Geodesic
Asymptotic sharpness of a~Bernstein-type inequality for rational functions in~$H^2$
Algebra i analiz, Tome 23 (2011) no. 2, pp. 147-161.

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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 $\frac1r\mathbb D$, $0$. The asymptotic sharpness is shown as $n\to\infty$ and $r\to1$.
Keywords: Bernstein inequality, finite Blaschke product, Hardy space. 
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R. Zarouf. Asymptotic sharpness of a~Bernstein-type inequality for rational functions in~$H^2$. Algebra i analiz, Tome 23 (2011) no. 2, pp. 147-161. http://geodesic.mathdoc.fr/item/AA_2011_23_2_a5/

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