Czechoslovak Mathematical Journal

, Volume 60, Issue 2, pp 513–516 | Cite as

Interpolation of bounded sequences

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Abstract

This paper deals with an interpolation problem in the open unit disc ⅅ of the complex plane. We characterize the sequences in a Stolz angle of ⅅ, verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on 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.

Keywords

interpolating sequence Carleson’s theorem uniformly separated Blaschke product Lipschitz class 

MSC 2010

30D50 30E05 
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References

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    K. R. M. Attele: Interpolating sequences for the derivatives of Bloch functions. Glasgow Math. J. 34 (1992), 35–41.MATHCrossRefMathSciNetGoogle Scholar
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    A. M. Kotochigov: 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.MATHCrossRefMathSciNetGoogle Scholar
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    E. P. Kronstadt: Interpolating sequences for functions satisfying a Lipschitz condition. Pacific J. Math. 63 (1976), 169–177.MATHMathSciNetGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2010

Authors and Affiliations

  1. 1.Facultad de CienciasUniversidad de VigoOurenseSpain

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