The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz–Sobolev spaces in ${\mathbb{R}}^n$. An improved embedding with an Orlicz–Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order $s\in (0,1)$, and higher-order spaces are considered. Related Hardy type inequalities are proposed as well.

中文翻译：

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分数Orlicz-Sobolev嵌入

最优的Orlicz目标空间对于分数阶Orlicz-Sobolev空间的嵌入表现出来。 ${\mathbb{[R}}^{ñ}$。还建立了一种改进的嵌入Orlicz-Lorentz目标空间的方法，该方法在所有重排不变空间的更广泛类中都是最佳的。订单的两个空格$s\in （0，\mathrm{1个}）$，并考虑高阶空间。还提出了相关的Hardy型不等式。