作者:胡雪梅，崔云安
Authors:HU Xuemei,CUI Yunan摘要:模空间是经典 Lebesgue 和 Orlicz 空间的推广 。在模空间引入 Orlicz 范数 ,研究赋 Luxemburg 范数模空间与赋 Orlicz 范数模空间的单调性 。首先证明了模空间中 Luxemburg 范数与 Orlicz 范数是等价的,且赋 Orlicz 范数模空间是 Banach 空间 ,其次证明了赋 Orlicz 范数模空间是严格单调的,最后给出了赋 Luxemburg 范数模空间是严格单调的充要条件。
Abstract:Modular function spaces are extensions of Lebesgue spaces and Orlicz spaces. We introduce Orlicz norm in Modular function spaces, and study the monotonicity in modular function spaces equipped with O-norm and L-norm. Firstly, the paper demonstrates O-norm is equivalent to L-norm in modular function spaces, and modular function spaces equipped with O-norm are Banach spaces. Then, the paper demonstrates modular function spaces equipped with O-norm are strictly monotone. Lastly, the necessary and sufficient conditions of strict monotonicity of modular function spaces equipped with L-norm are given.

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