Analysis Seminar: "Weighted Estimates for the Bergman Projection in Planar Domains"

Abstract: The Bergman projection, B_E, is the orthogonal projection from L^2(E) onto the closed subspace of holomorphic functions on E. When E is smooth enough, B_E is a singular integral operator and estimates on L^p(E) and even L^p(E,w) can be obtained using standard harmonic analysis techniques. When E is a simply connected domain in the complex plane, we can connect weighted estimates for B_E to properties of the conformal map from E to the unit disc. To do so, we study the properties of various weight classes under composition with conformal maps. This work is in progress with Nathan Wagner.