Hardy spaces in exotic geometries

Abstract: 

The Heisenberg group appears in complex analysis as the boundary of a Siegel domain.  Study of the boundary values of holomorphic functions leads to questions in analysis on the Heisenberg group, equipped with a flag geometry, in  which the balls of classical geometry are replaced by the products of a ball in the sub-Riemannian geometry and an interval in the central variable.

Flag Hardy spaces are a tool for solving problems in flag geometry; they present many features in common with Hardy spaces on product spaces.  This talk focusses on the theory of flag Hardy spaces on the Heisenberg group, and on the difficulties which arise when one tries to extend to more exotic geometries.