International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 429-434

Inclusions of Hardy Orlicz spaces

Roshdi Khalil

Department of Mathematics, The University of Michigan, Ann Arbor 48109, Michigan, USA

Received 9 September 1985; Revised 24 February 1986

Copyright © 1986 Roshdi Khalil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.