Abstract
In this paper, given \(f \in BMO\), for all possible \(0< p< q<\infty \), we characterize the boundedness (or compactness) of the Toeplitz operators \(T_{f}\) from the Fock space \(F^{p}\) to \(F^{q}\). With \(f\in IMO\) (the space of integrable mean oscillation functions), for all possible \(0< q< p<\infty \), we characterize those symbols f for which the Toeplitz operators \(T_{f}\) are bounded (or compact) from \(F^{p}\) to \(F^{q}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berger, C.A., Coburn, L.A.: Toeplitz operators and quantum mechanics. J. Funct. Anal. 68, 273–299 (1986)
Berger, C.A., Coburn, L.A.: Toeplitz operators on the Segal–Bargmann space. Trans. Am. Math. Soc. 301(2), 813–829 (1987)
Berger, C.A., Coburn, L.A.: Heat Flow and Berezin–Toeplitz estimates. Am. J. Math. 116(3), 563–590 (1994)
Coburn, L.A., Li, B., Isralowitz, J.: Toeplitz operators with \(BMO\) symbols on the Segal–Bargmann space. Trans. Am. Math. Soc. 363, 3015–3030 (2011)
Grudsky, S., Vasilevshi, N.: Toeplitz operators on the Fock space: radial component effects. Integral Equations Operator Theory 44, 10–37 (2002)
Hu, Z., Lv, X.: Toeplitz operators from one Fock space to another. Integral Equations Operator Theory 70, 541–559 (2011)
Hu, Z., Lv, X.: Toeplitz operators on Fock spaces \(F^{p}(\varphi )\). Integral Equations Operator Theory 80, 33–59 (2014)
Hu, Z., Lv, X.: Positive Toeplitz operators between different doubing Fock spaces. Taiwanese J. Math. 21, 467–487 (2017)
Hu, Z., Wang, E.: Hankel operators between Fock spaces. Integral Equations Operator Theory 90(3), 37 (2018)
Janson, S., Peetre, J., Rochberg, R.: Hankel forms and the Fock space. Rev. Mat. Iberoam. 3, 61–138 (1987)
Luecking, D.H.: Embedding theorems for spaces of analytic functions via Khinchine’s inequality. Mich. Math. J. 40, 333–358 (1993)
Stroethoff, K.: Hankel and Toeplitz operators on the Fock space. Mich. Math. J. 39, 3–16 (1992)
Tung, J.: Fock spaces. Ph.D thesis, University of Michigan (2005)
Zhu, K.H.: Analysis on Fock Spaces. Springer, New York (2012)
Zorboska, N.: Toeplitz operators with BMO symbols and the Berezin transform. Int. J. Math. Math. Sci. 46, 2929–2945 (2003)
Acknowledgements
The author would like to thank the referee for his(her) very careful reading and very good suggestions. I would also like to express my gratitude to Professor Zhangjian Hu (Huzhou University) for his support and encouragement along the way.
Funding
The work is supported by the National Natural Science Foundation of China (Grant No. 11771139) and Lingnan Normal University (Grant No. 1170919301).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, E. Toeplitz operators with BMO and IMO symbols between Fock spaces. Arch. Math. 114, 541–551 (2020). https://doi.org/10.1007/s00013-020-01445-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-020-01445-4