论文标题
$ p $ - 效果可区分结构的张力
Tensorization of $p$-weak differentiable structures
论文作者
论文摘要
我们认为$ p $ - 效果可区分的结构最近是由第一位和最后一个命名的作者引入的，并证明了$ p $ - weak图表的产品是$ p $ - 效果图。这意味着两个带有$ p $ weak可区分结构的空间的产物也承认了$ p $ - 效果可区分的结构。我们通过显示等轴测嵌入结果，在Sobolev空间的张力问题上进行部分进展。此外，当其中一个因素是PI时，我们会建立张力。
We consider $p$-weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of $p$-weak charts is a $p$-weak chart. This implies that the product of two spaces with a $p$-weak differentiable structure also admits a $p$-weak differentiable structure. We make partial progress on the tensorization problem of Sobolev spaces by showing an isometric embedding result. Further, we establish tensorization when one of the factors is PI.
