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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 0444958
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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 $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0444958-0
PII: S 0002-9939(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