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

Abstract

We find asymptotic equalities for upper bounds of approximations by Fourier partial sums in a uniform metric on classes of Poisson integrals of periodic functions belonging to unit balls of spaces $L_p,\quad 1 \leq p \leq \infty$. We generalize the results obtained to classes of $(\psi, \overline{\beta})$-differentiable functions (in the Stepanets sense) that admit analytical extension to a fixed strip of the complex plane.