Hankel operators lie at the junction of analytic and real-variables. We will explore this junction, from the point of view of Haar shifts and commutators. 1. Haar Functions We consider operators which satisfy invariance properties with respect to two well-known groups. The first group we take to the translation operators (1.1) Try f (x) := f (x − y) , y ∈ R . Note that formally, the adjoint ope...
