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Boundary functions on a bounded balanced domain

Authors:	Piotr Kot

Institution:	(1) Instytut Matematyki, Politechnika Krakowska, ul. Warszawska 24, 31-155 Krakow, Poland

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) = u(λ z) 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
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