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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Interpolating sequences for $ QA\sb{B}$


Authors: Carl Sundberg and Thomas H. Wolff
Journal: Trans. Amer. Math. Soc. 276 (1983), 551-581
MSC: Primary 30H05; Secondary 43A40, 46H15
MathSciNet review: 688962
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Abstract: Let $ B$ be a closed algebra lying between $ {H^\infty}$ and $ {L^\infty}$ of the unit circle. We define $ QA_B = H^\infty \cap \bar{B}$, the analytic functions in $ Q_B = B \cap \bar{B}$. By work of Chang, $ {Q_B}$ is characterized by a vanishing mean oscillation condition. We characterize the sequences of points $ \left\{{{z_n}} \right\}$ in the open unit disc for which the interpolation problem $ f({z_n}) = {\lambda _n}, n = 1, 2,\ldots$, is solvable with $ f \in {Q_B}$ for any bounded sequence of numbers $ \left\{{{\lambda _n}} \right\}$. Included as a necessary part of our proof is a study of the algebras $ Q{A_B}$ and $ {Q_B}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0688962-3
PII: S 0002-9947(1983)0688962-3
Article copyright: © Copyright 1983 American Mathematical Society