At first in the setting of the Heisenberg group we show the chain rule for a function u is an element of BVH (Omega) when composed with a Lipschitz function f : R --> R and prove that nu = f o u belongs to BV (H) (Omega) and D(H)nu much less than D(H)u. More precisely the following result is shown: D(H)nu = f' ((u) over tilde)del(H)uL(2n+1) + 2omega(2n-1)/omega(2n+1) (f(u(+)) - f(u(-)))nu(u)S(d)(Q-1) [J(u) + f' ((u) over tilde) D(H)(c)u. Secondly using the chain rule above we prove a compactness theorem for SBVH functions. ...
