Abstract
We establish the main theorems on polynomial approximation with respect to multiplicative systems in the Morrey space and estimate the best approximations and the moduli of smoothness of functions in terms of the growth of the generalized derivatives of their best approximation polynomials, Fourier sums, and Riesz–Zygmund means with respect to multiplicative systems. Also, we provide some criteria for a function to belong to the classes with prescribed majorants for the modulus of smoothness or best approximation in the Morrey space.
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Acknowledgment
The author is grateful to the referee whose remarks helped improve exposition.
Funding
The author was supported by the Ministry of Science and Higher Education of the Russian Federation (Project FWNF–2020–0006).
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 1, pp. 40–55. https://doi.org/10.33048/smzh.2023.64.104
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Volosivets, S.S. Polynomial Approximation with Respect to Multiplicative Systems in the Morrey Space. Sib Math J 64, 33–47 (2023). https://doi.org/10.1134/S0037446623010044
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DOI: https://doi.org/10.1134/S0037446623010044
Keywords
- Morrey space
- multiplicative system
- \( K \)-functional
- generalized derivative
- direct and inverse approximation theorems