On Singular Integrals and Quantitative Rectifiability in Parabolic Space and the Heisenberg Group

Abstract

David and Semmes proved that if all CZOs (of suitable dimension) are bounded with respect to an Ahlfors regular measure, then the measure is uniformly rectifiable. We extend this theorem to the parabolic space and to all Heisenberg groups.

arXiv commentExtended our results to all Heisenberg groups and to higher codimensions in the Heisenberg groups, with a unified treatment of the parabolic and Heisenberg settings. 62 pages