Szego Seminar: "The Bergman projection on L^p"

Abstract: The Bergman space A^2 on the unit ball B_n is a classical space of holomorphic functions. As an operator, the Bergman projection orthogonally projects L^2(B_n) onto A^2(B_n). In this talk, we will show that the Bergman projection can be realized as an integral operator and thus one can study its regularity on L^p(B_n). We present the well-known proof, originally due to Rudin and Forelli, that the Bergman projection preserves L^p(B_n) for p between 1 and infinity. We will also discuss some function-theoretic applications of this result.

Host: Nathan Wagner