Weighted Bergman Projection on the Hartogs Triangle

Abstract

We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a two-weight inequality on the upper half plane with Muckenhoupt weights, we can consider a slightly wider class of weights.