The Bergman projection on fat Hartogs triangles: L^p boundedness

A class of pseudoconvex domains in ${\mathbb{C}}^n$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the “fatness” of domains. This range of $p$ is shown to be sharp.