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dc.contributor.authorAkishev, G.en
dc.identifier.citationAkishev G. Eestimates of Best Approximations of Functions with Logarithmic Smoothness in the Lorentz Space with Anisotropic Norm / G. Akishev. — DOI 10.15826/umj.2020.1.002. — Text : electronic // Ural Mathematical Journal. — 2020. — Volume 6. — № 1. — P. 16-29.en
dc.description.abstractIn this paper, we consider the anisotropic Lorentz space L∗p¯,θ¯(Im) of periodic functions of m variables. The Besov space B(0,α,τ)p¯,θ¯ of functions with logarithmic smoothness is defined. The aim of the paper is to find an exact order of the best approximation of functions from the class B(0,α,τ)p¯,θ¯ by trigonometric polynomials under different relations between the parameters p¯,θ¯, and τ. The paper consists of an introduction and two sections. In the first section, we establish a sufficient condition for a function f∈L∗p¯,θ¯(1)(Im) to belong to the space L∗p¯,θ(2)(Im) in the case 1<θ2<θ(1)j,$$j=1,…,m, in terms of the best approximation and prove its unimprovability on the class Eλp¯,θ¯={f∈L∗p¯,θ¯(Im):En(f)p¯,θ¯≤λn, n=0,1,…}, where En(f)p¯,θ¯ is the best approximation of the function f∈L∗p¯,θ¯(Im) by trigonometric polynomials of order n in each variable xj, j=1,…,m, and λ={λn} is a sequence of positive numbers λn↓0 as n→+∞. In the second section, we establish order-exact estimates for the best approximation of functions from the class B(0,α,τ)p¯,θ¯(1) in the space L∗p¯,θ(2)(Im).en
dc.description.sponsorshipThis work was supported by the Competitiveness Enhancement Program of the Ural Federal University (Enactment of the Government of the Russian Federation of March 16, 2013 no. 211, agreement no. 02.A03.21.0006 of August 27, 2013).en
dc.publisherN.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciencesen
dc.publisherUral Federal University named after the first President of Russia B.N. Yeltsinen
dc.relation.ispartofUral Mathematical Journal. 2020. Volume 6. № 1en
dc.rightsCreative Commons Attribution Licenseen
dc.subjectLORENTZ SPACEen
dc.titleEestimates of Best Approximations of Functions with Logarithmic Smoothness in the Lorentz Space with Anisotropic Normen
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