Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii–Besov spaces

We have obtained the exact-order estimates for some approximative characteristics of Sobolev classes $$ {\mathbbm{W}}_{p,\alpha}^r and Nikоl’skii–Besov {\mathbbm{B}}_{p,\theta}^r periodic functions one several variables in norm space B∞,1. Properties linear operators realizing orders best approximation {\mathbbm{B}}_{\infty, \theta}^r this by trigonometric polynomials generated a set harmonics with “numbers” from step hyperbolic crosses are investigated.