Abstract
This paper shows that on the Bergman space of the open unit disk, the Toeplitz operator \(T_{{\overline{p}}+\varphi }\) and the small Hankel operator \(\Gamma _\psi\) commute only in the obvious cases, where \(\varphi\) and \(\psi\) are both bounded analytic functions, and p is an analytic polynomial.
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Acknowledgements
This work was partially supported by NSFC (grant number: 12371125) and Chongqing Natural Science Foundation (cstc2020jcyj-msxmX0700). Xianfeng Zhao (the corresponding author) was partially supported by the Fundamental Research Funds for the Central Universities (grant numbers: 2020CDJQY-A039).
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Wang, J., Zhang, J. & Zhao, X. Commuting Toeplitz and small Hankel operators on the Bergman space. Collect. Math. (2024). https://doi.org/10.1007/s13348-024-00438-8
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DOI: https://doi.org/10.1007/s13348-024-00438-8