2018
Том 70
№ 9

# 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 ${L_p}\left( \Gamma \right)$.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 5, pp 758-773.

Citation Example: Savchuk M. V., Savchuk V. V. Summation of p-Faber series by the Abel–poisson method in the integral metric // Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 660–673.

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