On the best approximations and Kolmogorov widths of besov classes of periodic functions of many variables

Abstract

Order estimates are obtained for the best approximations of the classesB _{1, θ} ^r in the spaceL _q with 1<q<∞ and classesB _{∞, θ} ^r in a uniform metric. The behavior of Kolmogorov widths of the classesB _{p, θ} ^r ,1<p≤∞, in the metric of L_∞ is studied.