Harmonic functions having no tangential limits
Author:
Hiroaki Aikawa
Journal:
Proc. Amer. Math. Soc. 108 (1990), 457-464
MSC:
Primary 31A20; Secondary 30D40, 30D55
DOI:
https://doi.org/10.1090/S0002-9939-1990-0990410-X
MathSciNet review:
990410
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a tangential curve in
which ends at 1 and let
be its rotation about the origin through an angle
. We construct a bounded harmonic function in
which fails to have limits along
for all
.
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- [2] E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
- [3] J. E. Littlewood, On a theorem of Fatou, J. London Math. Soc. 2 (1927), 172-176.
- [4] A. J. Lohwater and G. Piranian, The boundary behavior of functions analytic in a disk, Ann. Acad. Sci. Fenn. Ser. A. I. 1957 (1957), no. 239, 17. MR 91342
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1990-0990410-X
Keywords:
Fatou theorem,
harmonic functions,
tangential limits
Article copyright:
© Copyright 1990
American Mathematical Society