Analysis Seminar: "Hankel Operators, Commutators of the Hilbert transform and possible weighted generalizations"

Abstract: It is known that commutator of the Hilbert transform and a multiplication operator Mb, [Mb,H] is bounded if and only if b is a function of bounded mean oscillation. Projections and restrictions of the commutator to the Hardy space and its orthogonal complement in L2 give either Hankel operators or their adjoints. So, properties of Hankel operators are linked to properties of the commutator of the Hilbert transform. In particular, Hankel operators are bounded if and only if their antianalytic symbol, belong to the space of functions of bounded mean oscillation. We discuss known generalizations of the boundedness result of commutators of the Hilbert transform, and possible generalizations of the Hankel operator results.  

Host: Walton Green