Abstract
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.
Citation
Steven G. Krantz. "The Boundary Behavior of Holomorphic Functions: Global and Local Results." Asian J. Math. 11 (2) 179 - 200, June 2007.
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