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A short proof of an inequality of Carleson's


Author: Charles W. Neville
Journal: Proc. Amer. Math. Soc. 65 (1977), 131-132
MSC: Primary 30A78; Secondary 30A80
DOI: https://doi.org/10.1090/S0002-9939-1977-0444958-0
MathSciNet review: 0444958
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a simple proof that if $ {a_i},i = 1,2, \ldots $, is a uniformly separated sequence in the unit disk, then $ \Sigma (1 - \vert{a_i}{\vert^2})\vert f({a_i}){\vert^p} \leqslant K\left\Vert f\right\Vert _p^p$, for all $ f \in {H^p}$ and $ 1 \leqslant p < \infty $.


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

  • [1] L. Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921-930. MR 22 #8129. MR 0117349 (22:8129)
  • [2] P. L. Duren, Theory of $ {H^p}$ spaces, Academic Press, New York, 1970. MR 42 #3552. MR 0268655 (42:3552)
  • [3] J. P. Earl, On the interpolation of bounded sequences by bounded functions, J. London Math. Soc. (2) 2 (1970), 544-548 MR 44 #1813. MR 0284588 (44:1813)
  • [4] H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513-532. MR 24 #A3280. MR 0133446 (24:A3280)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0444958-0
Keywords: Carleson interpolation theorem, $ {H^p}$ space, Blaschke product, $ {A^{2,1}}$ space, uniformly separated sequence
Article copyright: © Copyright 1977 American Mathematical Society

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