On Differentiability at the Boundary in Conformal Mapping1

Introduction. The object of this note is to present a short and simple proof of the following two theorems. Theorem 1. Suppose that C is a closed rectifiable Jordan curve in the complex l-plane and that C has a continuously turning tangent in a neighborhood of one of its points, XoSuppose, furthermore, that the tangent angle t(s) as function of the arc length s has a modulus of continuity (¡)(t) at the point s0 which corresponds to f0, i.e.,