On exact estimates of the order of approximation of functions of several\n variables in the anisotropic Lorentz-Zygmund space

2021/06/14 by Г. Акишев, Akishev, Gabdolla
Mathematics · #41A10 and 41A25 #42A05 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2106.07188

openalex publication_date 2021/06/14 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper we consider L_\p, α,\n\\τ^*( mathbbT^m) anisotropic Lorentz-Zyg -mu -nd space \n2\π of periodic functions of m variables and Nikol'skii--Besov's class\nS_\p, α, \\τ, \\θ ^rB.\nIn this paper, we establish order-sharp estimates of the best approximation by\ntrigonometric polynomials with harmonic numbers from the step hyperbolic cross\nof functions from the Nikol'skii - Besov class in the norm of the anisotropic\nLorentz-Zygmund space.\n

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