Revistes Catalanes amb Accés Obert (RACO)

The exact value of Jung constants in a class of Orlicz function spaces

Y. Q. Yan

Resum


Let $\Phi$ be an $N$-function. Then the Jung constants of the Orlicz function spaces $L^\Phi[0,1]$ generated by $\Phi$, equipped with the Luxemburg and Orlicz norms, have the following exact values: \item{(i)} if $F_\Phi(t)=t\varphi(t)/\Phi(t)$ is decreasing and $1 60 C_\Phi 60 2$, then $$ JC(L^{(\Phi)}[0,1])=JC(L^\Phi[0,1])=2^{1/C_\Phi-1}; $$ \item{(ii)} if $F_\Phi(t)$ is increasing and $C_\Phi 62 2$, then $$ JC(L^{(\Phi)}[0,1])=JC(L^\Phi[0,1])=2^{-1/C_\Phi}, $$ where $$C_\Phi=\lim_{t\to +\infty}t\varphi(t)/\Phi(t)$$.

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