Weak Factorizations of the Hardy Space H 1(ℝn) in Terms of Multilinear Riesz Transforms

Abstract

This paper provides a constructive proof of the weak factorization of the classical Hardy space H ¹(ℝ ⁿ ) in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of BMO(ℝ ⁿ) (the dual of H ¹(ℝ ⁿ )) via commutators of the multilinear Riesz transforms.