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For 1 < p < ∞, the Privalov class Np consists of all holomorphic functions f  on the open unit disk D of the complex plane C such that sup 0≤r<1∫2π0  (log+ |f(reiθ)j|p dθ/2π < + ∞ M. Stoll [16] showed that the space Np with  the topology given by the metric dp defined as dp(f,g) = (∫2π0 (log(1 +  |f*(eiθ) - g*(eiθ)|))p dθ/2π)1/p, f,g  Np; becomes an F-algebra. Since  the map f → dp(f,0) (f  Np) is not a norm, Np is not a Banach algebra.  Here we investigate the structure of maximal ideals of the algebras Np (1 <  p < ∞). We also give a complete characterization of multiplicative linear  functionals on the spaces Np. As an application, we show that there exists a  maximal ideal of Np which is not the kernel of a multiplicative continuous  linear functional on Np.

Maximal ideals in some F-algebras of holomorphic functions