The scales of spaces $L_p$ and their connection with Orlicz spaces

We describe the classes of measurable functions which are estimated in the spaces $L_p$ with the norm $\omega(p)$ for all $p\in(\alpha,\beta)$. It is well-known for some simple functions $\omega$ and $\beta=+\infty$ that such classes are embedded into the appropriate Orlicz spaces. In this article we study the connection between these classes and other symmetric (Lorentz, Marcinkiewicz and Orlicz) spaces for arbitrary $\omega$, $\alpha$ and $\beta$. Our main goal is to show two-sided embedding or coincidence with Orlicz spaces.