Approach regions for domains in $\CC^2$ of finite type

Details Approach regions for domains in $\CC^2$ of finite type Approach regions for domains in $\CC^2$ of finite type

2010-02-08

arxiv.org/abs/1002.1524v2

Mathematics

Complex Variables

10 pages, 0 figure

Scientific paper

Recall the Fatou theorem for the unit disc in $\CC$. Consider a domain in
$\CC^2$ of finite type. In this paper we will show that the approach regions
studied by Nagel, Stein, Wainger and Neff are the best possible ones for the
boundary behavior of bounded analytic functions, and there is no Fatou theorem
for complex tangentially broader approach regions.

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