论文标题
Heisenberg组中固有的Lipschitz图的强烈几何引理
The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
论文作者
论文摘要
我们表明，$β$ - Heisenberg组的内在Lipschitz图$ \ Mathbb {H} _n $是本地Carleson可在$ N \ geq 2 $时进行的。我们的技术依赖于最近的Dorronsoro不平等\ cite {fo}以及一个新颖的切片论点。我们证明中的关键要素是欧几里得不等式的限制了$β$ - 使用$ \ mathbb {r}^n $的函数的数量，使用$β$ - 函数限制到condimension to Codioimension-1 slices of Cube的限制数量。
We show that the $β$--numbers of intrinsic Lipschitz graphs of Heisenberg groups $\mathbb{H}_n$ are locally Carleson integrable when $n \geq 2$. Our technique relies on a recent Dorronsoro inequality \cite{FO} as well as a novel slicing argument. A key ingredient in our proof is a Euclidean inequality bounding the $β$--number of a function on a cube of $\mathbb{R}^n$ using the $β$--number of the restriction of the function to codimension--1 slices of the cube.
