English

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

Functional Analysis 2025-11-20 v3

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)(1,1) estimate, as well as sharp weak-type (p,p)(p,p) bounds for p>1p>1 and mixed weighted weak-type (1,1)(1,1) inequalities. Our results, which hold for a wide class of simple domains in Cn\mathbb{C}^n, are new even in the classical settings of the upper half-plane and the unit disk.

Keywords

Cite

@article{arxiv.2507.22363,
  title  = {Weak-type bounds for the Bergman projection with Bekoll\'e-Bonami weights},
  author = {Jiale Chen and Zoe Nieraeth and Cody B. Stockdale and Nathan A. Wagner},
  journal= {arXiv preprint arXiv:2507.22363},
  year   = {2025}
}