$ BV $ -Spaces and the Bounded Composition Operators of $ BV $ -Functions on Carnot Groups

Abstract

Under study are the homeomorphisms that induce the bounded composition operators of \( BV \)-functions on Carnot groups. We characterize continuous \( BV_{\operatorname{loc}} \)-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 \( BV_{\operatorname{loc}} \)-mapping.