OPTIMAL CUBATURE FORMULAS FOR MORREY TYPE FUNCTION CLASSES ON MULTIDIMENSIONAL TORUS

Balgimbayeva Sh.A. Bazarkhanov D.B.
2024 L.N. Gumilyov Eurasian National University

Eurasian Mathematical Journal
2024 #15 Issue 3 25 - 37 pp.

In the paper, we establish estimates, sharp in order, for the error of optimal cubature formulas for the smoothness spaces B^{s τ} _{p q} (T^m) of Nikolskii - Besov type and F s τ p q (T m) of Lizorkin -Triebel type, both related to Morrey spaces, on multidimensional torus, for some range of the parameters s, p, q, τ (0 < s < ∞, 1 ≤ p, q ≤ ∞, 0 ≤ τ ≤ 1/p). In particular, we obtain those estimates for the isotropic Lizorkin -Triebel function spaces F ^s_{∞ q} (T^m).

multidi-mensional torus , Nikolskii-Besov/Lizorkin-Triebel smoothness spaces related to Morrey space , optimal cubature formula

Text of the article Перейти на текст статьи

Department of Function Theory and Functional Analysis, Institute of Mathematics and Mathematical Modelling, 28 Shevchenko St, Almaty, 050010, Kazakhstan

Department of Function Theory and Functional Analysis

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026