论文标题
当地消失的平均振荡
Local vanishing mean oscillation
论文作者
论文摘要
我们考虑了在（可能无限的）域$ω\ subset \ mathbb {r}^n $上的各种含义振荡的概念，并证明了萨拉森定理的类似物，为非杂音空间$ \ rm \ rm \ rm {vmo} $ {vmo} $ {vmo} $}（vmo} $}（））$ {vmo} $}（）$}（）我们还研究了连续功能的$ \ rm {cmo}（ω）$，$ \ rm {bmo}（ω）$，并在$ω$中进行紧凑的支持。使用这些近似结果，我们证明，从$ \ rm {vmo}（ω）$和$ \ rm {cmo}（ω）$从$ \ \ \ mathbb {rmathbb {r}^n $上的相应空间中有一个有限的扩展名。
We consider various notions of vanishing mean oscillation on a (possibly unbounded) domain $Ω\subset \mathbb{R}^n$, and prove an analogue of Sarason's theorem, giving sufficient conditions for the density of bounded Lipschitz functions in the nonhomogeneous space $\rm{vmo}(Ω)$. We also study $\rm{cmo}(Ω)$, the closure in $\rm{bmo}(Ω)$ of the continuous functions with compact support in $Ω$. Using these approximation results, we prove that there is a bounded extension from $\rm{vmo}(Ω)$ and $\rm{cmo}(Ω)$ to the corresponding spaces on $\mathbb{R}^n$, if and only if $Ω$ is a locally uniform domain.
