# Sobolev mapping of some holomorphic projections

## TL;DR

This paper investigates the Sobolev regularity of the Bergman projection on certain complex domains, revealing improved estimates for a sub-projection on the Hartogs triangle, thus advancing understanding of holomorphic projections' regularity.

## Contribution

It demonstrates Sobolev irregularity for the Bergman projection on specific domains and establishes better Sobolev estimates for a sub-Bergman projection on the Hartogs triangle.

## Key findings

- Sobolev irregularity of the Bergman projection on certain domains.
- Enhanced Sobolev estimates for a sub-Bergman projection on the Hartogs triangle.
- Insights into the regularity properties of holomorphic projections.

## Abstract

Sobolev irregularity of the Bergman projection on a family of domains containing the Hartogs triangle is shown. On the Hartogs triangle itself, a sub-Bergman projection is shown to satisfy better Sobolev norm estimates than its Bergman projection.