Theorem 2.1 in the book [‘Theory of Hp spaces by Peter. L Duren](https://books.google.co.in/books/about/Theory_of_Hp_Spaces.html?id=fs4rPPcJ7HUC&redir_esc=yhttp://) states that : Any function $f$ analytic on the unit disc belongs to the Nevanlinna class iff it is of the form $\frac{g}{h}$ where $g$ and $h$ are bounded analytic functions.


I have read the proof and know the construction of the functions $g$ and $h$. My question is, suppose $f$ is an outer function, then is the constructed $g$, the contant function 1? If yes, then can you tell me how?



Regarding representation of an outer function
No, g and h are the exp of the Poisson integral of the parts of log|f| that are less than 1 and bigger than 1 (last one taken with a minus and put in the denominator) respectively 


For example, f(z)=(1-z)/(1+z) is outer and is the ratio of the bounded functions 1-z and 1+z as obviously 1/f is not bounded either!


