Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon

Asghari, G., Hu, Z. and Virtanen, J. A. (2024) Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon. Journal of Mathematical Analysis and Applications, 540 (2). 128596. ISSN 0022-247X doi: 10.1016/j.jmaa.2024.128596

Abstract/Summary

Using the notion of integral distance to analytic functions, we give a characterization of Schatten class Hankel operators acting on doubling Fock spaces on the complex plane and use it to show that for f ∈ L∞, if Hf is Hilbert-Schmidt, then so is Hf¯. This property is known as the Berger-Coburn phenomenon. When 0 < p ≤ 1, we show that the Berger-Coburn phenomenon fails for a large class of doubling Fock spaces. Along the way, we illustrate our results for the canonical weights |z|m when m > 0.