Regularity of the Bergman Projection on Variants of the Hartogs Triangle

Abstract

OF THE DISSERTATION Regularity of the Bergman Projection on Variants of the Hartogs Triangle by Liwei Chen Doctor of Philosophy in Mathematics, Washington University in St. Louis, 2015. Professor Steven G. Krantz, Chair The Bergman projection is the orthogonal projection from the space of square integrable functions onto the space of square integrable holomorphic functions on a domain. Initially, the projection is defined on the L space, but its behavior on other function spaces, e.g. L, Sobolev and Holder spaces, is of considerable interest. In this dissertation, we focus on the Hartogs triangle which is a classical source of counterexamples in several complex variables, and generalize it to higher dimensions. We investigate the L mapping properties of the weighted Bergman projections on these Hartogs domains. As applications, we obtain the L regularity of the twisted-weighted Bergman projections and the weighted L Sobolev regularity of the ordinary Bergman projection on the corresponding domains.