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Czechoslovak Mathematical Journal

, Volume 59, Issue 2, pp 371–379 | Cite as

Boundary functions on a bounded balanced domain

  • Piotr Kot
Article
  • 41 Downloads

Abstract

We solve the following Dirichlet problem on the bounded balanced domain with some additional properties: For p > 0 and a positive lower semi-continuous function u on ∂Ω with u(z) = uz) for |λ| = 1, z ∈ ∂Ω we construct a holomorphic function f\( \mathbb{O} \)(Ω) such that \( u(z) = \int_{\mathbb{D}z} {|f|^p d\mathfrak{L}_{\mathbb{D}z}^2 } \) for z ∈ ∂Ω, where \( \mathbb{D} \)= {λ ∈ ℂ: |λ| < 1}.

Keywords

boundary behavior of holomorphic functions exceptional sets boundary functions Dirichlet problem Radon inversion problem 

MSC 2000

30B30 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.Instytut MatematykiPolitechnika KrakowskaKrakowPoland

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