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We prove that a $IR n+1$-valued vector field on IR n is the sum of the tracesof 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 ofvanishing potentials in divergence form. The results are stated in terms ofClifford Hardy spaces, the structure of which is important for our study.

Hardy-Hodge Decomposition of Vector Fields in $Rn$