Published Paper

Inserted: 17 jan 2025
Last Updated: 7 jun 2025

Journal: Siberian Mathematical Journal
Volume: 64
Number: 6
Pages: 1420-1438
Year: 2023
Doi: 10.1134/S0037446623060149
Links: ResearchGate page, Publisher page

Abstract:

Under study are the homeomorphisms that induce the bounded composition operators of $BV$-functions on Carnot groups. We characterize continuous $BV_{\rm loc}$-mappings on Carnot groups in terms of the variation on integral lines and estimate the variation of the $BV$-derivative of the composition of a $C^1$-function and a continuous $BV_{\rm loc}$-mapping.

Keywords: composition operator, Carnot group, function of bounded variation, mapping of bounded variation