Functional calculus in certainLizorkin-Triebel spaces
type: Item
instance of: scholarly article
title: Functional calculus in certainLizorkin-Triebel spaces
zbMATH Open document ID: 0817.46034
DOI: 10.1007/BF01193549
author: Gérard Bourdaud
published in: Archiv der Mathematik
publication date: 1995-07-17T00:00:00Z
review text: We prove that every real variable function \(G\) such that \(G(0)=0\) and \(G''\) is a bounded measure acts, via left composition, on the Lizorkin- Triebel space \(F_ p^{s,q} (\mathbb{R}^ n)\), for \(1<q< +\infty\), \(1<p <+\infty\) and \(1<s< 1+(1/p)\). More precisely, there exists a number \(C= C(G,n, s,p, q)>0\) such that \[ \| G\circ f \|_{F_ p^{s,q} (\mathbb{R}^ n)}\leq C\| f \|_{F_ p^{s,q} (\mathbb{R}^ n)}, \] for all real valued \(f\in F_ p^{s,q} (\mathbb{R}^ n)\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 734522
zbMATH Keywords: functional calculus
zbMATH Keywords: nonlinear operator
zbMATH Keywords: composition
zbMATH Keywords: Lizorkin-Triebel space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01193549
OpenAlex ID: W2127143776
description: scientific article; zbMATH DE number 734522