Mapping Properties of Weighted Bergman Projection Operators on Reinhardt Domains

Abstract

We show that on smooth complete Reinhardt domains, weighted Bergman projection operators corresponding to exponentially decaying weights are unbounded on $L^p$ spaces for all $p\ne 2$. On the other hand, we also show that the exponentially weighted projection operators are bounded on Sobolev spaces on the unit ball.

arXiv commentTo appear in the Proceedings of the AMS