Seminar

It is discovered recently that Calder\'on-Zygmund (CZ) operators are dominated pointwisely by sparse operators, which are positive, local, and of averaging type. This can be viewed as a finer quantification of the boundedness of CZ operators and in particular implies almost immediately sharp weighted norm inequalities. Surprisingly, such phenomenon continues to exist well beyond CZ theory and similar sparse bound can be obtained for many other singular integral operators. We will discuss the general framework of proving sparse bound and how it applies to operators such as rough homogeneous singular integrals, Bochner-Riesz multipliers, bilinear Hilbert transform, and Radon transforms.