Order of the trigonometric widths of the Nikol’skii-Besov classes with mixed metric in the metric of anisotropic Lorentz spaces - Bekmaganbetov, K.A.; Kervenev, K.Ye.; Toleugazy, Ye. (Bulletin of the Karaganda University. Mathematics Series, 2020)
In this paper we estimate the order of the triginometric width of the Nikol’skii–Besov classes Bατp(Tn) with mixed metric in the anisotropic Lorentz space Lqθ(Tn) 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 Wrp, Nikol’skii class Hrp 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 Brpq was investigated by A.S. Romanyuk, D.B. Bazarkhanov. The trigonometric width for the anisotropic Nikol’skii-Besov classes Bατpr(Tn) in the metric of the anisotropic Lorentz spaces Lqθ(Tn) was found by K.A. Bekmaganbetov and Ye. Toleugazy.