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arXiv · 2004.11447

The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups

Vasileios Chousionis·Sean Li·Robert Young
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Abstract

We show that the $\beta$--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 $\beta$--number of a function on a cube of $\mathbb{R}^n$ using the $\beta$--number of the restriction of the function to codimension--1 slices of the cube.

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Vasileios Chousionis, Sean Li, Robert Young. 2020-04-23. The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups. https://arxiv.org/abs/2004.11447

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