Asymptotic behavior of best approximations of classes of Poisson integrals of functions from HωHω

We find asymptotic formulas for the least upper bounds of approximation in the metric of the space CC by using a linear method Un∗ for classes of Poisson integrals of continuous 2π2π-periodic functions in the case where their moduli of continuity do not exceed fixed convex majorants. On the basis of these results, we obtain asymptotic formulas for the best uniform approximations by trigonometric polynomials and, under some restrictions, asymptotic formulas for Kolmogorov widths of these classes in the uniform metric.