On a necessary condition for $L^p$ $(0 < p < 1)$-convergence (upper boundedness) of trigonometric series
In this paper we prove that the condition $\sum_{k=\left[\frac{n}{2}\right] }^{2n}\frac{\lambda _{k}(p)}{(|n-k|+1)^{2-p}}=o(1)\, \left(=O(1) \right),$ is a necessary condition for the $L^{p} (0<p<1)$-convergence (upper boundedness) of a trigonometric series. Precisely, the results extend some...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2015-07-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1386 |