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

This paper provides an extension of a function u is an element of BVH(Omega) to a function u(o) is an element of BVH(G), when Omega subset of G 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 Omega that is C-1,C-alpha alpha < 1, that is not H-admissible. Further, when Omega is H-admissible a trace theorem is proved for u is an element of BVH(Omega).