论文标题
惠特尼扩展定理，用于在Banach空间的尺度上进行值
A Whitney extension theorem for functions taking values in scales of Banach spaces
论文作者
论文摘要
我们介绍了Whitney扩展运算符的修改版本，用于从$ \ Mathbb {R}^n $的封闭子集收集功能中，并带有平滑操作员的Banach空间秤。我们证明了集合的扩展定理，其元素在量表的不同空间中取值。考虑这种收藏的动机来自关于多个实际变量功能的组成的非常基本的观察。在Banach空间的尺度上，证明基础上的想法是自然而然的，并且包括在扩展的构建中引入平滑操作员，并具有与每个惠特尼二元立方体直径相关的平滑参数。还给出了带有平滑算子的Banach空间尺度的经典示例，并证明了一些新的相关观察结果。
We introduce a modified version of the Whitney extension operators for collections of functions from a closed subset of $\mathbb{R}^n$ into scales of Banach spaces with smoothing operators. We prove an extension theorem for collections whose elements take values in different spaces of the scale. A motivation for considering this kind of collections comes from very basic observations on the composition of functions of more than one real variable. The idea at the base of the proof is rather natural in the context of scales of Banach spaces, and consists in introducing smoothing operators in the construction of the extension, with smoothing parameters related to the diameter of each Whitney dyadic cube. Classical examples of scales of Banach spaces with smoothing operators are also given, and some new related observations are proved.
