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

TL;DR

This paper investigates the boundedness of the Bergman projection on a family of generalized Hartogs triangle domains in complex space, establishing sharp $L^p$ bounds that depend on the domain's geometric properties.

Contribution

It extends the understanding of Bergman projections to new classes of pseudoconvex domains, identifying precise $L^p$ boundedness ranges based on domain geometry.

Findings

Established $L^p$ boundedness for generalized Hartogs triangles

Identified sharp bounds depending on domain 'fatness'

Extended classical results to more general pseudoconvex domains

Abstract

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.