Concave shells of continuity modules
UDC 517.9 The inequality $$ \overline{\omega}(t)\leq\inf_{s>0}\left(\omega\left(\dfrac{s}{2}\right)+\dfrac{\omega(s)}{s}t\right) $$ is proved, where $\omega(t)$ is a function of the modulus of continuity type and $\overline{\omega}(t)$ is its smallest concave majorant. The consequences...
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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/1470 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.9
The inequality
$$
\overline{\omega}(t)\leq\inf_{s>0}\left(\omega\left(\dfrac{s}{2}\right)+\dfrac{\omega(s)}{s}t\right)
$$
is proved, where $\omega(t)$ is a function of the modulus of continuity type and $\overline{\omega}(t)$ is its smallest concave majorant. The consequences obtained for Jackson's inequalities in $C_{2\pi}$ are presented. |
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