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The boundary behavior of holomorphic functions: Global and local results

Steven G. Krantz
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Abstract

We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $Ω$ -- 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.

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Steven G. Krantz. 2006-08-26. The boundary behavior of holomorphic functions: Global and local results. https://arxiv.org/abs/math/0608650

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