A class of harmonic differential forms

We introduce a class of harmonic differential forms. It consists of the k-forms u defined in a domain $\Omega$ such that $u, *u, \delta u$ and $*d u$ do exist on $\partial\Omega$ in a weak sense and their coefficients are in $L^{p}(\partial\Omega)$. We prove that a form belongs to this space if and only if it can be written as a ``simple layer'' potential with $L^p$ densities. We obtain a regularization theorem on the boundary and some uniqueness properties. We give also the relevant Calderòn projector.