Summation of p-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 ${L_p}\left( \Gamma \right)$