Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenonAsghari, 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. 128596. ISSN 0022-247X (In Press)
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.jmaa.2024.128596 Abstract/SummaryUsing 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.
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