Por Andreas Seeger (University of Wisconsin-Madison).

Consider $\mathbb R^d\times \mathbb R^m$ with the group structure of a $2$-step Carnot Lie group and natural parabolic dilations. The maximal operator originally introduced by Nevo and Thangavelu in the setting of the Heisenberg groups is generated by (noncommutative) convolution associated with measures on spheres or generalized spheres in $\mathbb R^d$. We discuss a number of approaches that have been taken to prove $L^p$ boundedness and then talk about recent work with Jaehyeon Ryu in which we drop the nondegeneracy condition in the known results on Métivier groups. The new results have the sharp $L^p$ boundedness range for all two step Carnot groups with $d\ge 3$.

Transmissão via Zoom (pw: lisbonwade).

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.