$L^p$ Mapping Properties of the Bergman Projection on the Hartogs Triangle

Abstract

We prove optimal estimates for the mapping properties of the Bergman projection on the Hartogs triangle in weighted $L^p$ spaces when $p>\frac{4}{3}$, where the weight is a power of the distance to the singular boundary point. For $1<p\le \frac{4}{3}$ we show that no such weighted estimates are possible.

Small typos corrected. To appear in the Proceedings of the AMS