Georgia Institute of Technology College of Sciences

The Bergman projection is a fundamental operator in complex analysis. It is well-known that in the case of the unit ball, the Bergman projection is bounded on weighted L^p if and only if the weight belongs to the Bekolle-Bonami, or B_p, class. These weights are defined using a Muckenhoupt-type condition. Rahm, Tchoundja, and Wick were able to compute the dependence of the operator norm of the projection in terms of the B_p characteristic of the weight using modern tools of dyadic harmonic analysis. Moreover, their upper bound is essentially sharp. We establish that their results can be extended to a much wider class of domains in several complex variables. A key ingredient in the proof is that favorable estimates on the Bergman kernel have been obtained in these cases. This is joint work with Zhenghui Huo and Brett Wick.