Sharp Hardy inequalities in the half space with trace remainder term

In this paper, we deal with a class of inequalities which interpolate the Kato inequality and the Hardy inequality in the half space. Starting from the classical Hardy’s inequality in the half space R+n=Rn−1×(0,∞), we show that, if we replace the optimal constant (n−2)24 with a smaller one (β−2)24, 2≤β