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Zapiski Nauchnykh Seminarov LOMI, 1989, Volume 170, Pages 7–33
(Mi znsl4437)
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This article is cited in 18 scientific papers (total in 18 papers)
Inner functions and spaces of pseudocontinuable functions related to them
A. B. Aleksandrov
Abstract:
Let $\theta$ be an inner function; $\alpha\in\mathbb{C}$, $|\alpha|=1$. Then the harmonic function $\mathop{\mathrm{Re}}\frac{\alpha+\theta}{\alpha-\theta}$ is the Poisson integral of a singular measure $\sigma_\alpha$. The Clark theorem allows naturally to identify $H^2\ominus\theta H^2$ with $L^2(\sigma_\alpha)$. The aim of this paper is to investigate $L^p$-properties of this identification operator for $p\ne2$.
Citation:
A. B. Aleksandrov, “Inner functions and spaces of pseudocontinuable functions related to them”, Investigations on linear operators and function theory. Part 17, Zap. Nauchn. Sem. LOMI, 170, "Nauka", Leningrad. Otdel., Leningrad, 1989, 7–33; J. Soviet Math., 63:2 (1993), 115–129
Linking options:
https://www.mathnet.ru/eng/znsl4437 https://www.mathnet.ru/eng/znsl/v170/p7
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