Differentiability of the mappings of Carnot–Caratheodory spaces in the Sobolev and $BV$-topologies

We prove differentiability of the mappings of the Sobolev classes and $BV$-mappings of Carnot–Carathéodory spaces in the topology of these classes. We infer from these results a generalization of the Calderon–Zygmund theorems for mappings of the Carnot–Carathéodory spaces and other facts.