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Exceptional Sets in Hartogs Domains
Published online by Cambridge University Press: 20 November 2018
Abstract
Assume that $\Omega$ is a Hartogs domain in ${{\mathbb{C}}^{1+n}}$, defined as $\Omega =\left\{ \left( z,w \right)\,\in \,{{\mathbb{C}}^{1+n}}\,:\left| z \right|\,<\,\mu \left( w \right),w\,\in H \right\}$, where $H$ is an open set in ${{\mathbb{C}}^{n}}$ and $\mu$ is a continuous function with positive values in $H$ such that –ln $\mu$ is a strongly plurisubharmonic function in $H$. Let ${{\Omega }_{w}}=\Omega \cap \left( \mathbb{C}\times \left\{ w \right\} \right)$. For a given set $E$ contained in $H$ of the type ${{G}_{\delta }}$ we construct a holomorphic function $f\in \mathbb{O}\left( \Omega \right)$ such that
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- Copyright © Canadian Mathematical Society 2005
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