The factorizations of $H^\rho(\mathbb{R}^n)$ via multilinear Calder\'{o}n-Zygmund operators on weighted Lebesgue spaces

TL;DR

This paper extends Hardy factorization theorems to weighted Lebesgue spaces using multilinear Calderón-Zygmund operators, providing new characterizations of BMO and Lipschitz spaces without individual weight conditions.

Contribution

It establishes weight-independent factorization theorems and characterizations of function spaces via multilinear operators on weighted spaces.

Findings

Factorization theorems extended to weighted spaces

Characterizations of BMO and Lipschitz spaces via weighted boundedness

No individual weight conditions required for the theorems

Abstract

We extend the recently much-studied Hardy factorization theorems to the weight case. The key point of this paper is to establish the factorization theorems without individual condition on the weight functions. As a direct application, we obtain the characterizations of $BMO(\mathbb{R}^n)$ space and Lipschitz spaces via the weighted boundedness of commutators of multilinear Calder\'{o}n-Zygmund operators with the genuinely multilinear weights.