Hardy Factorization in Terms of Multilinear Fractional Operator

We establish a factorization theorem for the Hardy space $H^p(\mathbb{R}^n)$ $\bigl(\frac{n}{n+1}<p <1\bigr)$ in terms of a multilinear fractional integral operator. As an application, a characterization of Lipschitz spaces via the boundedness of commutators of the multilinear fractional integral operator is obtained.