Let $s\in R$ . Consider the classical definition :
$$H^{s}(R^n) = \{ f \in S^{'}(R^n) / (1 + \| \theta \|^2)^{s/2} \hat{f} \in L^{2}(R^n) \}.$$
My book says $\widehat{(H^s (R^n))}$" = $L^2({R^n} , (1+|\theta|^2) d \theta)$. The inclusion $\widehat{(H^s (R^n))} \subset L^2({R^n} , (1+|\theta|^2) d \theta)$ is immediate. But i dont know prove the another part. Someone can give me a hint ?
Thanks in .
