Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

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


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.