Geodesic
Restrictions of bounded analytic functions to a~finite union of Carleson sets
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 31-34

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Restriction of Hardy class $H^\infty$ to a union $\Lambda$ of $n$ Carleson sets is exactly the space of all functions on $\Lambda$ that have uniformly bounded divided difference (with respect to hyperbolic metric) of the order less than $n$. 
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     author = {V. I. Vasyunin},
     title = {Restrictions of bounded analytic functions to a~finite union of {Carleson} sets},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--34},
     publisher = {mathdoc},
     volume = {126},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a3/}
}
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V. I. Vasyunin. Restrictions of bounded analytic functions to a~finite union of Carleson sets. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 31-34. http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a3/