An extension and trace theorem for functions of H-bounded variation in Carnot groups of step 2

This paper provides an extension for a function $u\in B{V}_H(\mathrm{\Omega })$ to a function $u_0\in B{V}_H(G)$ when $\mathrm{\Omega }$ is ``H-admissible,‘’ and G is a step 2 Carnot group. It is shown that H-admissible domains include non-characteristic domains and domains in groups of Heisenberg type which have a partial symmetry about characteristic points. An example is given of a domain that is $C^{1,\alpha }$, $\alpha <1$, that is not H-admissible. Further, when $\mathrm{\Omega }$ is H-admissible a trace theorem is proved for $u\in B{V}_H(\mathrm{\Omega })$.