TY - JOUR
T1 - Domains of finite type and holder continuity of the perron-bremermann function
AU - Coman, Dan
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1997
Y1 - 1997
N2 - Let Ω be a smoothly bounded domain in ℂ™ such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω 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 ℂ2 is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Holder continuous boundary data is Hölder continuous.
AB - Let Ω be a smoothly bounded domain in ℂ™ such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω 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 ℂ2 is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Holder continuous boundary data is Hölder continuous.
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U2 - 10.1090/s0002-9939-97-04100-2
DO - 10.1090/s0002-9939-97-04100-2
M3 - Article
AN - SCOPUS:33646751355
VL - 125
SP - 3569
EP - 3574
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 12
ER -