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