Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 12 (2005), No. 2, 351--364Copyright 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 [ Fulltext-pdf  (427  KB)] for subscribers only.