## Local Boundedness of Nonautonomous Superposition Operators in BV[0,1]

### Piotr Kasprzak , Piotr Maćkowiak

#### Abstract

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.
 Author Piotr Kasprzak - Adam Mickiewicz University (UAM) Piotr Kasprzak,, - , Piotr Maćkowiak (WIiGE / KEM) Piotr Maćkowiak,, - Department of Mathematical Economics Journal series Bulletin of the Australian Mathematical Society, ISSN 0004-9727, (A 20 pkt) Issue year 2015 Vol 92 No 2 Pages 325-341 Publication size in sheets 0.8 Keywords in English acting conditions, locally bounded mapping, (nonautonomous) superposition operator, variation in the sense of Jordan ASJC Classification 2600 General Mathematics DOI DOI:10.1017/S0004972715000593 URL https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7ECCB9805A88092EC5AA2741E19A59A4/S0004972715000593a.pdf/local_boundedness_of_nonautonomous_superposition_operators_in_bv01.pdf Language en angielski Score (nominal) 20 Score source journalList Score Ministerial score = 20.0, 23-12-2019, ArticleFromJournalMinisterial score (2013-2016) = 20.0, 23-12-2019, ArticleFromJournal Publication indicators WoS Citations = 2; Scopus SNIP (Source Normalised Impact per Paper): 2015 = 0.763; WoS Impact Factor: 2015 = 0.566 (2) - 2015=0.55 (5) Citation count*
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