Sandra Pott

Commutators (or to an operator theorist, Hankel operators) and the standard class of operators considered in Harmonic Analysis, Calder\’on-Zygmund operators, exhibit different behaviours, including differences of the optimal bounds in a weighted setting, which are surprising at a first glance. We will start the course by introducing the setting of vector-valued functions and matrix-weighted weight and presenting some of the recent progress in the area. We will then show that the matrix-weighted setting offers a unified setting for weighted commutators and weighted Calder\’on-Zygmund operators, which is even interesting in the scalar case. Moreover, we will show that sharp bounds for weighted commutators imply those for Calder\’on-Zygmund operators and vice versa. This is joint work with Joshua Isralowitz, Israel Rivera-Rios, Andrei Stoica, and Sergei Treil.​