Weighted Sobolev regularity of the Bergman projection on the Hartogs triangle

TL;DR

This paper establishes weighted Sobolev estimates for the Bergman projection on the Hartogs triangle and its higher-dimensional generalizations, advancing understanding of boundary regularity in complex analysis.

Contribution

It introduces a new weighted Sobolev estimate for the Bergman projection on the Hartogs triangle and extends the method to higher dimensions.

Findings

Weighted Sobolev estimate proved for the Hartogs triangle

Method applicable to n-dimensional Hartogs triangle

Enhanced understanding of boundary regularity in complex analysis

Abstract

We prove a weighted Sobolev estimate of the Bergman projection on the Hartogs triangle, where the weight is some power of the distance to the singularity at the boundary. This method also applies to the $n$-dimensional generalization of the Hartogs triangle.