The boundary behavior of holomorphic functions: Global and local results

Details The boundary behavior of holomorphic functions: Global and local results The boundary behavior of holomorphic functions: Global and local results

2006-08-26

arxiv.org/abs/math/0608650v1

Mathematics

Complex Variables

Scientific paper

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 Calder\'{o}n 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.

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