Endpoint for the div-curl lemma in Hardy spaces

Abstract

We give a $\operatorname{div}$-$\operatorname{curl}$ type lemma for the wedge product of closed differential forms on ${\mathbb R}^n$ when they have coefficients respectively in a Hardy space and $L^\infty$ or $\mathit{BMO}$. In this latter case, the wedge product belongs to an appropriate Hardy-Orlicz space.