Lebesgue-type inequalities for de la Vallee Poussin sums and their interpolation analogues on the sets $(\psi ,\bar{\beta })$-differentiable functions

Abstract

We obtain the estimates of steady rates of deviations of the de Vallée Poussin sums and interpolation analogues of sums of Vallée Poussin from the functions that belong to the space $C_{\bar{\beta }}^{\psi }{L}_s,1\le s\le \infty$ and are represented through the best approximations of $(\psi ,\bar{\beta })$-differentiable functions of this sort by trigonometric polynomials in the metric $L_s$

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