The Sparse T1 Theorem

We impose standard $T1$-type assumptions on a Calderón-Zygmund operator $T$, and deduce that for bounded compactly supported functions $f, g$ there is a sparse bilinear form $Λ$ so that $\lvert \langle T f, g \rangle\rvert \lesssim Λ(f,g).$ The proof is short and elementary. The sparse bound quickly implies all the standard mapping properties of a Calderón-Zygmund on a (weighted) $L ^{p}$ space.

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