One inequality of the Landau – Kolmogorov type for periodic functions of two variable
We obtain a new sharp inequality of the Landau – Kolmogorov type for a periodic function of two variables that estimates the convolution of the best uniform approximations of its partial primitives by the sums of univariate functions with the help of its $L_{\infty}$ -norm and uniform norms of its m...
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| Datum: | 2019 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1428 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We obtain a new sharp inequality of the Landau – Kolmogorov type for a periodic function of two variables that estimates
the convolution of the best uniform approximations of its partial primitives by the sums of univariate functions with the help
of its $L_{\infty}$ -norm and uniform norms of its mixed primitives. Some applications of the obtained inequality are presented. |
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