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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00463664, version 4 |
| arXiv: 1003.5066 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-03-26) | v2 (2010-07-06) | v3 (2011-03-25) | v4 (2012-06-28) |
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| A Bernstein-type inequality for rational functions in weighted Bergman spaces |
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| Anton Baranov 1Rachid Zarouf 2 |
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| (2012-06-27) |
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| Given $n\geq1$ and $r\in[0,\,1),$ we consider the set $\mathcal{R}_{n,\, r}$ of rational functions having at most $n$ poles all outside of $\frac{1}{r}\mathbb{D},$ were $\mathbb{D}$ is the unit disc of the complex plane. We give an asymptotically sharp Bernstein-type inequality for functions in $\mathcal{R}_{n,\, r}\:$ (as n tends to infinity and r tends to 1-) in weighted Bergman spaces with ''polynomially'' decreasing weights. We also prove that this result can not be extended to weighted Bergman spaces with ''super-polynomially'' decreasing weights. |
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| 1: | Department of Mathematics and Mechanics |
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St. Petersburg State University |
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| 2: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Subject | : | Mathematics/Functional Analysis |
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| Rational function – Bernstein-type inequality – weighted Bergman norm |
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| hal-00463664, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00463664 | |
| oai:hal.archives-ouvertes.fr:hal-00463664 | |
| From: Rachid Zarouf | |
| Submitted on: Wednesday, 27 June 2012 15:17:22 | |
| Updated on: Thursday, 28 June 2012 08:46:41 | |
