Geodesic
An inequality in Orlicz function spaces with Orlicz norm
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 507-514.

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We use Simonenko quantitative indices of an $\Cal N$-function $\Phi$ to estimate two parameters $q_\Phi$ and $Q_\Phi$ in Orlicz function spaces $L^\Phi[0,\infty)$ with Orlicz norm, and get the following inequality: $\frac{B_\Phi}{B_\Phi-1}\leq q_\Phi\leq Q_\Phi\leq \frac{A_\Phi}{A_\phi-1}$, where $A_\Phi$ and $B_\Phi$ are Simonenko indices. A similar inequality is obtained in $L^\Phi [0,1]$ with Orlicz norm.
Classification : 46B20, 46E30
Keywords: Orlicz spaces; Simonenko indices; $\triangle_2$-condition 
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     title = {An inequality in {Orlicz} function spaces with {Orlicz} norm},
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Wang, Jincai. An inequality in Orlicz function spaces with Orlicz norm. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 507-514. http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a8/