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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Interpolation in $ H^{p}$ spaces


Authors: P. L. Duren and H. S. Shapiro
Journal: Proc. Amer. Math. Soc. 31 (1972), 162-164
MSC: Primary 30.67
DOI: https://doi.org/10.1090/S0002-9939-1972-0289781-0
MathSciNet review: 0289781
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Abstract: A construction is given to show that for each $ p < \infty $ there is a sequence of points in the unit disk which fails to satisfy Carleson's well-known condition, but which admits an $ {H^p}$ interpolation to every bounded sequence.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0289781-0
Keywords: Interpolation, $ {H^p}$ spaces, analytic functions, uniformly separated sequences, Blaschke products
Article copyright: © Copyright 1972 American Mathematical Society