Abstract

Subspaces of an Orlicz space L_M generated by probabilistically independent copies of a function \(f \in {{L}_{M}}\), \(\int_0^1 {f(t){\kern 1pt} dt} = 0\), are studied. In terms of dilations of f, we get a characterization of strongly embedded subspaces of this type and obtain conditions that guarantee that the unit ball of such a subspace has equi-absolutely continuous norms in L_M. A class of Orlicz spaces such that, for all subspaces generated by independent identically distributed functions, these properties are equivalent and can be characterized by Matuszewska–Orlicz indices is determined.

中文翻译：

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关于独立同分布函数跨越的 Orlicz 空间的子空间

摘要

Orlicz 空间L _M的子空间由函数\(f \in {{L}_{M}}\)、\(\int_0^1 {f(t){\kern 1pt} dt}的概率独立副本生成= 0\)，进行了研究。根据f的膨胀，我们得到了此类强嵌入子空间的表征，并获得了保证此类子空间的单位球在L _M中具有等绝对连续范数的条件。确定一类 Orlicz 空间，使得对于由独立同分布函数生成的所有子空间，这些属性是等价的并且可以用 Matuszewska-Orlicz 指数来表征。