关于一个加强的Hardy不等式

On a Strengthened Version of Hardy's Inequality

证明了如下权系数ω(k)的不等式:ω(k)=k∞∑n=k1n2∑nj=11j≤4(1-θk)(k∈N),这里,θ=1-14n=∞∑1n12kn=∑11k=0.13788928+是最佳值.从而建立了一个加强的Hardy不等式(p=2).

In this paper, we prove the inequality of the weight coefficient （ω（k）=√k∞∑n=kn2 n∑j=i 1/√j≤4（1-θ/√k）（k∈N）,whereθ=（1-1/4∞∑n=1 1/n2 m∑k=1 1/√k）=0.13788928^＋ is the best value. Hence a strengthened version of Hardy＇s inequality （p=2） is established.