Abstract

Let ϕ be a continuous positive increasing function defined on [0,) such that ϕ(x+y)ϕ(x)+ϕ(y) and ϕ(0)=0. The Hardy-Orlicz space generated by ϕ is denoted by H(ϕ). In this paper, we prove that for ϕψ, if H(ϕ)=H(ψ) as sets, then H(ϕ)=H(ψ) as topological vector spaces. Some other results are given.