On Cèsaro and Copson norms of nonnegative sequences
The C`esaro and Copson norms of a nonnegative sequence are lp-norms of its arithmetic means and the corresponding conjugate means. It is well known that, for $1 < p < \infty$, these norms are equivalent. In 1996, G. Bennett posed the problem of finding the best constants in the associa...
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| Date: | 2019 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1433 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | The C`esaro and Copson norms of a nonnegative sequence are lp-norms of its arithmetic means and the corresponding
conjugate means. It is well known that, for $1 < p < \infty$, these norms are equivalent. In 1996, G. Bennett posed the problem
of finding the best constants in the associated inequalities. The solution of this problem requires the evaluation of four
constants. Two of them were found by G. Bennett. We find one of the two unknown constants and also prove one optimal
weighted-type estimate regarding the remaining constant. |
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