论文标题
矢量值函数的Sobolev空间
Sobolev spaces of vector-valued functions
论文作者
论文摘要
我们在这里关注矢量值函数的Sobolev型空间。对于打开的子集$ω\ subset \ mathbb {r}^n $和banach space $ v $，我们比较经典的sobolev space $ w^{1，p}（ω，v）$与所谓的sobolev-reshetnyak space $ r^{1，p}（1，p}（p}（ω）（ω）$。我们看到，通常，$ w^{1，p}（ω，v）$是$ r^{1，p}（ω，v）$的封闭子空间。作为主要结果，我们获得了$ w^{1，p}（ω，v）= r^{1，p}（p}（ω，v）$，并且只有当banach space $ v $具有radon-nikodým属性时
We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset $Ω\subset\mathbb{R}^N$ and a Banach space $V$, we compare the classical Sobolev space $W^{1,p}(Ω, V)$ with the so-called Sobolev-Reshetnyak space $R^{1,p}(Ω, V)$. We see that, in general, $W^{1,p}(Ω, V)$ is a closed subspace of $R^{1,p}(Ω, V)$. As a main result, we obtain that $W^{1,p}(Ω, V)=R^{1,p}(Ω, V)$ if, and only if, the Banach space $V$ has the Radon-Nikodým property
