Multiplicative linear functionals and ring homomorphisms of

Abstract

The Hardy-Orlicz space Hϕ is the space of all analytic functions f on the open unit disk D such that the subharmonic function ϕ(|f|) has a harmonic majorant on D where Á is a modulus function.

is the space of all f ϵ H_ϕ such that ϕ(|f|) has a quasi-bounded harmonic majorant on D. Under certain constraints on Á we show that multiplicative linear functionals on

are exactly point evaluation and ring homomorphisms of

are just composition operators. Examples of such ϕ are ϕ(x)=(log(1+x))p and ϕ(x)=log(1+x^p ), 0 < p ≤ 1. This generalizes the special case p = 1 where

is the well known Smirnov class N ⁺.

Keywords and phrases:

• Hardy-Orlicz space
• F-space
• modulus function
• multiplicative linear functional
• composition operator
• rings of analytic functions
• ring homomorphisms