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IDA and Hankel operators on Fock spaces

Zhangjian Hu and Jani A. Virtanen

Vol. 16 (2023), No. 9, 2041–2077

We introduce a new space IDA of locally integrable functions whose integral distance to holomorphic functions is finite, and use it to completely characterize boundedness and compactness of Hankel operators on weighted Fock spaces. As an application, for bounded symbols, we show that the Hankel operator Hf is compact if and only if Hf¯ is compact, which complements the classical compactness result of Berger and Coburn. Motivated by recent work of Bauer, Coburn, and Hagger, we also apply our results to the Berezin–Toeplitz quantization.

Fock space, Hankel operator, boundedness, compactness, quantization, $\bar\partial$-equation
Mathematical Subject Classification
Primary: 47B35
Secondary: 32A25, 32A37, 81S10
Received: 10 November 2020
Revised: 24 March 2022
Accepted: 29 April 2022
Published: 11 November 2023
Zhangjian Hu
Huzhou University
Jani A. Virtanen
University of Reading
United Kingdom
University of Helsinki

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