikawa
Journal: Proc. Amer. Math. Soc. 108 (1990), 457-464
MSC: Primary 31A20; Secondary 30D40, 30D55
MathSciNet review: 990410
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Abstract: Let $ {C_0}$ be a tangential curve in $ D = \left\{ {\vert z\vert < 1} \right\}$ which ends at 1 and let $ {C_\theta }$ be its rotation about the origin through an angle $ \theta $. We construct a bounded harmonic function in $ D$ which fails to have limits along $ {C_\theta }$ for all $ \theta ,0 \leq \theta \leq 2\pi $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0990410-X
PII: S 0002-9939(1990)0990410-X
Keywords: Fatou theorem, harmonic functions, tangential limits
Article copyright: © Copyright 1990 American Mathematical Society