For $lim_{n \rightarrow \infty} \frac{ f(n) \log n } { g(n) } = 0$ we can construct languages in $DTime(g(n))$ but not in $DTime(f(n))$.

We know how to prove $Space(n) \neq NP$. Since $x \Rightarrow x 1^{|x|^2}$ is closed under NP but not Space due to the Space hierarchy theorem.

Question: do we know of any langauges in Space(n), but not in NP; or any languages in NP but not Space(n) ?