Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
type: Item
instance of: scholarly article
title: Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
zbMATH Open document ID: 1023.46031
DOI: 10.1007/PL00001378
author: Petru Mironescu
author: Haïm Brezis
published in: Journal of Evolution Equations
publication date: 2003-11-05T00:00:00Z
review text: Let \(1\leq s \leq m \in\mathbb{N}\) and \(1<p< \infty\). Let \(f\) be a function on \(\mathbb{R}\) having bounded derivatives up to order \(m\). It is the main aim of this paper to prove that \(\psi \mapsto f(\psi)\) is well-defined and continuous as a map from \(W^s_p (\mathbb{R}^n) \cap W^1_{sp} (\mathbb{R}^n)\) into \(W^s_p (\mathbb{R}^n)\). In addition, the paper deals with compositions and products in spaces of type \(F^s_{pq} (\mathbb{R}^n)\) and \(F^s_{pq} (\mathbb{R}^n) \cap L_\infty (\mathbb{R}^n)\), complementing existing results of this type by Runst and Sickel.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1757480
zbMATH Keywords: function spaces
MaRDI profile type: Publication
full work available at URL: pl00001378
OpenAlex ID: W2034796522
description: scientific article; zbMATH DE number 1757480