Optimal cubature formulas for Morrey type function classes on multidimensional torus
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Nikol'skii–Besov/Lizorkin–Triebel smoothness spaces related to Morrey space, multidimensional torus, optimal cubature formulaAbstract
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 \( F^s_{\infty, q}(\mathbb{T}^m) \).
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Published
2024-11-17
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Balgimbayeva, S., & Bazarkhanov, D. (2024). Optimal cubature formulas for Morrey type function classes on multidimensional torus. Eurasian Mathematical Journal, 15(3), 25–37. Retrieved from https://emj.enu.kz/index.php/main/article/view/413
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