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

Jingbo Xia, Dechao Zheng
2004 Indiana University Mathematics Journal  
We give a necessary and sufficient condition for Hankel operators H f and Hf on the Segal-Bargmann space H 2 (C n , dµ) to belong to the Schatten class C p for 1 ≤ p < ∞. We will explain that, since this condition is valid in the case 1 ≤ p ≤ 2 as well as in the case p ≥ 2, 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).
doi:10.1512/iumj.2004.53.2434 fatcat:4h652wdmfjdvtbzlmf4ywa3ajm