On the Cèsaro and Copson Norms of Nonnegative Sequences

The Cèsaro and Copson norms of a nonnegative sequence are the l p -norms of its arithmetic means and the corresponding conjugate means. It is well known that, for 1 < p < 1, these norms are equivalent. In 1996, G. Bennett posed the problem of finding the best constants in the associated inequa...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 71; no. 2; pp. 248 - 258
Main Author Kolyada, V. I.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2019
Springer
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Matematik
Mathematics
Mathematics and Statistics
Norms
Statistics
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Summary:The Cèsaro and Copson norms of a nonnegative sequence are the l p -norms of its arithmetic means and the corresponding conjugate means. It is well known that, for 1 < p < 1, 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 Bennett. We find one of the two unknown constants and also prove one optimal weighted-type estimate for the remaining constant.
ISSN:0041-5995
1573-9376
1573-9376
DOI:10.1007/s11253-019-01642-7