On the global Lipschitz continuity of the Bergman projection on a class of convex domains of infinite type in $\mathbb {C}^2$
Volume 150 / 2017
Colloquium Mathematicum 150 (2017), 187-205
MSC: Primary 32A25; Secondary 32A26, 32W35, 32F18.
DOI: 10.4064/cm7065-11-2016
Published online: 20 July 2017
Abstract
The main purpose of this paper is to prove the global Lipschitz continuity of the Bergman projection in a class of smoothly bounded, convex domains admitting maximal type $F$ in $\mathbb {C}^2$. The maximal type $F$ here is a geometric condition which includes all cases of finite type and many cases of infinite type in the sense of Range (1978). Let $\varOmega $ be such a domain. We prove that the Bergman projection $\mathcal {P}$ maps continuously $\varLambda ^{t^{\alpha }}(\varOmega )$ to $\varLambda ^{g_{\alpha }}(\varOmega )$ for $0 \lt \alpha \le 1$, where $g_\alpha $ is a function depending on $F$.
