Nevanlinna functions as quotients

Abstract

Let f be a holomorphic function in the unit ball. Then f is a Nevanlinna function if and only if there exist Smirnov functions f+, f_ such that f = f/fand f_ has no zeros in the ball. Let B = Bn be the open unit ball in C( and S = OB be the unit sphere. If n = 1, then E) = B1 is the open unit disc i1i C. The Nevanlinna class N(B) is the set of all holomorphic functions f on B such that sup log+ fri du 0, there exists 6 > 0 such that