Summation of p-Faber series by the Abel–poisson method in the integral metric
We establish conditions on the boundary \( \Gamma \) of a bounded simply connected domain \( \Omega \subset \mathbb{C} \) under which the p-Faber series of an arbitrary function from the Smirnov space \( {E_p}\left( \Omega \right),1 \leqslant p < \infty \), can be summed by the Abel–Poisson m...
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| Datum: | 2010 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2896 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We establish conditions on the boundary \( \Gamma \) of a bounded simply connected domain \( \Omega \subset \mathbb{C} \) under which the p-Faber series of an arbitrary function from the Smirnov space \( {E_p}\left( \Omega \right),1 \leqslant p < \infty \), can be summed by the Abel–Poisson method on the boundary of the domain up to the limit values of the function itself in the metric of the space \( {L_p}\left( \Gamma \right) \). |
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