I am trying to solve the following problem (9.33 in Folland's book).
If $H^s \subset C_0^k$, then $s>k+\frac{n}{2}$.
The hint suggests to use the closed graph theorem in order to show that the inclusion map $H^s \rightarrow C_0^k$ is continuous and hence that $\partial^{\alpha}\delta \in (H^s)^{*}$ for $|\alpha| \leq k$.
I tried to argue using sequences but I was not able to do it properly.
Can anyone help me?