On orders of $n$-term approximations of functions of many variables in the Lorentz space

In this paper, we consider the anisotropic Lorentz space of $2\pi$-periodic functions of many variables and the Nikolsky–Besov class in this space. We obtain estimates for the best approximations along the hyperbolic cross and the best $M$-term approximations of functions of the Nikolsky—Besov class with respect to the norm of the anisotropic Lorentz space for various relations between the parameters of the class and the space.