Let $\mathcal{F}L^1 (\mathbb R^d)= \{ f: \hat{f} \in L^1(\mathbb R^d)\}$ and standard Soboleve space norm is $\|f\|_{H^s} = \| \langle \cdot \rangle^s \hat{f}\|_{L^2}$ where $\langle \cdot \rangle = (1+ |\cdot|^2)^{1/2}.$
My Questions is: Can we expect that $\mathcal{F}L^1(\mathbb R^d) \subset H^s(\mathbb R^d)$ for $s<0$? If not, any counter example?