Abstract

Main result: the packing constants of Orlicz function spaces L(Φ)[0,1]L^{(\Phi)}[0,1] and LΦ[0,1]L^{\Phi}[0,1] with Luxemburg and Orlicz norm have the exact value. (i) If FΦ(t)=tφ(t)/Φ(t)F_\Phi(t)=t\varphi(t)/\Phi(t) is decreasing, 1<CΦ<2,1<C_\Phi< 2, then P(L(Φ)[0,1])=P(LΦ[0,1])=21/CΦ2+21/CΦ;P(L^{(\Phi)}[0,1])=P(L^{\Phi}[0,1])=\frac{2^{1/C_\Phi}}{2+2^{1/C_\Phi}}; (ii) If FΦ(t)F_\Phi(t) is increasing, CΦ>2,C_\Phi> 2, then P(L(Φ)[0,1])=P(LΦ[0,1])=11+21/CΦ,P(L^{(\Phi)}[0,1])=P(L^{\Phi}[0,1])=\frac{1}{1+2^{1/C_\Phi}}, where CΦ=lim⁡t→∞FΦ(t)C_\Phi=\lim\limits_{t\rightarrow\infty} F_\Phi(t).

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Keywords

  • Orlicz space
  • packing constants
  • Kottman constants

Mathematics Subject Classification

46E30

References

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Suggested citation

Y. Q. Yan. “On the Exact Value of Packing Spheres in a Class of Orlicz Function Spaces.” Journal of Convex Analysis 11 (2004), No. 2, 391–400. https://doi.org/10.68381/jca11024

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Published by Heldermann Verlag, 2004. Rights now held by Banach Press LLC.