Abstract
In this paper, we study several classes of H-Toeplitz operators (defined below) on the Hardy space \(H^2\). In particular, we prove that, for \(\varphi \in L^{\infty }\), the adjoint of H-Toeplitz operators is hyponormal. Next, we investigate several properties of H-Toeplitz operators on the weighted Bergman spaces. Finally, we give necessary and sufficient conditions for H-Toeplitz operators to be contractive and expansive on the weighted Bergman spaces.
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Funding
The first author was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. RS-2023-00244646). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A11051177) and (2019R1F1A1058633). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1H1A2091052). The fourth author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1C1C1008713).
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Communicated by Michael Kunzinger.
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Kim, S., Ko, E., Lee, J.E. et al. H-Toeplitz operators on the function spaces. Monatsh Math (2024). https://doi.org/10.1007/s00605-024-01985-9
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DOI: https://doi.org/10.1007/s00605-024-01985-9