It is a classical result that $L^p(\Omega) \subset L^q(\Omega)$ when $q<p$ and $|\Omega| < \infty$. I'd like to know if is there an Orlicz version of this fact. In other words, let $L^{G_1}$ and $L^{G_2}$ Orlicz spaces. When we have $L^{G_1} \subset L^{G_2}?$
It seems that this result holds only (maybe) if the Orlicz spaces $L^{G_1} \subset L^{G_2}$ satisfies the famous $\Delta_2$ and $\nabla_2$ conditions. That is
If you whant to know more about Orlicz Spaces see the beggining of https://arxiv.org/pdf/math/0602388.pdf
plug
Found as Theorem (2.2.3) in the text
Edgar, G. A.; Sucheston, Louis, Stopping times and directed processes, Encyclopedia of Mathematics and Its Applications. 47. Cambridge: Cambridge University Press. xii, 428 p. (1992). ZBL0779.60032.
The reference given there is Chapter II, section 13 of
Krasnosel’skiĭ, M. A.; Rutitskiĭ, Ya. B., Convex functions and Orlicz spaces, Groningen-The Netherlands: P. Noordhoff Ltd. ix, 249 p. (1961). ZBL0095.09103.