Uniform approximation of Poisson integrals of functions from the class H_omega by de la Vallee Poussin sums

Abstract

We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vallée Poussin sums on the sets C^{q}_βH_ωof Poisson integrals of functions from the class H_ωgenerated by convex upwards moduli of continuity ω(t) which satisfy the condition ω(t)/t\to\infty as t\to 0. As an implication, a solution of the Kolmogorov-Nikol'skii problem for de la Vallée Poussin sums on the sets of Poisson integrals of functions belonging to Lipschitz classes H^α, 0<α<1, is obtained

Cited by in corpus (2)

• Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric
• Lebesgue-type inequalities for de la Vallee Poussin sums on the sets of analytic and entire functions