Bergman projection on the symmetrized bidisk

TL;DR

This paper investigates the boundedness of the Bergman projection on weighted and unweighted spaces on the symmetrized bidisk, extending previous results and applying advanced estimates to establish new boundedness properties.

Contribution

It applies the Bekollé-Bonami estimate to the Bergman projection on the symmetrized bidisk, improving and extending boundedness results in weighted and unweighted spaces.

Findings

Boundedness of Bergman projection on weighted Sobolev spaces established

Improved boundedness results on unweighted L^p spaces

Extended previous results to the symmetrized bidisk setting

Abstract

We apply the Bekoll\'e-Bonami estimate for the (positive) Bergman projection on the weighted $L^p$ spaces on the unit disk. As the consequences, we obtain the boundedness of the Bergman projection on the weighted Sobolev space on the symmetrized bidisk. We also improve the boundedness result of the Bergman projection on the unweighted $L^p$ space on the symmetrized bidisk in \cite{CKY}.