Asian Journal of Mathematics
Volume 11 (2007)
The Boundary Behavior of Holomorphic Functions: Global and Local Results
Pages: 179 – 200
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.
Fatou theorem; admissible convergence; Calderón theorem; boundary limits
2010 Mathematics Subject Classification
Primary 32A40. Secondary 32A35, 32A50.