Boundary smoothness of analytic functions
Abstract
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent , with , 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.
Cite
@article{arxiv.1402.4307,
title = {Boundary smoothness of analytic functions},
author = {Anthony G. O'Farrell},
journal= {arXiv preprint arXiv:1402.4307},
year = {2015}
}
Comments
14 pages. This revision corrects a misprint on p.12: In equation (3), $\alpha$ should have been $1-\alpha$. Also a misprint on page 14 in the formula for $R_a-L_a$. The validity of the argument is not affected and the result stands