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}
}

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.