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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 2, Pages 7–15
DOI: https://doi.org/10.4213/faa144
(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
Full-text PDF (170 kB) Citations (1)
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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.
Received: 13.05.2002
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 2, Pages 86–93
DOI: https://doi.org/10.1023/A:1024400822042
Bibliographic databases:
Document Type: Article
UDC: 517.55
Language: Russian
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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  • https://www.mathnet.ru/eng/faa144
  • https://doi.org/10.4213/faa144
  • https://www.mathnet.ru/eng/faa/v37/i2/p7
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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