Journal of Convex Analysis 12 (2005), No. 2, 351--364
Copyright Heldermann Verlag 2005
Exceptional Sets in Convex Domains
Piotr Kot
Instytut Matematyki, Politechnika Krakowska, ul. Warszawska 24, 31-155 Kraków, Poland
pkot@usk.pk.edu.pl
[Abstract-pdf]
Assume that $\Omega$ is a strongly convex domain, balanced with boundary of class $C^{1}$. Fix number $p \geq 1$. For any set $E$ which is circular and of type $G_{\delta}$ in $\partial\Omega$ we find a holomorphic function $f\in \mathbb{O}(\Omega)$ such that \[ E=E_{\Omega}^{p}(f)=\left\{ z\in \partial \Omega: \:\int_{|\lambda| <1} \left|f(\lambda z)\right|^{p}d\mathfrak{L}^{2}(\lambda)=\infty\right\} .\]
Keywords: Boundary behavior of holomorphic functions, exceptional sets, power series, computed tomography.
MSC: 30B30; 30E25
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