Inclusions of Hardy-Orlicz spaces (Q1820358)

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