赋广义Orlicz范数的Orlicz空间中k_x的两个特征

Two Characteristics of k_x in Orlicz Spaces Equipped with Generalized Orlicz Norm

由N-函数生成的赋广义Orlicz范数的Orlicz函数空间中每一点x都对应唯一k_x:||x||_(M,p)=1/(k_x)[1+ρ_M^p(k_xx)]1/p.文中给出了inf{k_x:||x||_(M,p)=1}>1和{k_x:a≤||x||_(M,p)≤b}(b≥a>0)有界的充要条件.

On the Orlicz function spaces generated by N - a function and equipped with the generalized Orlicz norm, there exists kx such that ｜｜ x ｜｜（M,p）=1/Kx[1 ＋ρM^P（Kxx）]（1/p） for every x∈L（M,p）.Both sufficient and necessary conditions were presented to make the bounded of inf {kx：｜｜ x ｜｜（M,p）= 1}1 and {kx：a≤｜｜ x｜｜（M,p）≤b}（ba0）.