Weak-type bounds for the Bergman projection with Bekoll\'e-Bonami weights
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 Cn, are new even in the classical settings of the upper half-plane and the unit disk.
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