Analysis Seminar: Weak-type regularity of the Bergman projection on generalized Hartogs triangles

Abstract: In this talk, we give a complete characterization of the weak-type regularity of the Bergman projection on rational Hartogs triangles in C^2 and and power-generalized Hartogs triangles in C^3. In particular, we show that the Bergman projection satisfies a weak-type estimate only at the upper endpoint of $L^p$ boundedness on both of these domains. A similar result has been observed by Huo-Wick and Koenig-Wang for the classical Hartogs triangle and punctured unit ball, respectively. This work is joint with K.D. Koenig.

Host: Brett Wick, Washington University in St. Louis