Toeplitz Operators on Higher Cauchy–Riemann Spaces Over the Unit Ball

  • Lijia DingEmail author
  • Kai Wang
Open Access


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.


Berezin transform \(\mathcal {M}\)-harmonic function Higher Cauchy–Riemann space Toeplitz operator Pluriharmonic function 

Mathematics Subject Classification

Primary 46E22 Secondary 47B35 



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 Author(s) 2018

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Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiP.R. China

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