ON ESTIMATES OF M-TERM APPROXIMATIONS ON CLASSES OF FUNCTIONS WITH BOUNDED MIXED DERIVATIVE IN THE LORENTZ SPACE

Abstract

The paper considers spaces of periodic functions of several variables, namely, the Lorentz space Lq,τ(T m) , the class of functions with bounded mixed fractional derivative Wq,τr¯, 1 < q, τ< ∞, and studies the order of the best M-term approximation of a function f∈ Lp,τ(T m) by trigonometric polynomials. The article consists of the introduction, the main part, and the conclusion. In the introduction, we introduce basic concepts, definitions, and necessary statements for the proof of the main results. You can also find information about previous results on the topic. In the main part, we establish exact-order estimates for the best M-term approximations of functions of the class Wq,τ1r¯ in the norm of the space Lp,τ2(Tm) for various relations between the parameters p, q, τ1, τ2. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.