Fefferman--Stein type inequality in multiparameter settings and applications

Series
Analysis Seminar
Time
Wednesday, December 4, 2024 - 2:00pm for
Location
Speaker
ji Li – Macquarie University – ji.li@mq.edu.au
Organizer
Michael Lacey

A classical Fefferman-Stein inequality relates the distributional estimate for a square function for a harmonic function u to a non-tangential maximal function of u.   We extend this ineuality to certain multiparameter settings, including the Shilov boundaries of tensor product domains, and the Heisenberg groups  with flag structure.
Our technique bypasses the use of Fourier or the dependence of group structure. Direct applications include the  the (global) weak type endpoint estimate for multi-parameter Calderon–Zygmund operators and maximal function characterisation of multi-parameter Hardy spaces.

This talk is based on the recent progress: Ji Li, ``Fefferman–Stein type inequality'',  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2024.