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.

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