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

 

Domains of finite type and Hölder continuity
of the Perron-Bremermann function


Author: Dan Coman
Journal: Proc. Amer. Math. Soc. 125 (1997), 3569-3574
MSC (1991): Primary 32F25, 32F05; Secondary 32F15
MathSciNet review: 1422857
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Abstract: Let $\Omega$ be a smoothly bounded domain in ${\mathbb C}^n$ such that $0\in\partial\Omega$. We give a bound for the type of $\partial\Omega$ at 0 in terms of the Hölder exponent of its Perron-Bremermann function with simple boundary data. We then use this to show that a smoothly bounded domain in ${\mathbb C}^2$ is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Hölder continuous boundary data is Hölder continuous.


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Additional Information

Dan Coman
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Address at time of publication: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: dan.coman@math.lsa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04100-2
PII: S 0002-9939(97)04100-2
Received by editor(s): July 1, 1996
Communicated by: Eric Bedford
Article copyright: © Copyright 1997 American Mathematical Society