Hardy's inequality - a complement (Q1113052)

We present the following complement to Hardy's inequality: \[ \int^{\infty}_{0}(t^{-1}\int^{\infty}_{t}f(s)ds)^ pdt\leq \pi p/\sin \pi p\int^{\infty}_{0}f(t)^ pdt, \] where \(0<p<1\) and f is non-negative and non-increasing. A discrete analogue is also given.