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Analysis Seminar – Trang Nguyen (University of South Australia)
January 29, 2021 @ 3:00 pm - 4:00 pm
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.