论文标题
分数Orlicz-Sobolev嵌入
Fractional Orlicz-Sobolev embeddings
论文作者
论文摘要
最佳Orlicz目标空间用于$ \ Mathbb r^n $中的分数Orlicz-Sobolev空间的嵌入。还建立了具有Orlicz-Lorentz目标空间的改进的嵌入，该目标空间在所有重排空间的更广泛类别中都是最佳的。订单$ s \ in（0,1）$的两个空间都考虑了高阶空间。还提出了相关的耐力类型不平等。证明了扩展定理，使我们能够为Lipschitz域定义的空间得出嵌入。提供了分数orlicz-sobolev嵌入的紧凑性的必要条件。
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. An extension theorem is proved, that enables us to derive embeddings for spaces defined in Lipschitz domains. Necessary and sufficient conditions for the compactness of fractional Orlicz-Sobolev embeddings are provided.
