On estimates of the best M–term approximations of functions of the class Wrq,τ in the Lorentz space
Myrzagaliyeva A.K. Akishev G.
2026SINUS Association
Carpathian Journal of Mathematics
2026#42Issue 147 - 63 pp.
The article considers the Lorentz space Lp,τ (Tm) of 2π–periodic functions with m variables and the Sobolev class [Formula Presented] in Lp,τ (Tm). The main goal of the article is to find the order of the best M–term trigonometric approximation eM (f)p,τ2 of the class [Formula Presented] for a number of relations between the parameters p, q, τ1, τ2 ∈ (1, ∞) and rj, j = 1, …, m, r = (r1, …, rm). The article establishes order-sharp estimates for the value [Formula Presented] in the cases [Formula Presented] and [Formula Presented] and 1< τ1 < ∞ or q = 2 and 2 < τ1 < ∞. The exact order of this value are obtained for p = q and τ2 = τ1 = τ, as well as the upper estimate for 1 < p < q < ∞.
Lorentz space , M-term approximation , mixed derivative , Sobolev class , trigonometric polynomial
Text of the article Перейти на текст статьи
Astana It University, Astana, Kazakhstan
Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan
Astana It University
Lomonosov Moscow State University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026