On estimates of M-term approximations of the Sobolev class in the Lorentz space

Abstract

In the paper spaces of periodic functions of several variables were considered, namely the Lorentz space L_2,τ(T^m), the class of functions with bounded mixed fractional derivative W^r_2,τ, 1 ≤ τ < ∞, and the order of the best M-term approximation of a function f ∈ L_p,τ(T^m) by trigonometric polynomials was studied. The article consists of an introduction, a main part, and a conclusion. In the introduction, basic concepts, definitions and necessary statements for the proof of the main results were considered. One can be found information about previous results on the mentioned topic. In the main part, exact-order estimates are established for the best M-term approximations of functions of the Sobolev class W^r_2,τ1 in the norm of the space L_p,τ2(T^m) for various relations between the parameters p,τ₁,τ₂.