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In the recent paper, \cite{tilli} Nicola and Tilli proved the Faber-Krahninequality, which for $p=2$, states the following. If$f\in\mathcal{F}_\alpha^2$ is an entire function from the corresponding Fockspace, then $$\frac{1}{\pi}\int_{\Omega} |f(z)|^2 e^{-\pi |z|^2} dx dy \le(1-e^{-|\Omega|}) \|f\|^2_{2,\pi}.$$ Here $\Omega$ is a domain in the complexplane and $|\Omega|$ is its Lebesgue measure. This inequality is sharp andequality can be attained. We prove the following sharp inequality$$\int_{\Omega} \frac{|f^{(n)}(z)|^2e^{-\pi |z|^2}}{\pi^n n ! L_n(-\pi|z|^2)}dxdy \le (1-e^{-(n+1)|\Omega|})\|f\|^2_{2,\pi},$$ where $L_n$ isLaguerre polynomial, and $n\in\{0,1,2,3,4\} $. For $n=0$ it coincides with theresult of Nicola and Tilli.

Contraction property of differential operator on Fock space