Weighted Bergman Projection on the Hartogs Triangle

We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a two-weight inequality on the upper half plane with Muckenhoupt weights, we can consider a slightly wider class of weights.Comment: The article has been revised. There are 23 pages in tota

Regularity of the Bergman Projection on Variants of the Hartogs Triangle

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