Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions
Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions
It is shown that if we restrict the identity minus Hardy operator on the cone of nonnegative decreasing functions $f$ in $L^{p}$, then we have the sharp estimate \begin{equation*} \left \| (I-H)f\right \| _{L^p}\leq \frac {1}{(p-1)^{\frac {1}{p}}}\left \| f\right \| _{L^p} \end{equation*} for $p=2,3,4,....$ In other words, \begin{equation*} \left \| …