Date of Award
Doctor of Philosophy (PhD)
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 L2 space, but its behavior on other function spaces, e.g. Lp, 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 Lp mapping properties of the weighted Bergman projections on these Hartogs domains. As applications, we obtain the Lp regularity of the twisted-weighted Bergman projections and the weighted Lp Sobolev regularity of the ordinary Bergman projection on the corresponding domains.
Chair and Committee
Steven G Krantz
Steven G Krantz, Carl M Bender, Quo-Shin Chi, Renato Feres, Xiang Tang
Chen, Liwei, "Regularity of the Bergman Projection on Variants of the Hartogs Triangle" (2015). Arts & Sciences Electronic Theses and Dissertations. 461.