On the commuting problem of Toeplitz operators on the harmonic Bergman space

Hasan Iqtaish; Issam Louhichi; Abdelrahman Yousef; Hasan Iqtaish; Issam Louhichi; Abdelrahman Yousef

doi:10.3934/math.2025770

AIMS Mathematics

2025, Volume 10, Issue 7: 17232-17247. doi: 10.3934/math.2025770

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On the commuting problem of Toeplitz operators on the harmonic Bergman space

Department of Mathematics and Statistics, College of Arts and Sciences, American University of Sharjah, Sharjah, UAE

Received: 24 March 2025 Revised: 11 July 2025 Accepted: 22 July 2025 Published: 31 July 2025
MSC : Primary 47B35; Secondary 47L80

In this paper, we provide a complete characterization of bounded Toeplitz operators $ T_f $ on the harmonic Bergman space of the unit disk, where the symbol $ f $ has a polar decomposition truncated above, that commute with $ T_{z+\bar{g}} $ for a bounded analytic function $ g $.
- harmonic Bergman space,
- Toeplitz operators,
- Mellin transform
Citation: Hasan Iqtaish, Issam Louhichi, Abdelrahman Yousef. On the commuting problem of Toeplitz operators on the harmonic Bergman space[J]. AIMS Mathematics, 2025, 10(7): 17232-17247. doi: 10.3934/math.2025770

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Abstract

In this paper, we provide a complete characterization of bounded Toeplitz operators $ T_f $ on the harmonic Bergman space of the unit disk, where the symbol $ f $ has a polar decomposition truncated above, that commute with $ T_{z+\bar{g}} $ for a bounded analytic function $ g $.

References

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