On Copson’s inequalities for \(0< p<1\)

[摘要] Let $(\lambda_{n})_{n \geq1}$ be a positive sequence and let $\varLambda_{n}=\sum^{n}_{i=1}\lambda_{i}$. We study the following Copson inequality for $0p$: $$\begin{aligned} \sum^{\infty}_{n=1} \Biggl(\frac{1}{\varLambda_{n}} \sum^{\infty }_{k=n}\lambda_{k} x_{k} \Biggr)^{p} \geq \biggl( \frac{p}{L-p} \biggr)^{p} \sum^{\infty}_{n=1}x^{p}_{n}. \end{aligned}$$ We find conditions on $\lambda_{n}$ such that the above inequality is valid with the constant being the best possible.

[学科分类] 电力

[关键词] Copson’s inequalities