Analysis Seminar: Testing conditions for boundedness of Hankel operators between two weighted spaces

Abstract: We discuss the boundedness of Hankel operators between a weighted Hardy space and a weighted L^2 space, with two different Muckenhoupt weights. In the Lebesgue measure setting, Hankel operator with a symbol f is bounded if and only if its symbol has a bounded Garsia norm, or equivalently, a bounded BMO norm. We generalize this result to the case of two weights, with the appropriate generalization of the Carleson embedding theorem.