Exceptional Sets in Convex Domains

Abstract

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\}.

Contact details are reproduced from the original publication and may be historical.

Instytut Matematyki, Politechnika Krakowska, ul. Warszawska 24, 31-155 Kraków, Poland

30B30; 30E25

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.