Geodesic
The geometric structure of regions, and direct theorems of the constructive theory of functions
Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 39-56

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Sufficient conditions and necessary conditions close to them are obtained for a bounded domain $G$ with Jordan boundary $L=\partial G$ to admit direct theorems of approximation theory in terms of the distance $\rho_{1+\frac1n}(z)$ from boundary points $z\in L$ to the $\bigl(1+\frac1n\bigr)$th level line of the function that maps the complement of the domain on the exterior of the unit disk. Bibliography: 21 titles. 
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     author = {V. V. Andrievskii},
     title = {The geometric structure of regions, and direct theorems of the constructive theory of functions},
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V. V. Andrievskii. The geometric structure of regions, and direct theorems of the constructive theory of functions. Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 39-56. http://geodesic.mathdoc.fr/item/SM_1986_54_1_a1/