Interpolation sets for Lipschitz functions on curves of the unit sphere (Q1262978)

We show that if E is the set of complex-tangential points of a smooth simple curve contained in the unit sphere of \({\mathbb{C}}^ n\), then any function belonging to the Lipschitz space on E of order \(2\alpha\) \((0<\alpha <1)\) has an holomorphic extension in the unit ball which satisfies a Lipschitz condition of order \(\alpha\) with respect to the euclidean distance, that is E is an interpolation set for the space \(Lip_{\alpha}(B)\) of holomorphic Lipschitz functions.