Solution
= Solution
Let $\mathcal S'(\mathbb R^n)$ be the space of <tempered distributions>. For $s\in\mathbb R$, the <Sobolev space> $H^s(\mathbb R^n)$ is
$$
H^s(\mathbb R^n)=\left\{u\in\mathcal S'(\mathbb R^n):(1+|\xi|^2)^{s/2}\widehat u(\xi)\in L^2(\mathbb R^n)\right\},
$$
with norm
$$
\lVert u\rVert_{H^s}^2=\int_{\mathbb R^n}(1+|\xi|^2)^s|\widehat u(\xi)|^2\,d\xi.
$$
Changing the normalization of the <Fourier transform> changes this norm only by a fixed constant.