# $L^p$ regularity of the Bergman Projection on domains covered by the polydisk

## TL;DR

This paper investigates the $L^p$ regularity of the Bergman projection on domains covered by the polydisk via rational proper holomorphic maps, with applications to specific complex domains.

## Contribution

It establishes $L^p$ boundedness of the Bergman projection for domains covered by the polydisk, extending understanding to symmetrized polydisks and Hartogs triangles.

## Key findings

- Bergman projection is $L^p$-bounded within a specific range depending on the covering map.
- Results apply to symmetrized polydisks and Hartogs triangles with certain exponents.
- Provides conditions linking domain coverings and $L^p$ regularity of the Bergman projection.

## Abstract

If a bounded domain can be covered by the polydisk through a rational proper holomorphic map, then the Bergman projection is $L^p$-bounded for $p$ in a certain range depending on the ramified rational covering. This result can be applied to the symmetrized polydisk and to the Hartogs triangle with exponent $\gamma$.