Let me define it first,
Let $f:\mathbb{R}\to\mathbb{R^+}\cup\{\infty\}$ be a convex function with the following conditions
(1) $\Phi(x)=\Phi(-x)$
(2) $\Phi(0)=0$
(3)$lim_{x\to \infty}\Phi(x)=\infty$
The Orlicz space is defined by a collection of real-valued measurable functions on an arbitrary measure space $(\Omega, F,\mu)$ $f:\Omega\to \mathbb{R}$
$L^{\Phi}=\{f:\Omega\to \mathbb{R}\text{ such that } \int_{\Omega}\Phi(\alpha|f|)d\mu<\infty \text{ for some } \alpha>0\}$
I know that $L^{\Phi}$ is a Normed linear space.
$\textbf{My Question:}$ I am taking $\Phi$ which is of the type $e^{(\frac{-1}{x^2})}\Phi(x)$ as we see that this is also satisfying all the properties of $\Phi$.So now If I define the Orlicz space with the help of this we get
$$L^{e^{(\frac{-1}{x^2})}\Phi(x)}=\{f:\Omega\to \mathbb{R} \text{ such that } \int_{\Omega}e^{\frac{-1}{(\alpha f)^2}}\Phi(\alpha|f|)d\mu<\infty\}$$
If I defined it correctly, then can I say that this will be the subspace of $L^{\Phi}$?? My intuition say's it is a subspace but I am not sure.