论文标题
均匀分数Sobolev空间的表征
Characterisation of homogeneous fractional Sobolev spaces
论文作者
论文摘要
我们的目的是表征均质的sobolev-slobodecki \uıspaces $ \ nathcal {d}^{s，p}（\ sathbb {r}^n）$及其嵌入及其嵌入，以$ s \ in（0,1] $和$ p \ ge 1 $。 gagliardo-slobodecki \uıeminorms。函数的类别是添加剂常数，作为我们的主要工具之一，我们提出了一种莫雷 - 坎巴纳托不等式，其中gagliardo-slobobodecki \uıseminorm从上面的campanato seminorm上方控制。
Our aim is to characterize the homogeneous fractional Sobolev-Slobodecki\uı spaces $\mathcal{D}^{s,p} (\mathbb{R}^n)$ and their embeddings, for $s \in (0,1]$ and $p\ge 1$. They are defined as the completion of the set of smooth and compactly supported test functions with respect to the Gagliardo-Slobodecki\uı seminorms. For $s\,p < n$ or $s = p = n = 1$ we show that $\mathcal{D}^{s,p}(\mathbb{R}^n)$ is isomorphic to a suitable function space, whereas for $s\,p \ge n$ it is isomorphic to a space of equivalence classes of functions, differing by an additive constant. As one of our main tools, we present a Morrey-Campanato inequality where the Gagliardo-Slobodecki\uı seminorm controls from above a suitable Campanato seminorm.
