Bekollé-Bonami estimates on some pseudoconvex domains

Abstract

We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain, a pseudoconvex domain of finite type in ${\mathbb{C}}^2$, a convex domain of finite type in ${\mathbb{C}}^n$, or a decoupled domain of finite type in ${\mathbb{C}}^n$. The upper bound is related to the Bekollé-Bonami constant and is sharp. When the domain is smooth, bounded, and strictly pseudoconvex, we also obtain a lower bound for the weighted norm.

28 pages. An application to the weak-type estimate is added as a new section

References in corpus (1)

• Weighted estimates for the Bergman projection on the Hartogs triangle

Cited by in corpus (4)

• Weighted estimates of the Bergman projection with matrix weights
• A Békollè-Bonami Class of Weights for Certain Pseudoconvex Domains
• Dyadic Carleson embedding and sparse domination of weighted composition operators on strictly pseudoconvex domains
• Bergman projection on the symmetrized bidisk