The space H+ϕ and its containing frechet space F+ ϕ

Abstract EN

Let D be the open unit disk in the complex plane C, H be the space of all analytic functions in D, and ^ be a modulus function such that ^(| /1) is subharmonic on D for all / eH.

The Hardy-Orlicz space is the space of all / sH such that ^(|/i) has a harmonic majorant on D and is the space of all / e such that has a quasi-bounded harmonic majorant on D.

In this paper we assume that ^ is a strictly increasing unbounded modulus function.

We study mean growth and Taylor coefficients of functions in and bounded subsets of it.

This will be a generalization of special cases such as N+ where (x) = log(l + ;r), Np where {x) ~ xp, 0 < p < \.

Also,we define a Frechet space Ff containing H+ which generalizes the special case N+.