Multidimensional analogues of direct and converse Jackson and Bernshtein theorems and their generalizations
type: Item
instance of: scholarly article
title: Multidimensional analogues of direct and converse Jackson and Bernshtein theorems and their generalizations
zbMATH Open document ID: 0958.41008
DOI: 10.1007/BF02676409
author: A. Khatamov
published in: Mathematical Notes
publication date: 2000-11-16T00:00:00Z
review text: For a bounded domain \(G\) in \(\mathbb R^n\) \((n\geq 2)\) with Lipschitz boundary and a relatively compact, open subset \(D\) of \(G\), the author proves the embeddings \(B^\alpha_{p,q}(G)\subset E^\alpha_{p,q}(G)\subset B^\alpha_{p,q}(D)\), where \(E^\alpha_{p,q}(G)\) is an approximation subspace of \(L_p(G)\) [see \textit{J. Bergh} and \textit{J. Löfstrom}, Interpolation spaces. An Introduction, Springer, Heidelberg (1976; Zbl 0344.46071)], \(1\leq p<\infty\) and \(0<q\leq\infty\).
reviewed by: Wiesław Pleśniak
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 1531338
zbMATH Keywords: Besov spaces
zbMATH Keywords: approximation spaces in \(L_p\)
zbMATH Keywords: Jackson, Bernstein and de la Vallée Pousin theorems
MaRDI profile type: Publication
cites work: Q4112938
cites work: Q3049291
cites work: Approximation of functions of several variables by polynomials with preservation of the differential-difference properties
cites work: Q3726684
full work available at URL: https://doi.org/10.1007/bf02676409
OpenAlex ID: W2061066139
description: scientific article; zbMATH DE number 1531338