The composition of singular integral operators with nonsmooth kernels

Abstract

Let T1, T2 be two singular integral operators with nonsmooth kernels introduced by Duong and McIntosh. In this paper, by establishing certain bi‐sublinear sparse dominations, the authors obtain some quantitative bounds on Lpfalse(Rn,0.16emwfalse) with p∈(1,∞) and w∈Apfalse(Rnfalse) for the composite operator T1T2. Some weighted weak type endpoint estimates are also given.