The Cèsaro and Copson norms of a nonnegative sequence are the lp -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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 2, pp. 220–229, February, 2019.
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Kolyada, V.I. On the Cèsaro and Copson Norms of Nonnegative Sequences. Ukr Math J 71, 248–258 (2019). https://doi.org/10.1007/s11253-019-01642-7
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DOI: https://doi.org/10.1007/s11253-019-01642-7