Weighted Estimates for the Berezin Transform and Bergman Projection on the Unit Ball in $\mathbb{C}^{n}$

TL;DR

This paper establishes sharp weighted estimates for the Bergman projection and Berezin transform on the unit ball in complex n-space, utilizing dyadic harmonic analysis techniques to relate bounds to the Bekolle-Bonami constant.

Contribution

It introduces a novel approach using dyadic harmonic analysis to derive sharp weighted bounds for key operators in complex analysis.

Findings

Sharp estimates in terms of Bekolle-Bonami constant

Extension of techniques to more general operators

Improved bounds for weighted Bergman spaces

Abstract

Using modern techniques of dyadic harmonic analysis, we are able to prove sharp estimates for the Bergman projection and Berezin transform and more general operators in weighted Bergman spaces on the unit ball in $\mathbb{C}^n$. The estimates are in terms of the Bekolle-Bonami constant of the weight.