Sparse operators and the sparse T1 Theorem

Analysis Seminar
Wednesday, March 8, 2017 - 2:05pm
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
 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 $\Lambda$ so that $$   |\langle T f, g \rangle | \lesssim \Lambda (f,g). $$ 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.