About a property of weighted Sobolev spaces

Question

If we define the weighted Sobolev norm as $$ \|f\|_{H^{s,k}(\mathbb R^n)} := \|(1+|x|^2)^{k/2} (\sqrt{1-\Delta})^s f \|_{L^2(\mathbb R^n)} $$ where $f(x):\mathbb R^n \to \mathbb R$ and $\Delta$ is Laplacian, $k\ge 0,s >0$, then does the following property $$ \| f\|_{H^{s,0}(\mathbb R^n)} \le C\| f\|_{H^{s,k}(\mathbb R^n)} $$ hold for any $k>0$?