Estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions

الأصل · EN

We obtain order-exact estimates for uniform approximations by using Zygmund sums Zˢₙ of classes Cψᵦ,ₚ of 2π-periodic continuous functions f representable by convolutions of functions from unit balls of the space Lₚ, 1< p<∞, with a fixed kernels Ψβ∈ Lₚ', 1/p+1/p'=1. In addition, we find a set of allowed values of parameters (that define the class Cψᵦ,ₚ and the linear method Zˢₙ) for which Zygmund sums and Fejer sums realize the order of the best uniform approximations by trigonometric polynomials of those classes.