Wavelets and geometric structure for function spaces
type: Item
instance of: scholarly article
title: Wavelets and geometric structure for function spaces
zbMATH Open document ID: 1079.46026
publication date: 2004-11-25T00:00:00Z
review text: The dual spaces \(\dot{D}^{s,q}_ p\) of the homogeneous Triebel--Lizorkin spaces \(\dot{F}^{s,q}_ p\), \(s\in\mathbb R\), \(0<p\leq1\leq q\leq\infty\), are investigated. In this case, the structure of the dual spaces \(\dot{D}^{s,q}_ p\) is very different from that of Besov spaces or that of Triebel--Lizorkin spaces and cannot be analysed easily in the Littlewood--Paley analysis. The author characterizes the spaces \(\dot{D}^{s,q}_ p\), where \(s\in\mathbb R\), \(p=1\) and \(1\leq q\leq\infty\), in tent spaces with wavelets. Moreover, some inclusion relations between the spaces \(\dot{D}^{s,q}_ p\) and some relations between the spaces \(\dot{B}^{0,q}_1\), \(\dot{B}^{0,q}_1\) and \(L^1\) are studied.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 2119052
zbMATH Keywords: Triebel--Lizorkin spaces
zbMATH Keywords: dual spaces
zbMATH Keywords: wavelets
zbMATH Keywords: Besov spaces
author: Qixiang Yang
reviewed by: Petr Gurka
MaRDI profile type: Publication
full work available at URL: s10114-003-0290-2
OpenAlex ID: W2326254180
cites work: Q4129323
cites work: Q3336200
cites work: A boundedness criterion for generalized Calderón-Zygmund operators
cites work: Some new function spaces and their applications to harmonic analysis.
cites work: On the theory of harmonic functions of several variables
DOI: 10.1007/S10114-003-0290-2
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2119052