G. Akishev. On the best M-term approximations of functions from the Nikol’skii–Besov class in the Lorentz space ... P. 7-26

We consider spaces of periodic functions of many variables, specifically, 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 best $M$-term approximation of a function $f\in L_{p,\tau}(\mathbb{T}^{m})$ by trigonometric polynomials. Order-exact estimates for the best $M$-term approximations of functions from the Nikol'skii-Besov class $S_{p, \tau_{1}, \theta}^{\bar{r}}B$ in the norm of the space $L_{q,\tau_{2}}(\mathbb{T}^{m})$ are derived for different relations between the parameters $p$, $q$, $\tau_{1}$, $\tau_{2}$, and $\theta$.

Keywords: Lorentz space, Nikol'skii-Besov class, trigonometric polynomial, best $M$-term approximation

Received August 24, 2021

Revised October 14, 2021

Accepted October 18, 2021

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, Nur–Sultan, 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 the best M-term approximations of functions from the Nikol’skii–Besov class in the Lorentz space, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 1, pp. 7–26.