Abstract
The following assertion is proved: a discrete subset λ of the unit disk can be represented as the union of n Carleson sets if and only if the traces of functions from H∞ on λ form a space of functions on λ for which the first n−1 divided differences (with respect to the hyperbolic metric) are uniformly bounded.
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Literature cited
V. I. Vasyunin, “Traces of bounded analytic functions on finite unions of Carleson sets,” in: Studies on Linear Operators and Function Theory. XII, J. Sov. Math.,27, No. 1 (1984).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 31–35, 1984.
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Vasyunin, V.I. Characterization of finite unions of Carleson sets in terms of solvability of interpolational problems. J Math Sci 31, 2660–2662 (1985). https://doi.org/10.1007/BF02107247
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DOI: https://doi.org/10.1007/BF02107247