Weak-type bounds for the Bergman projection with Bekollé-Bonami weights

Abstract

We establish weighted weak-type bounds for the Bergman projection with respect to Bekollé-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.