Derivatives of $H^{p}$ functions
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- by Knut Øyma and Serge Rookshin
- Proc. Amer. Math. Soc. 84 (1982), 97-98
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633286-8
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Abstract:
We prove that if $\{ {z_n}\}$ is uniformly separated and $f \in {H^p}$, then $\{ {f^{(k)}}({z_n}){(1 - {\left | {{z_n}} \right |^2})^{k + 1/p}}\} _{n = 1}^\infty \in {l^p}\;{\text {for }}k = 1,2, \ldots$.References
- 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
- Knut Øyma, Interpolation in $H^{p}$-spaces, Proc. Amer. Math. Soc. 76 (1979), no. 1, 81–88. MR 534394, DOI 10.1090/S0002-9939-1979-0534394-2 F. A. Shamoian, Embedding theorems connected with problems of multiple interpolation in ${H^p}$, Proc. Armenian Academy of Sciences, No. 2 (1976). (Russian)
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 97-98
- MSC: Primary 30E05; Secondary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633286-8
- MathSciNet review: 633286