Optimal cubature formulas for Morrey type function classes on multidimensional torus

Sh. A. Balgimbayeva ; D. B. Bazarkhanov

Eurasian mathematical journal, Tome 15 (2024) no. 3, pp. 25-37

Résumé

In the paper, we establish estimates, sharp in order, for the error of optimal cubature formulas for the smoothness spaces $B_{pq}^{s\tau}(\mathbb{T}^m)$ of Nikol'skii–Besov type and $F_{pq}^{s\tau}(\mathbb{T}^m)$ of Lizorkin–Triebel type, both related to Morrey spaces, on multidimensional torus, for some range of the parameters $s, p, q, \tau$ ($0$, $1\leqslant p$, $q\leqslant\infty$, $0\leqslant\tau\leqslant1/p$). In particular, we obtain those estimates for the isotropic Lizorkin–Triebel function spaces $F^s_{\infty q}(\mathbb{T}^m)$ .