Approximation of classes of periodic functions of several variables

Abstract

We study classes of periodic functions of several variables with bounded generalized derivative in the metric of the space Lp. We obtain order estimates of deviations of Fourier sums, which are constructed depending on the behavior of functions that define the operator of generalized differentiation. We find estimates of the Kolmogorov widths, which are realized by the Fourier sums that are constructed.