SCHATTEN CLASS HANKEL OPERATORS ON THE SEGAL-BARGMANN SPACE AND THE BERGER-COBURN PHENOMENON

We give a complete characterization of Schatten class Hankel operators H-f acting on weighted Segal-Bargmann spaces F-2(phi) using the notion of integral distance to analytic functions in C-n and Hormander's partial derivative-theory. Using our characterization, for f epsilon L-infinity and 1 < p < infinity, we prove that H-f is in the Schatten class S-p if and only if H ((f) over bar) epsilon S-p,S- which was previously known only for the Hilbert-Schmidt class S-2 of the standard Segal-Bargmann space F-2(phi) with phi(z) = alpha vertical bar z vertical bar(2).

Automated summary

This paper provides a complete characterization of Schatten class Hankel operators H-f acting on weighted Segal-Bargmann spaces F-2(phi) using the notion of integral distance to analytic functions in C-n and Hörmander's partial derivative-theory. Based on our characterization, for f ∈ L-infinity and 1 < p < infinity, we prove that H-f is in the Schatten class S-p if and only if H ((f) over bar) ∈ S-p,S-, which was previously known only for the Hilbert-Schmidt class S-2 of the standard Segal-Bargmann space F-2(phi) with phi(z) = alpha vertical bar z vertical bar(2).