1301.1524 (Li Chen et al.)

Positivity of $|\gp|^a|\gq|^b+|\gq|^b|\gp|^a$    [PDF]

Li Chen, Heinz Siedentop

We show that $$\cJ_{a,b,n}:=\frac12(|\gp|^a|\gq|^b+|\gq|^b|\gp|^a)$$ is positive, if $n\geq b+a$. (Here $\gq$ is the multiplication by $x$ and $\gp:= \mathrm{i}^{-1}\nabla$.) Furthermore we show that it generalizes the generalized Hardy inequalities for the fractional Laplacians.

View original: http://arxiv.org/abs/1301.1524