Approximation of Classes of Analytic Functions by Fourier Sums in Uniform Metric

Abstract

We find asymptotic equalities for upper bounds of approximations by partial Fourier sums in the uniform metric on classes of Poisson integrals of periodic functions belonging to the unit balls in the spaces L p , 1 ≤ p ≤ ∞. We generalize the results obtained to the classes of (ψ, $${\bar \beta }$$ )-differentiable (in the sense of Stepanets) functions that admit an analytic extension to a fixed strip of the complex plane.