Geodesic
The scales of spaces $L_p$ and their connection with Orlicz spaces
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 33-56

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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. 
@article{VNGU_2006_6_2_a2,
     author = {A. E. Mamontov},
     title = {The scales of spaces $L_p$ and their connection with {Orlicz} spaces},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {33--56},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a2/}
}
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A. E. Mamontov. The scales of spaces $L_p$ and their connection with Orlicz spaces. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 33-56. http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a2/