Bergman theory of certain generalized Hartogs triangles

Luke D. Edholm

Vol. 284 (2016), No. 2, 327–342

DOI: 10.2140/pjm.2016.284.327

Abstract

The Bergman theory of domains $\left\{|z_1{|}^{\gamma }<|z_2|<1\right\}$ in ${ℂ}^2$ is studied for certain values of $\gamma$, including all positive integers. For such $\gamma$, we obtain a closed form expression for the Bergman kernel ${\mathbb{B}}_{\gamma }$. With these formulas, we make new observations relating to the Lu Qi-Keng problem and analyze the boundary behavior of ${\mathbb{B}}_{\gamma }\left(z,z\right)$.

Keywords

Bergman kernel, fat Hartogs triangle, Bell's transformation formula, Lu Qi-Keng

Mathematical Subject Classification 2010

Primary: 32A25, 32A36, 32W05

Milestones

Received: 27 June 2015

Revised: 26 February 2016

Accepted: 2 April 2016

Published: 30 August 2016