Approximate properties of Abel-Poisson integrals on classes of differentiable functions defined by moduli of continuity

Abstract

The paper deals with the problem of approximation in the uniform metric of $W^{1}H_{\omega}$ classes using one of the classical linear summation methods for Fourier series given by a set of functions of a natural argument, namely, using the Abel-Poisson integral. At the same time, emphasis is placed on the study of the asymptotic behavior of the exact upper limits of the deviations of the Abel-Poisson integrals from the functions of the mentioned class.

Keywords

• modulus of continuity
• abel-poisson integral
• uniform metric