Geodesic
The non-classical interpolation by analytic functions smooth up to the boundary
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 7-26

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Let $E$ be a closed subset of the unit circle $\mathbb T$. Necessary and sufficient conditions are found for validity of inclusion $X|_E\subset Y|_E$, $X$ being a Carleman class on $\mathbb T$ and $Y$ being an analytic Carleman or Hölder class. 
@article{ZNSL_1982_107_a0,
     author = {G. Ya. Bomash},
     title = {The non-classical interpolation by analytic functions smooth up to the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--26},
     publisher = {mathdoc},
     volume = {107},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a0/}
}
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G. Ya. Bomash. The non-classical interpolation by analytic functions smooth up to the boundary. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 7-26. http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a0/