On the global Lipschitz continuity of the Bergman projection on a class of convex domains of infinite type in $\mathbb {C}^2$

Ly Kim Ha¹

¹ Faculty of Mathematics and Computer Science University of Science Vietnam National University HoChiMinh City (VNU-HCM) 227 Nguyen Van Cu Street, District 5 Ho Chi Minh City, Vietnam

Colloquium Mathematicum, Tome 150 (2017) no. 2, pp. 187-205.

Résumé

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 $F$.

Détail

DOI : 10.4064/cm7065-11-2016

Keywords: main purpose paper prove global lipschitz continuity bergman projection class smoothly bounded convex domains admitting maximal type mathbb maximal type here geometric condition which includes cases finite type many cases infinite type sense range varomega domain prove bergman projection mathcal maps continuously varlambda alpha varomega varlambda alpha varomega alpha where alpha function depending nbsp