论文标题
基于BANACH功能空间的矢量值sobolev空间
Vector-valued Sobolev spaces based on Banach function spaces
论文作者
论文摘要
众所周知，对于Banach有价值的功能，有几种定义Sobolev类的方法。我们通过弱衍生物与Reshetnyak-Sobolev空间以及牛顿空间进行比较。特别是，当三个同意时，我们提供足够的条件。同样，我们还修改了Lipschitz映射的差异标准和属性，以保留Sobolev空间，当它充当叠加操作员时。
It is known that for Banach valued functions there are several approaches to define a Sobolev class. We compare the usual definition via weak derivatives with the Reshetnyak-Sobolev space and with the Newtonian space; in particular, we provide sufficient conditions when all three agree. As well we revise the difference quotient criterion and the property of Lipschitz mapping to preserve Sobolev space when it acting as a superposition operator.
