convergence of functions.

Question

Let a sequence of functions $v_m$ that converges to $v$ in the space $L^{10/3}(\Omega)$, Where $\Omega$ is a bounded domain. Additionally, $\sup\limits_{m} |v_m|<C$, where $C$ is a constant.

Can I conclude that $v_m$ converges to $v$ in $L^{\infty}(\Omega)$?