What is a sufficient condition for $s>0$ such that
$$\mathcal{F} \dot{H^s} (\mathbb{R}^n) \hookrightarrow L^2(\mathbb{R}^n)$$
where $\dot{H^s} (\mathbb{R}^n)$ is the homogeneous sobolev space: $\dot{H^s}= (- \Delta)^{\frac{s}{2}} L^2$,
$\mathcal{F}$ stand for the Fourier transform,
$\mathcal{F} \dot{H^s} =\{f \in \mathcal{S}^{\prime} ; \mathcal{F}^{-1} f \in \dot{H^s} \}$, and
$||f||_{\mathcal{F} \dot{H^s} } = ||\ |x|^s f\ ||_{L^2}$.