Standard deviation and Schatten class Hankel operators on the Segal-Bargmann space

We consider Hankel operators on the Segal-Bargmann space H 2 (C n ,dμ). Our main result is a necessary and sufficient condition for the simultaneous membership of H f and H f in the Schatten class Cp, 1 ≤ p < ∞. We will explain that, since this condition is valid in the case 1 ≤ p ≤ 2 as well as in the case 2 ≤ p < oo, this result reflects the structural difference between the Segal-Bargmann space and other reproducing-kernel spaces such as the Bergman space L 2 a (B n ,dv).