Consider two Sobolev spaces $H^s(\mathbb R^n)$ and $H^t(\mathbb R^n)$ where $s>t$, if $V$ is a linear subspace of $H^s(\mathbb R^n)$ such that there exists a constant $C$ and any $f \in V$, we have $||f||_{H^s}\leq C||f||_{H^t}$.
Then my question is, is $V$ necessarily finite dimentional?