Weak Factorizations of the Hardy Space H1(ℝn) in Terms of Multilinear Riesz Transforms

Abstract

AbstractThis paper provides a constructive proof of the weak factorization of the classical Hardy space H1(ℝn) in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of BMO(ℝn) (the dual of H1(ℝn)) via commutators of the multilinear Riesz transforms.