Approach regions for domains in ℂ² of finite type

Abstract

Recall Fatou's theorem for the unit disc in ℂ. Consider a domain in ℂ² of finite type. In this article, we show that the approach regions studied by Nagel, Stein, Wainger and Neff are the best possible ones for the boundary behaviour of bounded analytic functions, and there is no Fatou's theorem for complex tangentially broader approach regions

Keywords:

• several complex variables
• finite type
• approach region

AMS Subject Classification:

• 32A40