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Zapiski Nauchnykh Seminarov LOMI, 1989, Volume 170, Pages 7–33 (Mi znsl4437)  

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 $p\ne2$.
English version:
Journal of Soviet Mathematics, 1993, Volume 63, Issue 2, Pages 115–129
DOI: https://doi.org/10.1007/BF01099304
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Ale89}
\by A.~B.~Aleksandrov
\paper Inner functions and spaces of pseudocontinuable functions related to them
\inbook Investigations on linear operators and function theory. Part~17
\serial Zap. Nauchn. Sem. LOMI
\yr 1989
\vol 170
\pages 7--33
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4437}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1039571}
\zmath{https://zbmath.org/?q=an:0784.30030|0761.30017}
\transl
\jour J. Soviet Math.
\yr 1993
\vol 63
\issue 2
\pages 115--129
\crossref{https://doi.org/10.1007/BF01099304}
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  • https://www.mathnet.ru/eng/znsl/v170/p7
  • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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