On Lebesgue inequality of the Vallée-Poussin sums on classes ${C}^{\overline{\psi}}C$

Abstract

We consider the exact top limits of deviations Valle Poussin sums on classes of $ \overline {\psi} $-differentiable functions where the sequence $ \overline {\psi} = \left ({\psi}_1, {\psi}_2 \right) $ is a quasiconvex. These estimates are expressed in terms of best approximation $ \overline {\psi} $ - derivatives functions in terms of O.I. Stepanets'.