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). Since then, this classical result has been generalized to various settings, including replacing the underlying space R^n on which the operators act. In this talk, I will present our work on generalizing 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.

analysis of PDEsclassical analysis and ODEscomplex variablesdifferential geometrydynamical systemsfunctional analysismetric geometry

Audience: researchers in the topic

Analysis and Geometry Seminar