On an elementary approach to the fractional Hardy inequality
On an elementary approach to the fractional Hardy inequality
Let $H$ be the usual Hardy operator, i.e., $Hu(t)=\frac {1}{t}\int _0^tu(s) ds$. We prove that the operator $K=I-H$ is bounded and has a bounded inverse on the weighted spaces $L_p(t^{-\alpha },dt/t)$ for $\alpha >-1$ and $\alpha \not =0$. Moreover, by using these inequalities we derive a somewhat generalized form of …