If both the $L^{2}(\mathbb R)$ norm and $L^{\infty}(\mathbb R)$ norm of a function $f$ are finite, is there any relation between the two norms in this case?
I know that there is a relation in case of a set of finite measure $S$, (i.e., $L^{2}(S)$ norm and $L^{\infty}(S)$), but what about the $\mathbb R$ case? If in general there is no relation, when we could have it?