Geodesic
Boundary functions on a bounded balanced domain
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 371-379 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\Bbb D=\{\lambda \in \Bbb C\:|\lambda |1\}$.
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 $\Bbb D=\{\lambda \in \Bbb C\:|\lambda |1\}$.
Classification : 30B30, 30D60
Keywords: boundary behavior of holomorphic functions; exceptional sets; boundary functions; Dirichlet problem; Radon inversion problem 
@article{CMJ_2009_59_2_a6,
     author = {Kot, Piotr},
     title = {Boundary functions on a bounded balanced domain},
     journal = {Czechoslovak Mathematical Journal},
     pages = {371--379},
     year = {2009},
     volume = {59},
     number = {2},
     mrnumber = {2532382},
     zbl = {1224.30005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_2_a6/}
}
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%T Boundary functions on a bounded balanced domain
%J Czechoslovak Mathematical Journal
%D 2009
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Kot, Piotr. Boundary functions on a bounded balanced domain. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 371-379. http://geodesic.mathdoc.fr/item/CMJ_2009_59_2_a6/