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

  • V. V. Savchuk
  • M. V. Savchuk Iн-т пiдготовки кадрiв держ. служби зайнятостi України, Київ

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 \( {L_p}\left( \Gamma \right) \).
Published
25.05.2010
How to Cite
SavchukV. V., and SavchukM. V. “Summation of <em class="EmphasisTypeItalic ">p</Em&gt;-Faber Series by the Abel–poisson Method in the Integral Metric”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 5, May 2010, pp. 660–673, https://umj.imath.kiev.ua/index.php/umj/article/view/2896.
Section
Research articles