Some recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings. The limits of these spaces when the smoothness parameter \(s\in (0,1)\) tends to either of the endpoints of its range are also discussed. This note is based on recent papers of ours, where additional material and proofs can be found.

中文翻译：

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关于分数Orlicz-Sobolev空间

对分数Orlicz-Sobolev空间理论的一些最新结果进行了调查。它们涉及具有最佳Orlicz目标的这些空间的Sobolev型嵌入，相关的Hardy型不等式以及紧凑嵌入的标准。还讨论了当平滑度参数\（s \ in（0,1）\）趋向于其范围的两个端点时，这些空间的极限。本说明基于我们最近的论文，可在其中找到其他材料和证明。