Ukrainian Mathematical Journal

, Volume 62, Issue 5, pp 758–773 | Cite as

Summation of p-Faber series by the Abel–poisson method in the integral metric

  • V.V. Savchuk
  • M.V. Savchuk

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


Hardy Space Connected Domain Subharmonic Function Laurent Expansion Regular Curve 
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© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • V.V. Savchuk
    • 1
  • M.V. Savchuk
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.Institute for the Public Employment Service Personnel TrainingKyivUkraine

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