Possible Duplicate:
Analytic function in the punctured plane satisfying $|f(z)| \leq \sqrt{|z|} + \frac{1}{\sqrt{z}}$ is constant
Let $f$ be an holomorphic function in $\mathbb C-\{0\} $ so that $|f(z)|\leq\sqrt{|z|}+\frac{1}{\sqrt{|z|}}.$
Prove that $f=\text{const}$.
I'd be happy for a hint.
Thanks.