Free interpolation for holomorphic functions regular to the boundary (Q761570)

A closed subset E of the closure Cl \({\mathbb{D}}\) of the unit disc \({\mathbb{D}}\) is said to be an s-set \((0<s\leq 1)\) if every function from the Lipschitz class \(Lip_ s(E)\) coincides on E with a function from \(Lip_ s(Cl {\mathbb{D}}),\) analytic in \({\mathbb{D}}\). A geometric description of s-sets for \(s\in (0,1)\) was found by \textit{E. M. Dyn'kin} [Mat. Sb., Nov. Ser. 109(151), 107-128 (1979; Zbl 0407.30024)]. The article provides a geometric description of 1-sets (its form differs from Dyn'kin's result). Another theme of the article is ''the free interpolation'' of \(C^ 1\)- Whitney jets by jets of functions of the class \(C^ 1(Cl {\mathbb{D}})\), analytic in \({\mathbb{D}}\).