P. Kot, Politechnika Krakowska, Instytut Matematyki, ul. Warszawska 24, 31-155 Krakow, Poland, e-mail: pkot@pk.edu.pl
Abstract: We solve the following Dirichlet problem on the bounded balanced domain $\Omega$ with some additional properties: For $p>0$ and a positive lower semi-continuous function $u$ on $\partial\Omega$ with $u(z)=u(\lambda z)$ for $|\lambda|=1$, $z\in\partial\Omega$ we construct a holomorphic function $f\in\Bbb O(\Omega)$ such that $u(z)=\int_{\Bbb Dz}|f|^pd \frak{L}_{\Bbb Dz}^2$ for $z\in\partial\Omega$, where $\Bbb D=\{\lambda\in\Bbb C |\lambda|<1\}$.
Keywords: boundary behavior of holomorphic functions, exceptional sets, boundary functions, Dirichlet problem, Radon inversion problem
Classification (MSC 2000): 30B30
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