In this paper, we investigate the 2-local isometries between the vector-valued differentiable function spaces $C_0^p(X,E)$ and $C_0^q(Y,E)$, where X, Y are open subsets of $\mathbb{R}$ and E is a smooth, strictly convex, reflexive and 2-iso-reflexive Banach space (in particular, when $1\le p<\mathrm{\infty }$ and $p\ne 2$, ${\ell }^p$ satisfies such conditions). We show that such maps can be written as weighted composition operators.

中文翻译：

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向量值可微函数上的两局部等距

在本文中，我们研究了向量值可微函数空间之间的2-局部等距 $C_0^p（X，Ë）$ 和 $C_0^q（ÿ，Ë）$，其中X，Y是的开放子集$\mathbb{[R}$和Ë是平滑，严格凸，自反和2-异自反Banach空间（特别是，当$\mathrm{1个}\le p<\mathrm{\infty }$ 和 $p\ne 2$， ${\ell }^p$满足此类条件）。我们证明了这样的图可以写为加权合成算子。