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

TL;DR

This paper establishes optimal weighted $L^p$ estimates for the Bergman projection on the Hartogs triangle for $p>4/3$, and shows such estimates are impossible for smaller $p$, revealing boundary regularity limits.

Contribution

It provides the first sharp weighted $L^p$ bounds for the Bergman projection on the Hartogs triangle, identifying the precise range of $p$ where estimates hold.

Findings

Optimal weighted $L^p$ estimates for $p>4/3$

No such estimates exist for $p\,\leq\,4/3$

Clarifies the boundary regularity of the Bergman projection

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 $1<p\leq\frac{4}{3}$ we show that no such weighted estimates are possible.