Abstract:

In this talk, we discuss the problem of obtaining sharp L^p\\to L^q estimates for the local maximal operator associated with averaging over dilates of the Korányi sphere on Heisenberg groups. This is a codimension one surface compatible with the non-isotropic Heisenberg dilation structure. I will describe the main features of the problem, some of which are helpful while others are obstructive. These include the non-Euclidean group structure (the extra “twist” due to the Heisenberg group law), the geometry of the Korányi sphere (in particular, the flatness at the poles) and an “imbalanced” scaling argument encapsulated by a new type of Knapp example, which we shall describe in detail.

About Speaker:

Rajula Srivastava received her Ph.D. from University of Wisconsin, Madison in 2022, under the supervision of Andreas Seeger. She is currently a Hirzebruch Research Instructor at the Hausdorff Center for Mathematics, University of Bonn, and the Max Planck Institute for Mathematics.