Nevanlinna class

Summary

The Nevanlinna class $N$ is the space of holomorphic functions on the unit disc whose positive part of $\log \abs{f}$ has bounded averages on circles. Its elements are exactly the quotients of two bounded holomorphic functions with zero-free denominator, the functions of bounded type. It contains every Hardy space $H^p$, and its nonzero elements still have radial limits almost everywhere and zeros satisfying the Blaschke condition.