Summation of <em class="EmphasisTypeItalic ">p</em>-Faber series by the Abel–poisson method in the integral metric

Abstract

We establish conditions on the boundary \( \Gamma \) of a bounded simply connected domain \( \Omega \subset \mathbb{C} \) under which the p-Faber series of an arbitrary function from the Smirnov space \( {E_p}\left( \Omega \right),1 \leqslant p < \infty \), can be summed by the Abel–Poisson method on the boundary of the domain up to the limit values of the function itself in the metric of the space \( {L_p}\left( \Gamma \right) \).