Estimates of the order of approximation of functions of several\n variables in the generalized Lorentz space

2021/05/31 by Г. Акишев, Gabdolla Akishev, Akishev, Gabdolla
Mathematics · #Differential Equations and Boundary Problems #Mathematical Approximation and Integration #math.CA

paper · pdf · doi:10.48550/arxiv.2105.14810

openalex publication_date 2021/05/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper we consider X( φ) anisotropic symmetric space \n2\π of periodic functions of m variables, in particular, the generalized\nLorentz space L_\\ψ,\\τ^*( mathbbT^m) and\nNikol'skii--Besov's class S_X(\\φ),\\θ ^rB. The\narticle proves an embedding theorem for the Nikol'skii - Besov class in the\ngeneralized Lorentz space and establishes an upper bound for the best\napproximations by trigonometric polynomials with harmonic numbers from the\nhyperbolic cross of functions from the class\nS_X(\\φ),\\θ ^rB.\n

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