On orders of $n$-term approximations of functions of many variables in the Lorentz space

G. A. Akishev

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 1, Tome 227 (2023), pp. 3-19.

Résumé

In this paper, we consider the anisotropic Lorentz space of $2\pi$-periodic functions of many variables and the Nikolsky–Besov class in this space. We obtain estimates for the best approximations along the hyperbolic cross and the best $M$-term approximations of functions of the Nikolsky—Besov class with respect to the norm of the anisotropic Lorentz space for various relations between the parameters of the class and the space.

Détail

Keywords: Lorentz space, trigonometric polynomial, best $M$-term approximation

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