Weak factorizations of the Hardy space in terms of multilinear fractional integral operator

TL;DR

This paper provides a constructive factorization of Hardy spaces using multilinear fractional integral operators, extending to weighted cases and characterizing BMO via commutator boundedness without specific weight conditions.

Contribution

It introduces a new constructive proof for Hardy space factorization with multilinear fractional integrals and extends the results to weighted cases and BMO characterization.

Findings

Constructive proof of Hardy space factorization using fractional integrals

Extension to multilinear and weighted cases

Characterization of BMO via commutator boundedness

Abstract

We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the characterization of $BMO$ via the weighted boundedness of commutators of the multilinear fractional integral operator, without individual conditions on the weights class.