Inclusions of Hardy Orlicz spaces

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 ϕ≠ψ, if H(ϕ)=H(ψ) as sets, then H(ϕ)=H(ψ) as topological vector spaces. Some other results are given.

Keywords

• modulus function
• Orlicz spaces.