Weighted Sobolev regularity of the Bergman projection on the Hartogs triangle

Liwei Chen

Vol. 288 (2017), No. 2, 307–318

DOI: 10.2140/pjm.2017.288.307

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.

Keywords

Hartogs triangle, Bergman projection, Sobolev regularity

Mathematical Subject Classification 2010

Primary: 32A07, 32A25, 32A50

Milestones

Received: 10 November 2015

Revised: 9 October 2016

Accepted: 10 October 2016

Published: 28 April 2017