Relationships between the best approximations in different metrics
type: Item
instance of: scholarly article
title: Relationships between the best approximations in different metrics
zbMATH Open document ID: 0602.41029
DOI: 10.1007/BF01170249
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The following problem is solved: Let \(L_ p\) \((1\leq p<\infty)\) be a space of \(2\pi\)-periodical summable functions, \(\| f\|_ p=\{\int^{2\pi}_{0}| f(x)|^ p dx\}^{1/p}<\infty\) and let \(E_ n(f)_ p\) be a best approximation by trigonometric polynomials with order not exceeding n. For all \(\epsilon \in H=\{\{\epsilon_ n\}\); \(\epsilon_ n\searrow \emptyset \}\) denote \(L^*_ p(\epsilon)=\{f\in L_ pE_ n(f)_ p=O(\epsilon_ n)\}\). The author gives necessary and sufficient conditions for \(\epsilon\), \(\delta\in H\); \(1\leq p<q<\infty\) \(L^*_ p(\epsilon)\subset L^*_ q(\delta)\) to hold.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 42A10
zbMATH DE Number: 3971400
zbMATH Keywords: trigonometric polynomials
author: Viktor I. Kolyada
MaRDI profile type: Publication
cites work: Q4106622
cites work: Q3254471
full work available at URL: https://doi.org/10.1007/bf01170249
OpenAlex ID: W1978854240
description: scientific article; zbMATH DE number 3971400