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.
@article{119404,
author = {Jin Cai Wang},
title = {An inequality in Orlicz function spaces with Orlicz norm},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {44},
year = {2003},
pages = {507-514},
zbl = {1103.46011},
mrnumber = {2025816},
language = {en},
url = {http://dml.mathdoc.fr/item/119404}
}
Wang, Jin Cai. An inequality in Orlicz function spaces with Orlicz norm. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 507-514. http://gdmltest.u-ga.fr/item/119404/
Geometry of Orlicz spaces, Dissertationes Mathematicae, Warszawa, 1996. | MR 1410390 | Zbl 1089.46500
Convex Functions and Orlicz Space, Noordhoff Ltd., Groningen, 1961. | MR 0126722
Classical Banach Spaces, I and II, Springer, Berlin, 1977 and 1979. | MR 0500056 | Zbl 0852.46015
Indices and interpolation, Dissertationes Math. (Rozprawy Mat.) 234 (1985). | MR 0820076 | Zbl 0566.46038
Linear Functional Analysis, World Scientific Publishing, Singapore, 1992. | MR 1182560 | Zbl 0799.46002
Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. | MR 1113700 | Zbl 0724.46032
Applications of Orlicz Spaces, Marcel Dekker, New York, 2002. | MR 1890178 | Zbl 0997.46027
Interpolation and extrapolation of linear operators in Orlicz spaces, Dokl. Akad. Nauk SSSR 151 (1963), 1288-1291 (Russian). (1963) | MR 0152872 | Zbl 0131.12104
Interpolation and extrapolation of linear operators in Orlicz spaces, Mat. Sb. (N.S.) 63 (105) (1964), 536-553 (Russian). (1964) | MR 0199696
Calculation of Orlicz norm and rotundity of Orlicz spaces, J. Harbin Inst. Techn. 10 (1973), 2 1-12 (Chinese). (1973)
On a pair of geometric parameters of Orlicz norm, Comment. Math. Prace Mat. 41 (2001), 257-263. (2001) | MR 1876724 | Zbl 1029.46026
Some results on packing in Orlicz sequence spaces, Studia Math. 147 (1) (2001), 73-88. (2001) | MR 1853478 | Zbl 0986.46004
Packing constants, weakly convergent sequence coefficients and Riesz angles in Orlicz sequence spaces, Ph.D. Dissertation, Suzhou Univ., Suzhou, P. R. China, 2002.