On the best M-term approximations of functions from the Nikol'skii-Besov class in the Lorentz space

G. A. Akishev

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 1, pp. 7-26

Résumé

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 $\theta$.

Détail

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

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