Some new generalizations of inequalities of Hardy and Levin-Cochran-Lee (Q2716966)

The authors obtain generalizations of Hardy's discrete or integral inequalities, as well as certain improvements of the so-called Levin-Cochran-Lee inequalities. We quote only the following result: Let \(p> 1\), \(a_i\geq 0\). Then NEWLINE\[NEWLINE\sum^n_{k=1} \Biggl({1\over k} \sum^k_{s= 1} a_s\Biggr)^p\leq n^{1-p}\cdot b^p_{n,p} \sum^n_{k=1} (1- b_{k- 1,p}/ b_{n,p}) a^p_k,NEWLINE\]NEWLINE where \(b_{m,p}= \sum^m_{s= 1} s^{-1/p}\).