In this talk, we consider the space $\mathbb R^d \times \mathbb R^m$ endowed with the structure of a two-step nilpotent Lie group. We focus on a class of maximal operators initially introduced by Nevo and Thangavelu in the setting of the Heisenberg group, which involve noncommutative convolutions associated with measures supported on generalized spheres. Building upon and extending previous results for Métivier groups, we remove the non-degeneracy assumptions and establish sharp $L^p$ boundedness on all two-step nilpotent Lie groups in dimension $d \ge 3$. This talk is based on a joint work with Andreas Seeger.

The video of this talk is available on the IISc Math Department channel.