Isometries of composition operators on BMOA
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- by Tiantian Chen and Hasi Wulan;
- Proc. Amer. Math. Soc. 153 (2025), 2513-2525
- DOI: https://doi.org/10.1090/proc/17134
- Published electronically: April 8, 2025
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Abstract:
We characterize completely the analytic self-maps of the unit disc inducing isometric composition operators on the space BMOA equipped with a Möbius invariant $H^p$ norm. Our results answer a question raised by J. Laitila [Math. Nachr. 283(2010), pp. 1646–1653] for all $1\leq p<\infty$, which extends a result of S. Pouliasis [Bull. London Math. Soc. 53(2021), pp. 458–469] from $1\leq p<2$ to $1\leq p\le 4$. Meanwhile, we generalize the result of Laitila from $p=2$ to $1\leq p\le 4$ and we also show that the parameter $p=4$ is the best possible.References
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Bibliographic Information
- Tiantian Chen
- Affiliation: Department of Mathematics, Shantou University, Shantou 515063, People’s Republic of China
- ORCID: 0009-0008-7507-0683
- Email: 18ttchen@stu.edu.cn
- Hasi Wulan
- Affiliation: Department of Mathematics, Inner Mongolia Minzu University, Tongliao, People’s Republic of China; and Department of Mathematics, Shantou University Shantou 515063, People’s Republic of China
- ORCID: 0000-0001-6771-7311
- Email: wulan@stu.edu.cn
- Received by editor(s): June 17, 2024
- Received by editor(s) in revised form: September 24, 2024
- Published electronically: April 8, 2025
- Additional Notes: This research was supported by the National Natural Science Foundation of China (No. 12071272, 12371131)
- Communicated by: Javad Mashreghi
- © Copyright 2025 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 153 (2025), 2513-2525
- MSC (2020): Primary 30D45, 30D99, 30H25, 47B38
- DOI: https://doi.org/10.1090/proc/17134
- MathSciNet review: 4892624