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 $\alpha$, with $0<\alpha <1$, 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.

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

Cited by in corpus (1)

• Derivatives at the Boundary for Analytic Lipschitz Functions