  We prove that a $IR n+1$-valued vector field on IR n is the sum of the traces
of two harmonic gradients, one in each component of $IR n+1 \ IR n$ , and of a
$IR n$-valued divergence free vector field. We apply this to the description of
vanishing potentials in divergence form. The results are stated in terms of
Clifford Hardy spaces, the structure of which is important for our study.
