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arXiv · 1402.4307

Boundary smoothness of analytic functions

Anthony G. O'Farrell
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Abstract

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $α$, with $0<α<1$, in the vicinity of an exceptional boundary point where all such functions exhibit some kind of smoothness. Specifically, we consider the relation between the abstract idea of a bounded point derivation on the algebra of such functions and the classical complex derivative evaluated as a limit of difference quotients. We obtain a result which applies, for example, when the open set admits an interior cone at the special boundary point.

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Anthony G. O'Farrell. 2015-09-28. Boundary smoothness of analytic functions. https://doi.org/10.1007/s13324-014-0074-0

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