$BV$-spaces and the bounded composition operators of $BV$-functions on Carnot groups

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.