论文标题
无Lipschitz的空间中规范的不同性点
Points of differentiability of the norm in Lipschitz-free spaces
论文作者
论文摘要
我们考虑不利于Lipschitz的空间中的一系列分子，即$μ= \sum_nλ_n\ frac {Δ_{x_n}-Δ__{y_n}}} {d（x_n，y_n，y_n，y_n）} $ _____我们根据几何条件在点上的几何条件来表征这些元素，$ x_n $，基础度量空间的$ y_n $，并确定它们何时是标准的gâteaux可不同性的点。特别是，我们表明，gâteaux和fréchet的可不同性是在均匀离散和有限的度量空间上有限支撑的不含Lipschitz的空间的有限支撑元素，并且其具有Gâteaux（res.fréchet）banach空间不同元素的张量产品是banach空间的gâteaux（fréchet）的gâteaux（fréchet）的fréchet产品。
We consider convex series of molecules in Lipschitz-free spaces, i.e. elements of the form $μ=\sum_n λ_n \frac{δ_{x_n}-δ_{y_n}}{d(x_n,y_n)}$ such that $\|μ\|=\sum_n |λ_n |$. We characterise these elements in terms of geometric conditions on the points $x_n$, $y_n$ of the underlying metric space, and determine when they are points of Gâteaux differentiability of the norm. In particular, we show that Gâteaux and Fréchet differentiability are equivalent for finitely supported elements of Lipschitz-free spaces over uniformly discrete and bounded metric spaces, and that their tensor products with Gâteaux (resp. Fréchet) differentiable elements of a Banach space are Gâteaux (resp. Fréchet) differentiable in the corresponding projective tensor product.
