What does $f \in H^\infty$ mean?

I am reading this research paper about polynomials with non-negative coefficients. Can some one tell what does the notation $f \in H^\infty$ mean so that I can research about this function class?

• To me it looks like a Hardy space, that is, that of bounded holomorphic functions on the unit disk with the supremmum norm. – busman Jul 14 '13 at 20:04

$H^\infty$ is the class of bounded holomorphic functions on the open unit disc (or sometimes the upper half-plane).