Flag Hardy space theory—an answer to a question by E.M. Stein.

Analysis Seminar
Wednesday, September 20, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Ji Li – Macquarie University – ji.li@mq.edu.au
Michael Lacey

In 1999, Washington University in Saint Louis hosted a conference on Harmonic Analysis to celebrate the 70th birthday of G. Weiss. In his talk in flag singular integral operators, E. M. Stein asked “What is the Hardy space theory in the flag setting?” In our recent paper, we characterise completely a flag Hardy space on the Heisenberg group. It is a proper subspace of the classical one-parameter Hardy space of Folland and Stein that was studied by Christ and Geller. Our space is useful in several applications, including the endpoint boundedness for certain singular integrals associated with the Sub-Laplacian on Heisenberg groups, and representations of flag BMO functions.