Katrin Fässler

Singular integrals on regular curves in the Heisenberg group

This talk concerns certain singular integral operators in a non-Euclidean metric space, the Heisenberg group. According to a recent result joint with T. Orponen, smooth -1-homogeneous odd or 'horizontally odd' kernels induce L^2 bounded operators on regular curves in this setting. This extends a theorem of G. David from 1984 to the Heisenberg group. In the talk, I will discuss some of the challenges we encountered along the way, both regarding the structure of the kernels and the regular curves in the Heisenberg setting. I will not assume a priori knowledge of the Heisenberg group and give some motivation for studying this problem.