Quantitative weighted bounds for the composition of Calderón–Zygmund operators

Abstract

Let $T_1$, $T_2$ be two Calderón–Zygmund operators, and let $T_{1,b}$ be the commutator of $T_1$ with symbol $b\in BMO\left({\mathbb{R}}^n\right)$. In this article, we establish the quantitative weighted bounds on $L^p({\mathbb{R}}^n,w)$ with $w\in A_p\left({\mathbb{R}}^n\right)$ for the composite operator $T_{1,b}{T}_2$.