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Keywords:
interpolating sequence; Carleson's theorem; uniformly separated; Blaschke product; Lipschitz class
interpolating sequence; Carleson's theorem; uniformly separated; Blaschke product; Lipschitz class
Summary:
This paper deals with an interpolation problem in the open unit disc $\mathbb D$ of the complex plane. We characterize the sequences in a Stolz angle of $\mathbb D $, verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on $\mathbb D $, but very close to the bounded ones. We prove that these interpolating sequences are also uniformly separated, as in the case of the interpolation by bounded holomorphic functions.
References:
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[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. DOI 10.1007/s10958-005-0339-0 | MR 2037538 | Zbl 1151.30339
[4] Kronstadt, E. P.: Interpolating sequences for functions satisfying a Lipschitz condition. Pacific J. Math. 63 (1976), 169-177. DOI 10.2140/pjm.1976.63.169 | MR 0412431 | Zbl 0306.30030
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