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Journal of Convex Analysis 11 (2004), No. 2, 391--400
Copyright Heldermann Verlag 2004

On the Exact Value of Packing Spheres in a Class of Orlicz Function Spaces

Ya Qiang Yan
Dept. of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, P. R. China,


Main result: the packing constants of Orlicz function spaces $L^{(\Phi)}[0,1]$ and $L^{\Phi}[0,1]$ with Luxemburg and Orlicz norm have the exact value. \medskip (i) If $F_\Phi(t)=t\varphi(t)/\Phi(t)$ is decreasing, $1 2,$ then $$ P(L^{(\Phi)}[0,1])=P(L^{\Phi}[0,1])=\frac{1}{1+2^{1/C_\Phi}}, $$ where $C_\Phi=\lim\limits_{t\rightarrow\infty} F_\Phi(t)$.

Keywords: Orlicz space, packing constants, Kottman constants.

MSC 2000: 46E30.

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