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

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.