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 -