Approximation of classes of analytic functions by Fourier sums in the metric of the space Lp

@article{Serdyuk2005ApproximationOC,
  title={Approximation of classes of analytic functions by Fourier sums in the metric of the space Lp},
  author={A. Serdyuk},
  journal={Ukrainian Mathematical Journal},
  year={2005},
  volume={57},
  pages={1635-1651}
}
  • A. Serdyuk
  • Published 2005
  • Mathematics
  • Ukrainian Mathematical Journal
AbstractWe establish asymptotic equalities for upper bounds of approximations by partial Fourier sums in the metrics of the spaces Lp, 1 ≤ p ≤ ∞, on classes of Poisson integrals of periodic functions belonging to the unit ball of the space L1. The results obtained are generalized to the classes of $$(\psi ,\bar \beta )$$ -differentiable (in the sense of Stepanets) functions that admit an analytic extension to a fixed strip of the complex plane. 
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