Commuting Toeplitz operators on weighted harmonic Bergman spaces and hyponormality on the Bergman space of the punctured unit disk

Houcine Sadraoui; Borhen Halouani; Houcine Sadraoui; Borhen Halouani

doi:10.3934/math.2024977

AIMS Mathematics

2024, Volume 9, Issue 8: 20043-20057. doi: 10.3934/math.2024977

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Research article

Commuting Toeplitz operators on weighted harmonic Bergman spaces and hyponormality on the Bergman space of the punctured unit disk

Houcine Sadraoui ,
Borhen Halouani ^,

Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 16 April 2024 Revised: 08 June 2024 Accepted: 14 June 2024 Published: 20 June 2024
MSC : 15B05, 15B48, 47B20, 47B35, 47B47

We first describe commuting Toeplitz operators with harmonic symbols on weighted harmonic Bergman spaces. Then, a sufficient condition for hyponormality on weighted Bergman spaces of the punctured unit disk, when the analytic part of the symbol is a monomial, is shown.
- Bergman space,
- Toeplitz operator,
- hyponormality
Citation: Houcine Sadraoui, Borhen Halouani. Commuting Toeplitz operators on weighted harmonic Bergman spaces and hyponormality on the Bergman space of the punctured unit disk[J]. AIMS Mathematics, 2024, 9(8): 20043-20057. doi: 10.3934/math.2024977

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Abstract

We first describe commuting Toeplitz operators with harmonic symbols on weighted harmonic Bergman spaces. Then, a sufficient condition for hyponormality on weighted Bergman spaces of the punctured unit disk, when the analytic part of the symbol is a monomial, is shown.

References

[1]	S. Axler, Z. Cuckovic, Commuting Toeplitz operators with harmonic symbols, Integr. Equ. Oper. Theory, 14 (1991), 1–12. https://doi.org/10.1007/BF01194925 doi: 10.1007/BF01194925
[2]	B. R. Choe, Y. J. Lee, Commuting Toeplitz operators on the harmonic Bergman space, Michigan Math. J., 46 (1999), 163–174. https://doi.org/10.1307/mmj/1030132367 doi: 10.1307/mmj/1030132367
[3]	H. Sadraoui, M. Guediri, Hyponormality of Toeplitz operators on the Bergman space of an annulus, Rev. Union Mat. Argent., 61 (2020), 303–313.
[4]	H. Sadraoui, Hyponormality of Toeplitz operators and cohyponormality of composition operators, PhD Thesis, Purdue University, 1992.
[5]	P. Ahern, Z. Cuckovic, A mean value inequality with applications to Bergman space operators, Pacific J. Math., 173 (1996), 295–305.
[6]	H. Sadraoui, M. Garayev, H. Guediri, On Hyponormality of Toeplitz operators, Rocky Mountain J. Math., 51 (2021), 1821–1831. https://doi.org/10.1216/rmj.2021.51.1821 doi: 10.1216/rmj.2021.51.1821
[7]	H. Hedenmalm, B. Korenblum, K. H. Zhu, Theory of Bergman spaces, New York: Springer, 2000. https://doi.org/10.1007/978-1-4612-0497-8
[8]	N. Ghiloufi, M. Zaway, Meromorphic Bergman spaces, Ukr. Math. J., 74 (2023), 1209–1224. https://doi.org/10.1007/s11253-023-02130-9 doi: 10.1007/s11253-023-02130-9

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