论文标题
Laakso空间中的最大定向衍生物
Maximal Directional Derivatives in Laakso Space
论文作者
论文摘要
我们研究了最大定向衍生物与Lipschitz函数的不同定向衍生物之间的联系。我们表明，Lipschitz函数的定向衍生物的最大性仅意味着仅对于$σ$孔子集的点而言。另一方面，除了$σ$孔的点外，到达固定点的距离是可以区分的。这种行为与先前研究的欧几里得空间和Carnot组的设置完全不同。
We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiability only for a $σ$-porous set of points. On the other hand, the distance to a fixed point is differentiable everywhere except for a $σ$-porous set of points. This behavior is completely different to the previously studied settings of Euclidean spaces and Carnot groups.
