Possible Duplicate:
if $f$ is entire and $|f(z)| \leq 1+|z|^{1/2}$, why must $f$ be constant?
Suppose $f$ is entire and $\exists c < \infty$ such that $|f(z)| \leq c (1+|z|^{\frac{1}{2}})$ for all $z \in \mathbb{C}$. Prove that $\exists \omega$ such that $f(z) = \omega$.
I've been stuck as it seems I can't use the maximum principle nor Liouville's theorem.