Approximation of poisson integrals by repeated de la Vallée Poussin sums

We obtain asymptotic equalities for upper bounds of deviations of the repeated de la Vallee Poussin sums on classes of Poisson integrals. Under certain conditions, these equalities guarantee the solvability of the Kolmogorov-Nikol’skii problem for the repeated de la Vallee Poussin sums and classes of Poisson integrals. We indicate conditions under which the repeated de la Vallee Poussin sums guarantee a better order of approximation than ordinary de la Vallee Poussin sums.