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

Abstract

We establish asymptotic equalities for upper bounds of approximations by partial Fourier sums in the metrics of the spaces L p , 1 ≤ p ≤ ∞, on classes of Poisson integrals of periodic functions belonging to the unit ball of the space L 1. 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.