The factorizations of $H^{\rho }({\mathbb{R}}^n)$ via multilinear Calder\'{o}n-Zygmund operators on weighted Lebesgue spaces

We extend the recently much-studied Hardy factorization theorems to the weight case. The key point of this paper is to establish the factorization theorems without individual condition on the weight functions. As a direct application, we obtain the characterizations of $BMO({\mathbb{R}}^n)$ space and Lipschitz spaces via the weighted boundedness of commutators of multilinear Calder'{o}n-Zygmund operators with the genuinely multilinear weights.