Question 33. from Folland's book is the following:
(Converse of the Sobolev Theorem) If $H_{s}(\mathbb{R}^n) \subset C_{0}^{k}(\mathbb{R}^n)$, then $s>k+\frac{1}{2} n$. (Use the closed graph theorem to show that the inclusion map $H_{s} \rightarrow C_{0}^{k}$ is continuous and hence that $\partial^{\alpha} \delta \in\left(H_{s}\right)^{*}$ for $|\alpha| \leq k$.)
To use the closed graph theorem, we need to know how to compare convergence in $ C_{0}^{k}$ and $H_{s}$. This is the first key point that I don't see. Moreover, I don't know how to proof the other facts too. I will appreciate any help or suggestions.