An admissibility for topological degree of Herz-type Besov and Triebel-Lizorkin spaces
type: Item
instance of: scholarly article
title: An admissibility for topological degree of Herz-type Besov and Triebel-Lizorkin spaces
zbMATH Open document ID: 1200.46032
DOI: 10.12775/TMNA.2009.022
published in: Topological Methods in Nonlinear Analysis
publication date: 2009-11-27T00:00:00Z
review text: A quasi-normed space \(X\) is called admissible if, for every compact subset \(E \subset X\) and for every \(\varepsilon > 0\), there exists a continuous map \(T:\,E \to X\) such that \(T(E)\) is contained in a finite dimensional subset of \(X\) and \(x \in E\) implies that \(\|Tx-x\|_X \leqslant \varepsilon\). In this paper, the author shows that the Herz spaces, the Herz type Besov spaces and the Herz-type Triebel-Lizorkin spaces are admissible.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 42B15
zbMATH DE Number: 5639938
zbMATH Keywords: Herz space
zbMATH Keywords: Besov space
zbMATH Keywords: Triebel-Lizorkin space
zbMATH Keywords: admissibility
zbMATH Keywords: maximal function
author: Jingshi Xu
reviewed by: Dachun Yang
MaRDI profile type: Publication
full work available at URL: tmna.2009.022
OpenAlex ID: W2474684015
description: scientific article; zbMATH DE number 5639938