The Boundary Behavior of Holomorphic Functions: Global and Local Results

@article{Krantz2006TheBB,
  title={The Boundary Behavior of Holomorphic Functions: Global and Local Results},
  author={Steven G. Krantz},
  journal={Asian Journal of Mathematics},
  year={2006},
  volume={11},
  pages={179-200}
}
  • S. Krantz
  • Published 26 August 2006
  • Mathematics
  • Asian Journal of Mathematics
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… 
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