Functions which operate on Besov spaces
type: Item
instance of: scholarly article
title: Functions which operate on Besov spaces
zbMATH Open document ID: 0835.46026
DOI: 10.1007/BF01461010
author: D. Kateb
author: Gérard Bourdaud
published in: Mathematische Annalen
publication date: 1996-04-16T00:00:00Z
full work available at URL: https://eudml.org/doc/165386
review text: We determine a new class of real variable functions which act, via left composition, on the Besov space \(B^s_{p, q}(\mathbb{R}^n)\), for \(0< s< 1+ (1/p)\). \(F^{1+ (1/p)}_p\) is the set of functions \(F\) such that there exists a constant \(C> 0\) for which \[ \int_{\mathbb{R}} \Biggl(\sup_{|\rho|\leq \rho} |F'(x+ h)- F'(x)|\Biggr)^p dx\leq Ch, \] whatever be \(h> 0\). Every function \(F\in F^{1+ (1/p)}_p\) such that \(F(0)= 0\) and \(F'\in L^\infty\) acts on \(B^s_{p, q}(\mathbb{R}^n)\). The space \(F^{1+ (1/p)}_p\) includes the Besov spaces \(B^t_{p, q}(\mathbb{R})\), for \(t> 1+ (1/ p)\), and the function classes known as acting on \(B^s_{p, q}(\mathbb{R}^n)\) (works of Yves Meyer and the first author).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 840205
zbMATH Keywords: left composition
zbMATH Keywords: Besov space
MaRDI profile type: Publication
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OpenAlex ID: W2002649491
description: scientific article; zbMATH DE number 840205