Orlicz准范‖·‖_ρ与其亲模ρ的关系及其反演问题

The Relations Between Orlicz F-norm‖·‖_ρand Its Parental Modular ρ and the Inverting Problem

讨论了线性空间X上的模数ρ与其生成的Orlicz准范‖·‖，之间的关系，给出了六个关系命题；提出了准范的反演问题，得到了两个重要结果：线性空间上的任何β-范数（0＜β＜1）都是可反演的，而任何范数（β＝1）都是不可反演的．

In this paper, the relations between Orlicz F-norm ‖. ‖ ρ and its parental modular ρ are discussed and six propositions of such relations are given. The authors also proposed the inverting problem of F-norm and gave two important results:in every linear space,each β -norm (0＞ β＜1 ) can be inverted,but any norm (β = 1 ) cann't be inverted.