论文标题
分数Orlicz-Sobolev空间中功能的界限
Boundedness of functions in fractional Orlicz-Sobolev spaces
论文作者
论文摘要
展示了将分数orlicz-sobolev空间连续嵌入$ l^\ infty（\ mathbb r^n）$的必要条件。在相同的假设下，来自相关分数空间的任何函数都显示为连续。还提供了此结果的改进。它们提供了最佳的ORLICZ目标空间，以及所讨论的嵌入中最佳重排的目标空间。这些结果补充了在亚临界情况下已经可用的结果，其中将嵌入到$ l^\ infty（\ mathbb r^n）$失败中。它们还增加了标准分数Sobolev空间的经典嵌入定理。
A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into $L^\infty(\mathbb R^n)$ is exhibited. Under the same assumption, any function from the relevant fractional-order spaces is shown to be continuous. Improvements of this result are also offered. They provide the optimal Orlicz target space, and the optimal rearrangement-invariant target space in the embedding in question. These results complement those already available in the subcritical case, where the embedding into $L^\infty(\mathbb R^n)$ fails. They also augment a classical embedding theorem for standard fractional Sobolev spaces.
