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Interpolation for a subclass of \(H^\infty\). (English) Zbl 1307.30076

Summary: We introduce and characterize two types of interpolating sequences in the unit disc \(\mathbb D\) of the complex plane for the class of all functions being the product of two analytic functions in \(\mathbb D\), one bounded and another regular up to the boundary of \(\mathbb D\), concretely in the Lipschitz class, and at least one of them vanishing at some point of \(\bar{\mathbb D}\).

MSC:

30E05 Moment problems and interpolation problems in the complex plane
30H05 Spaces of bounded analytic functions of one complex variable
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References:

[1] Bruna J, Nicolau A and Øyma K, A note on interpolation in the Hardy spaces of the unit disc, Proc. Amer. Math. Soc.124 (1996) 1197-1204 · Zbl 0841.30032
[2] Carleson L, An interpolation problem for bounded analytic functions, Amer. J. Math.80 (1958) 921-930 · Zbl 0085.06504
[3] Kotochigov A M, Free interpolation in the spaces of analytic functions with derivative of order s from the Hardy space, J. Math. Sci. (N. Y.)129 (2005) 4022-4039 · Zbl 1151.30339
[4] Kronstadt E P, Interpolating sequences for functions satisfying a Lipschitz condition, Pacific. J. Math.63 (1976) 169-177 · Zbl 0306.30030
[5] Vasyunin V I, Characterization of finite unions of Carleson sets in terms of solvability of interpolation problems. (Russian) Investigations on linear operators and the theory of functions, XIII. Zap. Nauchn. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)135 (1984) 31-35 · Zbl 0545.41005
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