We define the Sobolev Space of order $s \in \mathbb{R}$ by:
$H^s(\mathbb{R^n})=${$f \in S'(\mathbb{R^n})$ s.t $(1+|\xi|^2)$$^\frac{s}{2}\hat{f} \in L^2(\mathbb{R^n)}$}
My question is, why if $s \gt \frac{n}{2}$, and $f$, $g \in H^s(\mathbb{R^n})$, then $f.g \in H^s(\mathbb{R^n})$
and
$||fg||_{H^s(\mathbb{R^n})} \le cst.||f||_{H^s(\mathbb{R^n})}.||g||_{H^s(\mathbb{R^n})}$?
I need some help please