Trigonometric diameters of the Sobolev classes \(W^ r_ p\) in the space \(L_ q\)
type: Item
instance of: scholarly article
title: Trigonometric diameters of the Sobolev classes \(W^ r_ p\) in the space \(L_ q\)
zbMATH Open document ID: 0623.41024
DOI: 10.1007/BF01159113
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The estimates for the trigonometric n-diameters of the Sobolev class \(W^ r_ p\) (a subclass of \(L_ p\)-space, the rth derivative of whose elements also belongs to \(L_ p\) and has \(L_ p\)-norm \(\leq 1)\) in the space \(L_ q\) are given. Various results are obtained and, in particular, it is shown that with suitable restrictions on parameters p, q and r, the trigonometric diameter is order equivalent to the Kolmogorov diameter and the linear trigonometric diameter is order equivalent to the linear diameter.
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 42A05
zbMATH DE Number: 4011120
zbMATH Keywords: estimates
zbMATH Keywords: trigonometric n-diameters
zbMATH Keywords: Sobolev class
zbMATH Keywords: Kolmogorov diameter
author: Vitaly Maiorov
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
cites work: Q4115573
cites work: DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
cites work: Q5849047
cites work: Q5824439
description: scientific article; zbMATH DE number 4011120