Weak-type regularity of the Bergman projection on rational Hartogs triangles

Abstract

For the rational power-generalized Hartogs triangles in C 2 \mathbb {C}^2 , we give a complete characterization of the weak-type regularity of the Bergman projection at the upper and lower endpoints of L p L^p boundedness. Our result extends work of Huo-Wick for the classical Hartogs triangle by showing that the Bergman projection satisfies a weak-type estimate only at the upper endpoint of L p L^p boundedness.