Weak Factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of   Multilinear Riesz Transforms
  This paper provides a constructive proof of the weak factorizations of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of ${\rm BMO}(\mathbb{R}^n)$ (the dual of $H^1(\mathbb{R}^n)$) via commutators of the multilinear Riesz transforms. 
Ji Li and Brett D. Wick
math.CA