Approximation of functions of many variables from the generalized Nikol’skii–Besov classes in the uniform and integral metrics

We obtain the exact order estimates for approximation of the functions of many variables from the generalized Nikol’skii–Besov classes \({B}_{p,\theta }^{\Omega }\left({\mathbb{R}}^{d}\right)\) $B_{p,\theta }^{\mathrm{\Omega }}\left({\mathbb{R}}^d\right)$ by de la Vallée Poussin sums in the metrics of the spaces \({L}_{\infty }\left({\mathbb{R}}^{d}\right)\) $L_{\infty }\left({\mathbb{R}}^d\right)$ and \({L}_{1}\left({\mathbb{R}}^{d}\right)\) $L_1\left({\mathbb{R}}^d\right)$ . These classes of functions for some given Ω coincide with the well-known classical isotropic Nikol’skii–Besov classes.