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Algebra i Analiz, 2011, Volume 23, Issue 2, Pages 147–161 (Mi aa1237)  

This article is cited in 4 scientific papers (total in 4 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

Abstract: A Bernstein-type inequality for the standard Hardy space $H^2$ in the unit disk $\mathbb D=ż\in\mathbb C\colon|z|<1\}$ 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.

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English version:
St. Petersburg Mathematical Journal, 2012, 23:2, 309–319

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Received: 29.01.2010
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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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\paper Asymptotic sharpness of a~Bernstein-type inequality for rational functions in~$H^2$
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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. J. Math. Sci. (N. Y.), 182:5 (2012), 639–645  mathnet  crossref
    2. Baranov A. Zarouf R., “A Bernstein-Type Inequality for Rational Functions in Weighted Bergman Spaces”, Bull. Sci. Math., 137:4 (2013), 541–556  crossref  mathscinet  zmath  isi  elib  scopus
    3. Zarouf R., “Effective H-Infinity Interpolation”, Houst. J. Math., 39:2 (2013), 487–514  mathscinet  zmath  isi  elib
    4. Baranov A. Zarouf R., “A Model Space Approach To Some Classical Inequalities For Rational Functions”, J. Math. Anal. Appl., 418:1 (2014), 121–141  crossref  mathscinet  zmath  isi  elib  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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