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Mat. Zametki, 1971, Volume 10, Issue 1, Pages 53–56 (Mi mz7066)  

This article is cited in 2 scientific papers (total in 2 papers)

An extremal property of outer functions

B. I. Korenblum

Kiev State Technical University of Construction and Architecture

Abstract: Our main result is the following: if $f(z)$ is in the space $H^2$, and $F(z)$ is its outer part, then $\|F^{(n)}\|_{H^2}\le\|f^{(n)}\|_{H^2}$ $(n=1,2,…)$, the left side being finite if the right side is finite. Under certain essential restrictions, this inequality was proved by B.I. Korenblyum and V.S. Korolevich [1].

Full text: PDF file (282 kB)

English version:
Mathematical Notes, 1971, 10:1, 456–458

Bibliographic databases:

UDC: 517.5
Received: 19.06.1970

Citation: B. I. Korenblum, “An extremal property of outer functions”, Mat. Zametki, 10:1 (1971), 53–56; Math. Notes, 10:1 (1971), 456–458

Citation in format AMSBIB
\Bibitem{Kor71}
\by B.~I.~Korenblum
\paper An~extremal property of outer functions
\jour Mat. Zametki
\yr 1971
\vol 10
\issue 1
\pages 53--56
\mathnet{http://mi.mathnet.ru/mz7066}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=288274}
\zmath{https://zbmath.org/?q=an:0219.30022}
\transl
\jour Math. Notes
\yr 1971
\vol 10
\issue 1
\pages 456--458
\crossref{https://doi.org/10.1007/BF01747069}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. I. Korenblum, “Invariant subspaces of the shift operator in weighted Hilbert space”, Math. USSR-Sb., 18:1 (1972), 111–138  mathnet  crossref  mathscinet  zmath
    2. F. A. Shamoyan, “A boundedness criterion for Toeplitz operators in weighted Sobolev spaces of holomorphic functions on the polydisk”, Siberian Math. J., 53:3 (2012), 554–572  mathnet  crossref  mathscinet  isi
  • Математические заметки Mathematical Notes
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