  We give a weak factorization proof of the Hardy space $H^{p}(\mathbb{R}^{n})$
in the multilinear setting, for $\frac{n}{n+1} < p <1$. As a consequence, we
obtain a characterization of the boundedness of the commutator $[b,T]$ from
$L^{r_{1}}(\mathbb R^n) \text{~x ... x~} L^{r_{m}} (\mathbb R^n) \text{ to }
L^{q^\prime} (\mathbb R^n)$, where $b \in \text{Lip}_\alpha (\mathbb R^n)$, and
$\frac{\alpha}{n} = \sum_{i=1}^{m} \frac{1}{r_{i}} +\frac{1}{q} - 1$.

Classical Analysis and ODEs