Superposition operators and functions of bounded \(p\)-variation
type: Item
instance of: scholarly article
title: Superposition operators and functions of bounded \(p\)-variation
zbMATH Open document ID: 1134.46015
DOI: 10.4171/RMI/463
author: Gérard Bourdaud
author: Massimo Lanza de Cristoforis
author: Winfried Sickel
published in: Revista Matemática Iberoamericana
publication date: 2007-05-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/116187134
full work available at URL: https://eudml.org/doc/41980
review text: An exhaustive standard reference on properties and applications of Nemytskii operators in Sobolev and related spaces is the well-known monograph by \textit{Th. Runst} and the third author [``Sobolev spaces of fractional order, Nemytskii operators and nonlinear partial differential equations''. Berlin: de Gruyter (1996; Zbl 0873.35001)]. On the other hand, apart from some degeneracy results, not much is known about Nemytskii operators in spaces of functions of bounded variation. In the present paper, the authors provide a thorough study of Nemytskii operators in the space \(\text{BV}^1_p(\mathbb R)\) of Lipschitz continuous functions whose first distributional derivatives belong to \(\text{BV}_p(\mathbb R)\) \((1\leq p\leq\infty)\). This is related to boundedness properties of Nemytskii operators in the Besov space \(B^s_{p,q}(\mathbb R)\) which are also considered in this paper.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 5152580
zbMATH Keywords: functions of bounded \(p\)-variation
zbMATH Keywords: homogeneous and inhomogeneous Besov spaces
zbMATH Keywords: Peetre's embedding theorem
zbMATH Keywords: boundedness of superposition operators
reviewed by: Jürgen Appell
MaRDI profile type: Publication
cites work: Q4040886
cites work: Q4039801
cites work: Q4112938
cites work: Réalisations des espaces de Besov homogènes. (Realization of homogeneous Besov spaces)
cites work: Le calcul fonctionnel dans les espaces de Sobolev. (Functional calculus in Sobolev spaces)
cites work: Q4284441
OpenAlex ID: W1969451315
description: scientific article; zbMATH DE number 5152580