Is it true that the space $H^{1}(I)$ is contained compactly in $L^{2}(I)$?

Question

Consider $I$ a limited range. Is it true that the space $H^{1}(I)$ is contained compactly in $L^{2}(I)$?

I ask this question because Brezis, the author states that $W^{1,1}(I)$ is contained compactly in $L^{2}(I)$. What about $H^{1} (I) = W^{1,2}(I)$?