The Bergman Projection on Hartogs Domains in C 2

A study of the Bergman projection in certain Hartogs domains

We show that the Bergman projection does not preserve smoothness of functions in some pseudoconvex domains in the space of two complex variables.

Irregularity of the Bergman Projection on Worm Domains in C

We construct higher-dimensional versions of the Diederich-Fornæss worm domains and show that the Bergman projection operators for these domains are not bounded on high-order Lp-Sobolev spaces for 1 ≤ p < ∞.

$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles

‎In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle‎. ‎We prove optimal estimates for the mapping properties of the Bergman projection on these domains.

The Bergman Projection on Sectorial Domains

Zeroes of the Bergman kernel of Hartogs domains

We exhibit a class of bounded, strongly convex Hartogs domains with realanalytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.