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 $u\in B{V}_H(\Omega )$ to a function $u_0\in B{V}_H(G)$ 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 $u\in B{V}_H(\Omega )$.

20 pages

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