Weighted Bergman Projection on the Hartogs Triangle

TL;DR

This paper establishes the $L^p$ regularity of weighted Bergman projections on the Hartogs triangle, identifying sharp ranges of $p$, and extends results to broader weights using two-weight inequalities with Muckenhoupt weights.

Contribution

It proves sharp $L^p$ regularity ranges for weighted Bergman projections on the Hartogs triangle and extends the class of weights via two-weight inequalities.

Findings

Sharp $L^p$ regularity range established

Extended weight class using Muckenhoupt weights

Results applicable to singular boundary points

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.