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IDA and Hankel
operators on Fock spaces
Zhangjian Hu and Jani A. Virtanen |
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Vol. 16 (2023), No. 9, 2041–2077
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Abstract |
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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 is compact if and only if 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. |
Keywords
Fock space, Hankel operator, boundedness, compactness,
quantization, $\bar\partial$-equation
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Mathematical Subject Classification
Primary: 47B35
Secondary: 32A25, 32A37, 81S10
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Milestones
Received: 10 November 2020
Revised: 24 March 2022
Accepted: 29 April 2022
Published: 11 November 2023
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Authors |
| Zhangjian Hu | |
| Huzhou University Huzhou China |
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| Jani A. Virtanen | |
| University of Reading Reading United Kingdom |
University of Helsinki Helsinki Finland |
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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