Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
IDA and Hankel operators on Fock spaces

Zhangjian Hu and Jani A. Virtanen

Vol. 16 (2023), No. 9, 2041–2077
Abstract

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.

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

Open Access made possible by participating institutions via Subscribe to Open.