Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II

Abstract

In normed spaces of functions analytic in the Jordan domain Ω⊂ℂ, we establish exact order estimates for the Kolmogorov widths of classes of functions that can be represented in Ω by Cauchy-type integrals along Γ = ∂Ω with densities f(·) such that $f \circ \Psi \in L_{\beta ,p}^\Psi (T)$ . Here, Ψ is a conformal mapping of $C\backslash \overline \Omega$ onto {w: |w| > 1}, and $L_{\beta ,p}^\Psi (T)$ is a certain subset of infinitely differentiable functions on T = {w: |w| = 1}.