The boundary behavior of holomorphic functions

Abstract

The Boundary Behavior of Holomorphic Functions by MIN, Baili Doctor of Philosophy in Mathematics, Washington University in St. Louis, May, 2011. Professor Steven Krantz, Chairperson In the theory of several complex variables, the Fatou type problems, the Lindelof principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou’s theorem for approach regions complex tangentially broader than admissible ones, in domains of finite type. In Chapter 3 discussing the Lindelof principle, we provide some conditions which yield admissible convergence. In Chapter 4 we construct inner functions for a type of domains more general than strongly pseudoconvex ones. Discussion is carried out in C.