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 BΩp,θ(Rᵈ) by sums of de la Vallee Poussin type in the metrics space L∞(Rᵈ) and L₁(Rᵈ). These classes of functions for some given Ω coincide with the well-known classical Nikol'skii-Besov isotropic classes.