Abstract: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.
Keywords: Orlicz spaces, Simonenko indices, $\triangle _2$-condition
AMS Subject Classification: 46B20, 46E30