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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.

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    Do you have any sort of library available, or are looking for an online reference? What books have you tried? I bet one of Evans' "Partial Differential Equations," Grafakos' "Classical Fourier Analysis," or Stein's "Harmonic Analysis" have a proof.2011-03-29
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    Hi @Martin, did you end up looking through those books?2011-04-14
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    you find it in the book "weak convergence methods...." by evans2012-06-21
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    http://arxiv.org/abs/0712.2133 may be relevant.2012-06-21

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