Is there a smooth cut off function with compact support such that $\phi: \Omega \subset \mathbb R^N \to \mathbb R$, $\mathrm{supp} \phi \subset B_R(0) \subset \Omega$ and $$(-\Delta)^s \phi \le C R^{-2s} \text{ and } D^k(-\Delta)^s \phi \le C R^{-2s - k}?$$

Here (-\Delta)^s denotes the spectral fractional Laplacian