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Proceedings of the American Mathematical Society

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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
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.


References [Enhancements On Off] (What's this?)

  • [1] Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 0117349
  • [2] Peter L. Duren, Theory of 𝐻^{𝑝} spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
  • [3] V. Kabaila, Interpolation sequences for the 𝐻_{𝑝} classes in the case 𝑝<1, Litovsk. Mat. Sb. 3 (1963), no. 1, 141–147 (Russian, with Lithuanian and English summaries). MR 0182735
  • [4] H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513–532. MR 0133446
  • [5] A. K. Snyder, Sequence spaces and interpolation problems for analytic functions, Studia Math. 39 (1971), 137–153. MR 0306924

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Additional Information

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