A short proof of an inequality of Carleson’s
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- by Charles W. Neville
- Proc. Amer. Math. Soc. 65 (1977), 131-132
- DOI: https://doi.org/10.1090/S0002-9939-1977-0444958-0
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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 $\Sigma (1 - |{a_i}{|^2})|f({a_i}){|^p} \leqslant K\left \|f\right \|_p^p$, for all $f \in {H^p}$ and $1 \leqslant p < \infty$.References
- Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 117349, DOI 10.2307/2372840
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- J. P. Earl, On the interpolation of bounded sequences by bounded functions, J. London Math. Soc. (2) 2 (1970), 544–548. MR 284588, DOI 10.1112/jlms/2.Part_{3}.544
- H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513–532. MR 133446, DOI 10.2307/2372892
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- 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