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