Estimates of the deviations of partial Fourier sums on classes of continuous periodic functions of several variables

The author studies the magnitudes of the suprema of the deviations of rectangular Fourier sums on classes of continuous periodic functions determined by arbitrary partial moduli of continuity. Order precise upper estimates for these magnitudes are found, and in the case where the moduli of continuity are convex asymptotic equalities are obtained that are full analogues of the corresponding one-dimensional equalities of A. N. Kolmogorov and S. M. Nikol'skii.
Bibliography: 12 titles.