Analysis Seminar: Inequalities for the Bergman Projection: A Story Linking Harmonic Analysis, Complex Analysis, and Operator Theory I

Speaker: Nathan Wagner, GMU

Title: Inequalities for the Bergman Projection: A Story Linking Harmonic Analysis, Complex Analysis, and Operator Theory I

Abstract: The Bergman space is an important space of analytic functions on the unit disk in complex analysis, and the Bergman projection is the orthogonal Hilbert space projection from L^2 onto the Bergman space. Inequalities for the Bergman projection on a wide variety of function spaces have been studied using a mix of real-variable harmonic analysis and complex analysis tools, and have important implications. In this talk, we will introduce the Bergman space as a reproducing kernel Hilbert space and define the Bergman projection. From there, we will present a foundational result which states the Bergman projection extends to a bounded operator on L^p for all p in the reflexive range. We will discuss the key ingredients to proving this theorem, including estimates on integration of the Bergman kernel due to Rudin/Forelli and Schur's test for integral operators with positive kernel. 

Date/Time: Friday October 3, 11:30am

Location: Exploratory Hall, Room 3301