Аннотация:In this paper we consider anisotropic Lorentz-Karamata space $2\pi$ of periodic functions of $m$ variables and Nikol'skii--Besov's class .
In this paper, we establish order-sharp estimates of the best approximation by trigonometric polynomials with harmonic numbers from the step hyperbolic cross of functions from the Nikol'skii - Besov class in the norm of the anisotropic Lorentz-Karamata space.