Analysis Seminar on "Non-homogeneous T(1) theorem for singular integrals on product quasimetric spaces" by Trang Nguyen (UNISA, Adelaide, Australia)
Event Description:
Title: Non-homogeneous T(1) theorem for singular integrals on product quasimetric spaces
Abstract: In the Calderón--Zygmund Theory of Singular Integrals, the T(1) theorem of David and Journé is one of the most celebrated theorems. It gives easily-checked criteria for a singular integral operator T to be bounded from L^2(R^n) to L^2(R^n), meaning T(f) is bounded for all functions f in L^2(R^n). Since then, this classical result has been generalised to various settings, including replacing the underlying space R^n on which the operators act.
In this talk, I will present our work on generalising the T(1) theorem, that brings together three attributes: 'product space', 'quasimetric' and 'non-doubling measure'. Specifically, we prove a T(1) theorem that can be applied to operators acting on product spaces equipped with a quasimetric and an upper doubling measure, which only satisfies an upper control on the size of balls.
About the Speaker: Trang Nguyen received her PhD in 2020 from University of South Australia under the direction of LesLey Ward. Her research interestes are in harmonic analysis and quasiconformal maps and their generalizations to spaces of homogeneous type and non-homogeneous spaces.
We hope in the not to distant future Trang will be able to visit in person UNM.