The Sparse T1 Theorem

We impose standard $T1$-type assumptions on a Calder\'on-Zygmund operator $T$, and deduce that for bounded compactly supported functions $f, g$ there is a sparse bilinear form $\Lambda$ so that $$\lvert \langle T f, g \rangle\rvert \lesssim \Lambda (f,g).$$ The proof is short and elementary. The sparse bound quickly implies all the standard mapping properties of a Calder\'on-Zygmund on a (weighted) $L ^{p}$ space.