Dissertation Defense: "A Different Approach to Endpoint Weak-type Estimates for Calderón-Zygmund Operators"
Abstract: The weak-type (1,1) estimate for Calderón-Zygmund operators is fundamental in harmonic analysis. We investigate weak-type inequalities for Calderón-Zygmund singular integral operators using the Calderón-Zygmund decomposition and ideas inspired by Nazarov, Treil, and Volberg. We discuss applications of these techniques in the Euclidean setting, in weighted settings, for multilinear operators, for operators with weakened smoothness assumptions, and in studying the dimensional dependence of the Riesz transforms.
Host: Brett Wick