St. Petersburg Mathematical Journal

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Asymptotic sharpness of a Bernstein-type inequality for rational functions in

Author: R. Zarouf
Original publication: Algebra i Analiz, tom 23 (2011), nomer 2.
Journal: St. Petersburg Math. J. 23 (2012), 309-319
MSC (2010): Primary 30H10, 30J10
Posted: January 24, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: A Bernstein-type inequality for the standard Hardy space in the unit disk $\mathbb{D}=\{z\in \mathbb{C}\,:\,\vert z\vert <1\}$ is considered for rational functions in $\mathbb{D}$ having at most poles all outside of $\frac {1}{r}\mathbb{D}$ , . The asymptotic sharpness is shown as $n\rightarrow \infty$ and $r\rightarrow 1$ .

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