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arXiv · 1806.07664

On Copson's inequalities for $0<p<1$

Peng Gao·Huayu Zhao
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Abstract

Let $(\lambda_n)_{n \geq 1}$ be a non-negative sequence with $\lambda_1>0$ and let $\Lambda_n=\sum^n_{i=1}\lambda_i$. We study the following Copson inequality for $0 p$, \begin{align*} \sum^{\infty}_{n=1}\left (\frac 1{\Lambda_n} \sum^{\infty}_{k=n}\lambda_k x_k \right )^p \geq \left ( \frac {p}{L-p}\right )^p \sum^{\infty}_{n=1}x^p_n. \end{align*} We find conditions on $\lambda_n$ such that the above inequality is valid with the constant being best possible.

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Peng Gao, Huayu Zhao. 2018-06-20. On Copson's inequalities for $0<p<1$. https://arxiv.org/abs/1806.07664

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