The Sparse T1 Theorem

Abstract

We impose standard T1-type assumptions on a Calderon-Zygmund operator T, and deduce that for bounded compactly supported functions f and g there is a sparse bilinear form B so that |< Tf, g >|; < B(f,g). The proof is short and elementary. The sparse bound quickly implies all the standard mapping properties of a Calderon-Zygmund on a (weighted) L^p space.