On the Calderón-Zygmund theory of singular integrals

Abstract: The seminal work of Calderón and Zygmund on singular integral operators has greatly influenced modern harmonic analysis. We begin our discussion with some classical aspects of CZ theory, including examples and applications, and then focus on the crucial weak-type $(1,1)$ estimate for CZ operators. We investigate techniques for obtaining weak-type inequalities that use the CZ decomposition and ideas inspired by Nazarov, Treil, and Volberg. We discuss various applications of these methods.

Mathematics

Audience: advanced learners

Trends in Mathematical Research