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Keywords:
boundary behavior of holomorphic functions; exceptional sets; boundary functions; Dirichlet problem; Radon inversion problem
boundary behavior of holomorphic functions; exceptional sets; boundary functions; Dirichlet problem; Radon inversion problem
Summary:
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 $\Bbb D=\{\lambda \in \Bbb C\:|\lambda |<1\}$.
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