Approximation of $\overline \psi$-Integrals of Periodic Functions by de la Vallée-Poussin Sums (Low Smoothness)

Abstract

We investigate the asymptotic behavior of the upper bounds of deviations of linear means of Fourier series from the classes $C_{\infty} ^{\psi}$. In particular, we obtain asymptotic equalities that give a solution of the Kolmogorov – Nikol'skii problem for the de la Vallée-Poussin sums on the classes $C_{\infty} ^{\psi}$.