ON THE NEVANLINNA CLASSES OF HOLOMORPHIC FUNCTIONS ON COMPACT BORDERED RIEMANN SURFACES

摘要

In this paper, the Nevanlinna class of holomorphlc functions on compact bordered Riemann surface Ω is discussed. This class is denoted by N(Ω), containing the class H~p(Ω). It is proved that f∈N(Ω) if and only if f=φ/ψ,where φ and ψ are bounded holomorphic functions in Ω,and the Fatou boundary property is discussed.