Decomposition of the Hardy space \({\mathcal H}_z^1(\Omega)\) (Q2581229)

In this article, the authors give an atomic decomposition for the Hardy space \({\mathcal H}^1_z(\Omega)\) into ``div-curl'' quantities for Lipschitz domains in \({\mathbb R}^n\). The authors also obtain an atomic decomposition of \({\mathcal H}^1_z(\Omega)\) into Jacobians \(\det(Du)\), \(u\in W_0^{1,2}(\Omega, {\mathbb R}^2)\), for \(\Omega\) in \({\mathbb R}^2\). The paper is very well-written and answers partially an open problem along this research direction.