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This article is cited in 3 scientific papers (total in 3 papers)
The interpolation of $l^r$ sequences by $H^p$ functions
S. V. Shvedenko
Abstract:
The sequence space $H^p(Z)=\{\{f(z_k)\}:f\in H^p\}$ is defined for a fixed sequence $Z=\{z_k\}$ of different points of the open unit disk and the Hardy class $H^p$ of analytic functions in the disk. For an arbitrary p $p\in[1,\infty)$ is constructed a point sequence $Z=\{z_k\}$ such that $l^1\subset H^p(Z)$, but $l^r\not\subset H^p(Z)$ for $r>1$. It follows from a well-known result of L. Carleson that the inclusions $l^r\subset H^\infty(Z)$ for all $r\in[1,\infty]$ are equivalent.
Received: 21.10.1974
Citation:
S. V. Shvedenko, “The interpolation of $l^r$ sequences by $H^p$ functions”, Mat. Zametki, 21:4 (1977), 503–508; Math. Notes, 21:4 (1977), 281–284
Linking options:
https://www.mathnet.ru/eng/mzm7978 https://www.mathnet.ru/eng/mzm/v21/i4/p503
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Abstract page: | 368 | Full-text PDF : | 72 | First page: | 1 |
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