On the boundedness of Bergman projection

TL;DR

This survey reviews the boundedness of the Bergman projection, emphasizing norm equivalences on weighted Bergman spaces and focusing on radial weights with the doubling property.

Contribution

It compiles and discusses various results on the boundedness of the Bergman projection, highlighting norm equivalences and decomposition theorems for specific weight classes.

Findings

Norm equivalences on weighted Bergman spaces are established.

Decomposition norm theorem for radial weights with doubling property is presented.

The survey consolidates key results on the boundedness criteria of the Bergman projection.

Abstract

The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In particular, we shall focus on a decomposition norm theorem for radial weights~$\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$.