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arXiv · 1512.07265

Characterization of the Hardy property of means and the best Hardy constants

Zsolt Páles·Paweł Pasteczka
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Abstract

The aim of this paper is to characterize in broad classes of means the so-called Hardy means, i.e., those means $M\colon\bigcup_{n=1}^\infty \mathbb{R}_+^n\to\mathbb{R}_+$ that satisfy the inequality $$ \sum_{n=1}^\infty M(x_1,\dots,x_n) \le C\sum_{n=1}^\infty x_n $$ for all positive sequences $(x_n)$ with some finite positive constant $C$. One of the main results offers a characterization of Hardy means in the class of symmetric, increasing, Jensen concave and repetition invariant means and also a formula for the best constant $C$ satisfying the above inequality.

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Zsolt Páles, Paweł Pasteczka. 2015-12-22. Characterization of the Hardy property of means and the best Hardy constants. https://doi.org/10.7153/mia-19-84

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