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Algebra i Analiz, 2011, Volume 23, Issue 2, Pages 147–161 (Mi aa1237)  
This article is cited in 5 scientific papers (total in 5 papers)

Research Papers

Asymptotic sharpness of a Bernstein-type inequality for rational functions in $H^2$

R. Zarouf

CMI-LATP, UMR 6632, Université de Provence, Marseille cedex, France
Full-text PDF (241 kB) Citations (5)
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Abstract: A Bernstein-type inequality for the standard Hardy space $H^2$ in the unit disk $\mathbb D=\{z\in\mathbb C\colon|z|<1\}$ is considered for rational functions in $\mathbb D$ having at most $n$ poles all outside of $\frac1r\mathbb D$, $0<r<1$. The asymptotic sharpness is shown as $n\to\infty$ and $r\to1$.
Keywords: Bernstein inequality, finite Blaschke product, Hardy space.
Received: 29.01.2010
English version:
St. Petersburg Mathematical Journal, 2012, Volume 23, Issue 2, Pages 309–319
DOI: https://doi.org/10.1090/S1061-0022-2012-01198-2
Bibliographic databases:
Document Type: Article
Language: English
Citation: R. Zarouf, “Asymptotic sharpness of a Bernstein-type inequality for rational functions in $H^2$”, Algebra i Analiz, 23:2 (2011), 147–161; St. Petersburg Math. J., 23:2 (2012), 309–319
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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