Duality for some large spaces of analytic functions

We characterize the duals and biduals of the L-p-analogues N-alpha(p) of th e standard Nevanlinna classes N-alpha, alpha greater than or equal to -1 an d 1 less than or equal to p < infinity. We adopt the convention to take N-- 1(p) to be the classical Smirnov class N+ for p = 1, and the Hardy-Orlicz s pace LHp (= (Log(+) H)(p)) for 1 < p < infinity. Our results generalize and unify earlier characterizations obtained by Eoff for alpha = 0 and alpha = -1, and by Yanigahara for the Smirnov class. Each N-alpha(p) is a complete metrizable topological vector space (in fact, even an algebra); it fails to be locally bounded and locally convex but ad mits a separating dual. Its bidual will be identified with a specific nucle ar power series space of finite type; this turns out to be the 'Frechet env elope' of N-alpha(p) as well. The generating sequence of this power series space is of the form (n(theta) ),GN for some 0 < theta < 1. For example, the thetas in the interval (1/2, 1) correspond in a bijective fashion to the Nevanlinna classes N-alpha, alp ha > -1, whereas the thetas in the interval (0, 1/2) correspond bijectively to the Hardy-Orlicz spaces LHp, 1 < p < infinity. By the work of Yanagihar a, theta =1/2 corresponds to N+. As in the work by Yanagihara, we derive our results from characterizations of coefficient multipliers from N-alpha(p) into various smaller classical s paces of analytic functions on Delta.