G. Akishev. On estimates of linear widths for classes of multivariate functions in the Lorentz space ... P. 23-39

We consider spaces of periodic multivariate functions, namely, the Lorentz space $L_{p,\tau}(\mathbb{T}^{m})$ and the Nikol'skii—Besov space $S_{p, \tau, \theta}^{\bar{r}}B$, and study the order of linear widths of the class $S_{p, \tau, \theta}^{\bar{r}}B$. The paper consists of the introduction and two sections. The introduction gives definitions, the notation used in the paper, and brief information on previous results on the issue under consideration. The first section contains two well-known statements that are often used in the proof of the main results. In the second section, order-exact estimates are established for the linear widths of the Nikol'skii—Besov class $S_{p, \tau_{1}, \theta}^{\bar{r}}B$ in the norm of the space $L_{q,\tau_{2}}(\mathbb{T}^{m})$ for different ratios of the parameters $p$, $q$, $\tau_{1}$, $\tau_{2}$, and $\theta$.

Keywords: linear widths, Lorentz space, the Nikol'skii—Besov class

Received May 19, 2022

Revised October 27, 2022

Accepted October 31, 2022

Funding Agency: This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP08855579).

Gabdolla Akishev, Dr. Phys.-Math. Sci., Prof., Kazakhstan Branch, Lomonosov Moscow University, Astana, 100008 Republic Kazakhstan; Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: akishev_g@mail.ru

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Cite this article as: G. Akishev. On estimates of linear widths for classes of multivariate functions in the Lorentz space. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 4, pp. 23–39