Quantitative weighted bounds for composite operators on spaces of homogeneous type

Abstract

Let $T_1$ and $T_2$ be Calderón–Zygmund operators, and let $T_{1,b}$ denote the commutator of $T_1$ and the BMO function $b$. By establishing bisublinear sparse dominations, we obtain the quantitative weighted bounds for composite operators $T_1{T}_2$ and $T_{1,b}{T}_2$ on $L^p(X,\omega )$, with $\omega \in A_p(X)$.