Lp estimates for the bergman projection on some reinhardt domains

We obtain L^p regularity for the Bergman projection on some Reinhardt domains. We start with a bounded initial domain Ω with some symmetry properties and generate successor domains in higher dimensions. We prove: If the Bergman kernel on Ω satisfies appropriate estimates, then the Bergman projection on the successor is L^p bounded. For example, the Bergman projection on successors of strictly pseudoconvex initial domains is bounded on L^p for 1 < p < ∞. The successor domains need not have smooth boundary nor be strictly pseudoconvex.

Duke Scholars

Author Zhenghui Huo DKU Faculty