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


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.


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


Published: June 2007
First available in Project Euclid: 31 July 2007

zbMATH: 1141.32002
MathSciNet: MR2328891

Primary: 32A40
Secondary: 32A35‎ , 32A50

Keywords: admissible convergence , boundary limits , Calderón theorem , Fatou theorem

Rights: Copyright © 2007 International Press of Boston

Vol.11 • No. 2 • June 2007
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