ON ESTIMATES OF LINEAR WIDTHS FOR CLASSES OF MULTIVARIATE FUNCTIONS IN THE LORENTZ SPACE

Akishev G.
2022 Krasovskii Institute of Mathematics and Mechanics

Trudy Instituta Matematiki i Mekhaniki UrO RAN
2022 #28 Issue 4

We consider spaces of periodic multivariate functions, namely, the Lorentz space Lp,τ(T^m) and the Nikol’skii–Besov space S_p,τ,θ^r¯ B, and study the order of linear widths of the class S_p,τ,θ^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,τ^r¯_1,θB in the norm of the space Lq,τ₂(T^m) for different ratios of the parameters p, q, τ1, τ2, and θ.

linear widths , Lorentz space , the Nikol’skii–Besov class

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Lomonosov Moscow University, Kazakhstan Branch, Astana, 100008, Kazakhstan
Ural Federal University, Yekaterinburg, 620000, Russian Federation

Lomonosov Moscow University
Ural Federal University

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