Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
Orlicz spaces; Simonenko indices; $\triangle_2$-condition
Orlicz spaces; Simonenko indices; $\triangle_2$-condition
Summary:
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.
References:
[1] Chen S.T.: Geometry of Orlicz spaces. Dissertationes Mathematicae, Warszawa, 1996. MR 1410390 | Zbl 1089.46500
[2] Krasnosel'skii M.A., Rutickii Ya.B.: Convex Functions and Orlicz Space. Noordhoff Ltd., Groningen, 1961. MR 0126722
[3] Lindenstrauss J., Tzafriri L.: Classical Banach Spaces. I and II, Springer, Berlin, 1977 and 1979. MR 0500056 | Zbl 0852.46015
[4] Maligranda L.: Indices and interpolation. Dissertationes Math. (Rozprawy Mat.) 234 (1985). MR 0820076 | Zbl 0566.46038
[5] Orlicz W.: Linear Functional Analysis. World Scientific Publishing, Singapore, 1992. MR 1182560 | Zbl 0799.46002
[6] Rao M.M., Ren Z.D.: Theory of Orlicz Spaces. Marcel Dekker, New York, 1991. MR 1113700 | Zbl 0724.46032
[7] Rao M.M., Ren Z.D.: Applications of Orlicz Spaces. Marcel Dekker, New York, 2002. MR 1890178 | Zbl 0997.46027
[8] Simonenko I.B.: Interpolation and extrapolation of linear operators in Orlicz spaces. Dokl. Akad. Nauk SSSR 151 (1963), 1288-1291 (Russian). MR 0152872 | Zbl 0131.12104
[9] Simonenko I.B.: Interpolation and extrapolation of linear operators in Orlicz spaces. Mat. Sb. (N.S.) 63 (105) (1964), 536-553 (Russian). MR 0199696
[10] Wu C.X., Zhao S.Z., Chen J.O.: Calculation of Orlicz norm and rotundity of Orlicz spaces. J. Harbin Inst. Techn. 10 (1973), 2 1-12 (Chinese).
[11] Yan Y.: On a pair of geometric parameters of Orlicz norm. Comment. Math. Prace Mat. 41 (2001), 257-263. MR 1876724 | Zbl 1029.46026
[12] Yan Y.: Some results on packing in Orlicz sequence spaces. Studia Math. 147 (1) (2001), 73-88. MR 1853478 | Zbl 0986.46004
[13] Yan Y.Q.: Packing constants, weakly convergent sequence coefficients and Riesz angles in Orlicz sequence spaces. Ph.D. Dissertation, Suzhou Univ., Suzhou, P. R. China, 2002.
Search
Partner of
