Characteristics of the linear and nonlinear approximations of the Nikol’skii-Besov-type classes of periodic functions of several variables

Abstract

Estimates that are accurate by order of magnitude have been obtained for some characteristics of the linear and nonlinear approximations of the isotropic classes of the Nikol'skii--Besov-type \textit{$\mathbf{B}% ^{\,\omega}_{p,\theta}$} of periodic functions of several variables in the spaces $B_{q,1}, 1 \leq q \leq \infty$. A specific feature of those spaces, as linear subspaces of $L_q$, is that the norm in them is ``stronger'' than the $L_q$-norm.