On exact estimates of the order of approximation of functions of several variables in the anisotropic Lorentz--Zygmund space

In this paper we consider Lp̄, α, τ̄*(Tᵐ) anisotropic Lorentz-Zyg\-mu\-nd space 2π of periodic functions of m variables and Nikol'skii--Besov's class Sp̄, α, τ̄, θ̄ʳB. 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--Zygmund space.