Work

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

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2507.22363

Authors: Chen, Jiale, Nieraeth, Zoe, Stockdale, Cody B., Wagner, Nathan A.

Institutions: Shaanxi Normal University, University of the Basque Country, Clemson University, George Mason University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China, Eusko Jaurlaritza

Awards: G1790160662, Modern Harmonic Analysis Techniques in Complex Variables and Non-Homogeneous Settings, G3170345866, PostDoctoral Research Fellowship

OpenAlex ID: W4416258709

Cites: 6

Cited by: 1

Related to: 10