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 L2,τ(Tm), the class of functions with bounded mixed fractional derivative Wr2,τ, 1 ≤ τ < ∞, and the order of the best M-term approximation of a function f ∈ Lp,τ(Tm) 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 Wr2,τ1 in the norm of the space Lp,τ2(Tm) for various relations between the parameters p,τ1,τ2.

Keywords

• Lorentz space
• Sobolev class
• mixed derivative
• trigonometric polynomial
• M-term approximation