Bekollé-Bonami estimates on some pseudoconvex domains

Abstract

We establish a weighted Lp norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted Lp norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain, a pseudoconvex domain of finite type in C2, a convex domain of finite type in Cn, or a decoupled domain of finite type in Cn. 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. As an additional application of the method of proof, we obtain the result that the Bergman projection is weak-type (1,1) on these domains.