Weak Factorizations of the Hardy Spaces in Terms of Multilinear Calder\'on-Zygmund Operators on Ball Banach Function Spaces

TL;DR

This paper establishes a weak factorization of Hardy spaces using multilinear Calderón-Zygmund operators on ball Banach function spaces and characterizes BMO spaces via commutator boundedness, with broad applications.

Contribution

It introduces a general weak factorization framework for Hardy spaces and a new BMO characterization via commutators on diverse function spaces.

Findings

Weak factorization of Hardy spaces established.

BMO space characterized via commutator boundedness.

Results applicable to various function spaces like weighted Lebesgue and Lorentz spaces.

Abstract

In this paper, our main purpose is to establish a weak factorization of the classical Hardy spaces in terms of a multilinear Calder\'on-Zygmund operator on the ball Banach function spaces. Furthermore, a new characterization of the BMO space via the boundedness of the commutator generated by the multilinear Calder\'on-Zygmund operator is also obtained. The results obtained in this paper have generality. As examples, we apply the above results to weighted Lebesgue space, variable Lebesgue space, Herz space, mixed-norm Lebesgue space, Lorentz space and so on.