On the approximation by trigonometric polynomials in weighted Lorentz spaces

Abstract

We obtain estimates of structural characteristics of 2π-periodic functions by the best trigonometric approximations in weighted Lorentz spaces, and show that the order of generalized modulus of smoothness depends not only on the rate of the best approximation, but also on the metric of the spaces. In weighted Lorentz spaces L^ps, this influence is expressed not only in terms of the parameter p, but also in terms of the second parameter s.