A Survey of the $L^p$ Regularity of the Bergman Projection

TL;DR

This survey reviews recent advances in understanding the behavior of the Bergman projection operator on various $L^p$ spaces beyond the classical $L^2$ setting, highlighting ongoing research challenges.

Contribution

It compiles and discusses recent results on $L^p$ estimates for the Bergman projection, providing a comprehensive overview of current research progress.

Findings

Summarizes key $L^p$ regularity results for the Bergman projection.

Identifies open problems and directions for future research.

Highlights the complexity of $L^p$ behavior for the Bergman projection.

Abstract

Although the Bergman projection operator $\mathbf{B}_{\Omega}$ is defined on $L^2(\Omega)$, its behavior on other $L^p(\Omega)$ spaces for $p\not =2$ is an active research area. We survey some of the recent results on $L^p$ estimates on the Bergman projection.