Domains of finite type and holder continuity of the perron-bremermann function

Dan Coman

doi:10.1090/s0002-9939-97-04100-2

Domains of finite type and holder continuity of the perron-bremermann function

Dan Coman

Department of Mathematics

Research output: Contribution to journal › Article

4 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	3569-3574
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	125
Issue number	12
DOIs	https://doi.org/10.1090/s0002-9939-97-04100-2
State	Published - 1997

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/s0002-9939-97-04100-2

Fingerprint Dive into the research topics of 'Domains of finite type and holder continuity of the perron-bremermann function'. Together they form a unique fingerprint.

Cite this

Coman, D. (1997). Domains of finite type and holder continuity of the perron-bremermann function. Proceedings of the American Mathematical Society, 125(12), 3569-3574. https://doi.org/10.1090/s0002-9939-97-04100-2

@article{cbe545f8c9f74eff8afc2e6ba57a046a,

title = "Domains of finite type and holder continuity of the perron-bremermann function",

abstract = "Let Ω be a smoothly bounded domain in ℂ{\texttrademark} such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω at 0 in terms of the H{\"o}lder 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 H{\"o}lder continuous.",

author = "Dan Coman",

year = "1997",

doi = "10.1090/s0002-9939-97-04100-2",

language = "English (US)",

volume = "125",

pages = "3569--3574",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "12",

}

TY - JOUR

T1 - Domains of finite type and holder continuity of the perron-bremermann function

AU - Coman, Dan

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.

UR - http://www.scopus.com/inward/record.url?scp=33646751355&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646751355&partnerID=8YFLogxK

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 -