Average Widths and Optimal Recovery of Multivariate Besov Classes in Orlicz Spaces

Abstract

In this paper, we study the average Kolmogorov σ–widths and the average linear σ–widths of multivariate isotropic and anisotropic Besov classes in Orlicz spaces and give the weak asymptotic estimates of these two widths. At the same time, we also give the asymptotic property of the optimal recovery of isotropic Besov classes in Orlicz spaces.