The ortho-diameters of Nikol'skii and Besov classes in the Lorentz spaces
type: Item
instance of: scholarly article
title: The ortho-diameters of Nikol'skii and Besov classes in the Lorentz spaces
zbMATH Open document ID: 1189.46019
DOI: 10.3103/S1066369X09020029
author: G. Akishev
published in: Russian Mathematics
publication date: 2009-10-26T00:00:00Z
review text: \textit{V.\,N.\thinspace Temlyakov} has introduced the notion of the ortho-diameter of functional classes and he has obtained estimates for ortho-diameters of Sobolev and Nikol'skii classes in Lebesgue spaces [Sov.\ Phys.\ Dokl.\ 267, 314--317 (1982; Zbl 0524.41013); ``Approximation of functions with bounded mixed derivative'' (Trudy Matematicheskogo Instituta im.\ V.\ A.\ Steklova 178; Moskva:\ ``Nauka'') (1986; Zbl 0625.41028)]. This research has been developed in [\textit{D.\,Zung}, Math.\ USSR, Sb.\ 59, 247--267 (1988); translation from Mat.\ Sb., Nov.\ Ser.\ 131(173), No.\,2(10), 251--271 (1986; Zbl 0634.42005)], \textit{E.\,M.\thinspace Galeev} [Math.\ Notes 43, No.\,2, 110--118 (1988); translation from Mat.\ Zametki 43, No.\,2, 197--211 (1988; Zbl 0659.42008)] and \textit{N.\,N.\thinspace Pustovoitov} [Izv.\ Math.\ 64, No.\,1, 121--141 (2000); translation from Izv.\ Ross.\ Akad.\ Nauk, Ser.\,Mat.\ 64, No.\,1, 123--144 (2000; Zbl 1007.42004)]. The aim of the paper under review is to estimate the ortho-diameters of Nikol'skij and Besov classes in norms of anisotropic Lorentz spaces.
reviewed by: Bohumír Opic
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 5621403
zbMATH Keywords: approximation
zbMATH Keywords: anisotropic Lorentz space
zbMATH Keywords: ortho-diameter
zbMATH Keywords: Nikol'skii classes
MaRDI profile type: Publication
cites work: Multivariate Rearrangements and Banach Function Spaces with Mixed Norms
cites work: Q3027578
cites work: Q3808629
cites work: Q5385247
cites work: Nikol'skij inequalities for trigonometric polynomials in Lorentz spaces
description: scientific article; zbMATH DE number 5621403