论文标题
一个和更高维度的常规度量的加性能量以及分形不确定性原理
Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle
论文作者
论文摘要
我们获得了一个和更高维度（AHLFORS-DAVID类型）常规度量的加性能量的新界限，这意味着相关常规集合的总和和产物的扩展结果以及这些集合的更通用的非线性函数。作为较高维度结果的推论，我们在奇数维度中获得了一些分形不确定性原理的新病例。
We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions of these sets. As a corollary of the higher-dimensional results we obtain some new cases of the fractal uncertainty principle in odd dimensions.
