Best approximation methods and widths for some classes of functions in Hq,ρ, 1 ≤ q ≤ ∞, 0 < ρ ≤ 1

Abstract

We compute the exact values of widths for various widths for the classes W_q,a^(r)(Φ, μ), μ ≥ 1, of analytic functions in the disk belonging to the Hardy space H_q, q ≥ 1, whose averaged moduli of continuity of the boundary values of the derivatives with respect to the argument f_a^(r), r ∈ N, are dominated by a given function Φ. For calculating the linear and Gelfand n-widths, we use best linear approximation for these functions.