Vol. 67, No. 1, 1976

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Smoothness of analytic functions at boundary points

Mikihiro Hayashi

Vol. 67 (1976), No. 1, 171–202

Let U be a bounded open set in the plane. We study the smoothness at boundary points of the continuous functions on U which are analytic in U. A main result is the characterization of sequences xn U, xn x, with the property that the functions are of class Ck along xn at x. As an application of this characterization, we can find an open set U for any twice continuously differentiable arc J such that U contains J in its boundary and the functions are of class C on J.

Mathematical Subject Classification 2000
Primary: 30A72, 30A72
Secondary: 46J15, 30A98
Received: 15 September 1975
Revised: 6 July 1976
Published: 1 November 1976
Mikihiro Hayashi