In Strang's book on Finite Element Method, the Sobolev's inequality is stated as followed: If $v$ is a function in $H^s$ and $s>n/2$, then $v$ is continuous and:
$$ \max \left| v(x_1, \cdots, x_n) \right| \leq C ||v||_s $$
Do we have similar results for functions that are C-continuous, i.e. $v \in C^s$?