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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 2, Pages 7–15 (Mi faa144)  

This article is cited in 1 scientific paper (total in 1 paper)

Weakly Outer Inner Functions

E. Doubtsov

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: An inner function $I$ in the unit ball $B_n\subset\mathbb{РЎ}^n$ is said to be weakly outer if the closed subspace $IH^p(B_n)$ is weakly dense in the Hardy space $H^p(B_n)$, $0<p<1$. We construct weakly outer inner functions in the ball $B_n$ for all $n\ge 1$. We also investigate inner functions $I$ such that the subspace $I H^p(B_n)$ is not weakly dense in $H^p(B_n)$.

Keywords: Hardy class, pluriharmonic measure

DOI: https://doi.org/10.4213/faa144

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English version:
Functional Analysis and Its Applications, 2003, 37:2, 86–93

Bibliographic databases:

UDC: 517.55
Received: 13.05.2002

Citation: E. Doubtsov, “Weakly Outer Inner Functions”, Funktsional. Anal. i Prilozhen., 37:2 (2003), 7–15; Funct. Anal. Appl., 37:2 (2003), 86–93

Citation in format AMSBIB
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\pages 7--15
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  • https://doi.org/10.4213/faa144
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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. E. Doubtsov, “Bounded cyclic functions in the ball”, J. Math. Sci. (N. Y.), 129:4 (2005), 3985–3989  mathnet  crossref  mathscinet  zmath
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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