Abstract
In this paper, we investigate some algebraic properties of Toeplitz operators over higher Cauchy–Riemann spaces \(C_{\alpha ,m}\) on the unit ball \(\mathbb {B}^d\) with \(d\ge 2\). We first discuss the Berezin transform on higher Cauchy–Riemann spaces. By making use of Berezin transform, we completely characterize (semi-)commuting Toeplitz operators with bounded pluriharmonic symbols over higher Cauchy–Riemann space \(C_{\alpha ,m}\). Moreover, we show that compact products of finite Toeplitz operators with a class of bounded pluriharmonic symbols only happen in the trivial case.
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Acknowledgements
The authors would like to express their great gratitude to Professor K. Guo for his valuable guidance and encouragement over the years. The authors would also like to thank Professor G. Zhang for his helpful discussions and support.
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The project was partially supported by NSFC (11722102), the Alexander von Humboldt Foundation (1151823), Shanghai Pujiang Program(16PJ1400600).
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Ding, L., Wang, K. Toeplitz Operators on Higher Cauchy–Riemann Spaces Over the Unit Ball. Integr. Equ. Oper. Theory 90, 69 (2018). https://doi.org/10.1007/s00020-018-2494-y
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DOI: https://doi.org/10.1007/s00020-018-2494-y