I am reading one book which states the following fact:
Suppose $f$ is an injective holomorphic function on $\{|z|>1\}$ and $$f(z)=z+b_0+b_1z^{-1}+b_2z^{-2}+\cdots$$ then $$\sum_{i=0}^nn|b_n|^2\leq 1$$ Is this a standard fact from complex analysis? How do we see it? Thank you very much.