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

Abstract

This paper provides an extension for a function $u \in BV_H(\Omega)$ to a function $u_0 \in BV_H(G)$ when $\Omega$ 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 $\Omega$ is H-admissible a trace theorem is proved for $u \in BV_H(\Omega)$.