Solution
= Solution
$H^s(\mathbb R^d)=\{u\in\mathcal S':\int(1+|\xi|^2)^s|\widehat u(\xi)|^2d\xi<\infty\}$. For integer $s\ge0$, an equivalent norm is $\sum_{|\alpha|\le s}\|D^\alpha u\|_2^2$.
= Solution
$H^s(\mathbb R^d)=\{u\in\mathcal S':\int(1+|\xi|^2)^s|\widehat u(\xi)|^2d\xi<\infty\}$. For integer $s\ge0$, an equivalent norm is $\sum_{|\alpha|\le s}\|D^\alpha u\|_2^2$.