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p-Radial Exceptional Sets and Conformal Mappings
Published online by Cambridge University Press: 20 November 2018
Abstract
For $p\,>\,0$ and for a given set $E$ of type ${{G}_{\delta }}$ in the boundary of the unit disc $\partial \mathbb{D}$ we construct a holomorphic function $f\,\in \,\mathbb{O}\left( \mathbb{D} \right)$ such that
In particular if a set $E$ has a measure equal to zero, then a function $f$ is constructed as integrable with power $p$ on the unit disc $\mathbb{D}$.
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- Copyright © Canadian Mathematical Society 2007