Lp-Hodge decomposition with Sobolev classes in sub-Riemannian contact manifolds

Abstract

Let $1<p<\infty$. In this article we establish an $L^p$-Hodge decomposition theorem on sub-Riemannian compact contact manifolds without boundary, related to the Rumin complex of differential forms. Given an $L^p$- Rumin's form, we adopt an approach in the spirit of Morrey's book [26] (further performed in [18]) to obtain a decomposition with higher regular “primitives” i.e. that belong to suitable Sobolev classes. Our proof relies on recent results obtained in [4] and [6].