Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 23I / a / Solution

Let ${\mathcal{S}}^{\prime }({\mathbb{R}}^n)$ be the space of tempered distributions. For $s\in \mathbb{R}$, the Sobolev space $H^s({\mathbb{R}}^n)$ iswith normChanging the normalization of the Fourier transform changes this norm only by a fixed constant.