let $1 = \frac{1}{p} + \frac{1}{q}$ as usual. Let $f \in L^p, g \in L^q$ be vector fields from $\mathbb R^n$ to itself.
Assume $div f = 0$ and there exists a function $G$ s.t. $\nabla G = g$. Then $f \cdot g \in \mathcal H^1$ is a Hardy space function.
Do you know where I can find a proof of this conclusion? I am aware of a paper by Coifman et al. "Compensated compactness and Hardy spaces", but I am not granted access to this journal. Hence I am looking for an alternative resource.