ON THE BEST M-TERM APPROXIMATIONS OF FUNCTIONS FROM THE NIKOL’SKII–BESOV CLASS IN THE LORENTZ SPACE

Akishev G.
2022 Krasovskii Institute of Mathematics and Mechanics

Trudy Instituta Matematiki i Mekhaniki UrO RAN
2022 #28 Issue 1 7 - 26 pp.

We consider spaces of periodic functions of many variables, specifically, the Lorentz space Lp,τ(T^m) and the Nikol’skii–Besov space S_p,τ,θ^r¯ B, and study the best M-term approximation of a function f ∈ Lp,τ(T^m) by trigonometric polynomials. Order-exact estimates for the best M-term approximations of functions from the Nikol’skii–Besov class S_p,τ^r¯_1,θB in the norm of the space Lq,τ₂(T^m) are derived for different relations between the parameters p, q, τ1, τ2, and θ.

Best M-term approximation , Lorentz space , Nikol’skii–Besov class , Trigonometric polynomial

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Lomonosov Moscow University, Nur–Sultan, 100008, Kazakhstan
Ural Federal University, Yekaterinburg, 620000, Russian Federation

Lomonosov Moscow University
Ural Federal University

10 лет помогаем публиковать статьи Международный издатель

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