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LOCAL BOUNDEDNESS OF NONAUTONOMOUS SUPERPOSITION OPERATORS IN $BV[0,1]$

Part of: Real functions Nonlinear operators and their properties

Published online by Cambridge University Press:  08 July 2015

PIOTR KASPRZAK  and
PIOTR MAĆKOWIAK
PIOTR KASPRZAK*
Affiliation:
Optimization and Control Theory Department, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland email kasp@amu.edu.pl
PIOTR MAĆKOWIAK
Affiliation:
Department of Mathematical Economics, Poznań University of Economics, Al. Niepodległości 10, 61-875 Poznań, Poland email p.mackowiak@ue.poznan.pl
*
✉kasp@amu.edu.pl
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Abstract

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The main goal of this paper is to give the answer to one of the main problems of the theory of nonautonomous superposition operators acting in the space of functions of bounded variation in the sense of Jordan. Namely, we prove that if the superposition operator maps the space $BV[0,1]$ into itself, then it is automatically locally bounded, provided its generator is a locally bounded function.

Keywords

acting conditionslocally bounded mapping(nonautonomous) superposition operatorvariation in the sense of Jordan

MSC classification

Primary: 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Secondary: 26A45: Functions of bounded variation, generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 325 - 341
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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