Interpolation in $H^{p}$ spaces
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- by P. L. Duren and H. S. Shapiro
- Proc. Amer. Math. Soc. 31 (1972), 162-164
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289781-0
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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 Carlesonβs well-known condition, but which admits an ${H^p}$ interpolation to every bounded sequence.References
- Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921β930. 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
- V. Kabaila, Interpolation sequences for the $H_{p}$ classes in the case $p<1$, Litovsk. Mat. Sb. 3 (1963), no.Β 1, 141β147 (Russian, with Lithuanian and English summaries). MR 0182735
- H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513β532. MR 133446, DOI 10.2307/2372892
- A. K. Snyder, Sequence spaces and interpolation problems for analytic functions, Studia Math. 39 (1971), 137β153. MR 306924, DOI 10.4064/sm-39-2-137-153
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 162-164
- MSC: Primary 30.67
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289781-0
- MathSciNet review: 0289781