Global derivative contraction conjecture for Fock space

Let $\mathcal{F}_\alpha^2$ be the Fock space, let $f^{(n)}$ denote the $n$th derivative of $f$, and let $\mu_{n,\alpha}$ be the measure used in the weighted derivative norm. For $n\geqslant 0$, define

$$\|f^{(n)}\|^2_{2,n,\alpha}:=\int_{\mathbb{C}} {|f^{(n)}(z)|^2}d\mu_{n,\alpha}(z).$$

The global derivative contraction conjecture. For every $f\in\mathcal{F}_\alpha^2$,

$$\|f^{(n)}\|^2_{2,n,\alpha}\le \|f\|^2_{2,\alpha}.$$

The paper states this as a reduction of the preceding local inequality conjecture. Its resolution is not given in the supplied text.