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arXiv · 1807.05010

The local symmetry condition in the Heisenberg group

Tuomas Orponen
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Abstract

I propose an analogue in the first Heisenberg group $\mathbb{H}$ of David and Semmes' local symmetry condition (LSC). For closed $3$-regular sets $E \subset \mathbb{H}$, I show that the (LSC) is implied by the $L^{2}(\mathcal{H}^{3}|_{E})$ boundedness of $3$-dimensional singular integrals with horizontally antisymmetric kernels, and that the (LSC) implies the weak geometric lemma for vertical $\beta$-numbers.

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Tuomas Orponen. 2018-07-13. The local symmetry condition in the Heisenberg group. https://arxiv.org/abs/1807.05010

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