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

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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 languageEnglish (US)
Pages (from-to)3569-3574
Number of pages6
JournalProceedings of the American Mathematical Society
Volume125
Issue number12
DOIs
StatePublished - 1997

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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