Bergman projections induced by doubling weights on the unit ball of Cn

TL;DR

This paper investigates the boundedness properties of Bergman projections induced by doubling weights on the unit ball in complex n-dimensional space, extending understanding of their behavior on various function spaces.

Contribution

It provides new results on the boundedness of weighted Bergman projections and their compositions on the unit ball in several complex variables.

Findings

Boundedness of $P_rrow$ from $L^rrow$ to $rrow$ spaces established.

Boundedness of $P_
arrow P_
arrow$ on weighted $L^p$ spaces shown.

Results extend previous one-variable cases to higher dimensions.

Abstract

The boundedness of $P_\omega:L^\infty(\mathbb{B})\to \mathcal{B}(\mathbb{B})$ and $P_\omega(P_\omega^+):L^p(\mathbb{B},\upsilon dV)\to L^p(\mathbb{B},\upsilon dV)$ on the unit ball of $\mathbb{C}^n$ with $p>1$ and $\omega,\upsilon\in \mathcal{D}$ are investigated in this paper.