The Boundary Behavior of Holomorphic Functions: Global and Local Results

We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $\Omega$ -- both in one and several complex variables. The approach involves two new localized maximal functions.

As a result of this methodology, theorems of Calderón type about local boundary behavior on a set of positive measure may be proved in a new and more natural way.

We also study the question of nontangential boundedness (on a set of positive measure) versus admissible boundedness. Under suitable hypotheses, these two conditions are shown to be equivalent.

Keywords

Fatou theorem, admissible convergence, Calderón theorem, boundary limits

2010 Mathematics Subject Classification

Primary 32A40. Secondary 32A35, 32A50.

Full Text (PDF format)

Published 1 January 2007