The local symmetry condition in the Heisenberg group

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.

17 pages, 1 figure

Cited by in corpus (1)

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