Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics
We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^Ω_{p,θ}(\mathbb{R}^d)$ by sums of de la Vallee Poussin type in the metrics space $L_{\infty}(\mathbb{R}^d)$ and $L_{1}(\mathbb{R}^d)$. These classes of functions for some given $Ω$ coincide with the well-known classical Nikol'skii-Besov isotropic classes.
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