Analysis Seminar: "Commutators: boundedness, compactness and Schatten class— recent progress on stratified Lie groups"

Abstract: Originated from Nehari and Coifman—Rochberg—Weiss, commutator of singular integral with a symbol function provides a connection between real, complex analysis and operator theory. The boundedness, compactness and Schatten class characterisations of commutator correspond to the symbol function to be in the BMO (bounded mean oscillation), VMO (vanishing mean oscillation) and Besov spaces. At the same time, it outlines the parallel story of the real Hardy space and weak factorization of these functions. In this talk I will recall the history along this line briefly, and then report on some of our recent progresses on boundedness, compactness and Schatten class of commutator of Riesz transforms on stratified Lie groups.

Host: Brett Wick