Approximation of differentiable functions by rectangular repeated de la Vallee Poussin means

The study is devoted to the approximation by arithmetic means of Fourier sums of classes of periodic functions of high smoothness. In some cases, asymptotic equalities are found for upper bounds of deviations in the uniform metric of repeated de la Vallee Poussin sums on classes of periodic functions of two variables generated by multipliers and shifts on the argument, provided that the sequences that define the specified classes tend to zero at the rate of a geometric progression. In one-dimensional case these classes consist of analytic functions which can be regularly extended in the corresponding strip of complex plane and called the classes of Poisson integrals.