Approximation of functions from $B^\ell_{p,\theta}(G)$ by anisotropic averages

The article considers the approximation of functions from O. V. Besov's class $B^\ell_{p,\theta}(G)$ by anisotropic average functions. Proofs are given of the approximation theorem, the inverse theorem of approximation theory, and the saturation theorem associated with the choice of the averaging kernel.