Weak-type bounds for the Bergman projection with Bekoll\'e-Bonami weights

TL;DR

This paper proves new weighted weak-type bounds for the Bergman projection with Bekollé-Bonami weights, providing improved estimates and sharp bounds that apply to various complex domains, including classical cases.

Contribution

It introduces two proofs of an improved weak-type (1,1) estimate and establishes sharp weak-type (p,p) bounds for p>1 for the Bergman projection with Bekollé-Bonami weights.

Findings

Established weighted weak-type bounds for the Bergman projection.

Provided two proofs of an improved weak-type (1,1) estimate.

Derived sharp weak-type (p,p) bounds for p>1.

Abstract

We establish weighted weak-type bounds for the Bergman projection with respect to Bekoll\'e-Bonami characteristics. We present two proofs of an improved quantitative weak-type $(1,1)$ estimate, as well as sharp weak-type $(p,p)$ bounds for $p>1$ and mixed weighted weak-type $(1,1)$ inequalities. Our results, which hold for a wide class of simple domains in $\mathbb{C}^n$, are new even in the classical settings of the upper half-plane and the unit disk.