Duality of Type H1-BMO and Bilinear Operators

In this paper we consider the renormalization problem of product of two distributions in the setting of Sobolev spaces. This problem is known to be related to compensated compactness and paracompact operators. We establish a dual theorem of type H1-BMO and prove the div-curl Lemma in the case of Sobolev spaces. As a particular case we obtain a compensated compactness theorem for Sobolev spaces.