Abstract
Order of the trigonometric widths of the Nikol'skii-Besov classes with mixed metric in the metric of anisotropic Lorentz spacesIn this paper we estimate the order of the triginometric width of the Nikol'skii-Besov classes B ατ p (T n ) with mixed metric in the anisotropic Lorentz space L qθ (T n ) when 1<p= (p1, . . .,pn) < 2 < q= (q1, . . .,qn).The concept of a trigonometric width in the one-dimensional case was first introduce by R.S. Ismagilov and he established his estimates for certain classes in the space of continuous functions.For a function of several variables exact orders of trigonometric width of Sobolev class W r p , Nikol'skii class H r p in the space Lq are established by E.S. Belinsky, V.E.Majorov, Yu.Makovoz, G.G. Magaril-Ilyaev, V.N.Temlyakov.This problem for the Besov class B r pq was investigated by A.S. Romanyuk, D.B. Bazarkhanov.The trigonometric width for the anisotropic Nikol'skii-Besov classes B ατ pr (T n ) in the metric of the anisotropic Lorentz spaces L qθ (T n ) was found by K.A. Bekmaganbetov and Ye.Toleugazy.