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Commuting Toeplitz operators on the Fock–Sobolev space

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Abstract

The purpose of this paper is to study the commutator and the semi-commutator of Toeplitz operators on the Fock–Sobolev space \(F^{2,m}({\mathbb {C}})\) in a different function theoretic way instead of Berezin transform. We determine conditions for \((T_{f}, T_{\overline{g}}]=0\) and \([T_{f}, T_{\overline{g}}]=0\) in the cases when the symbol functions f and g are both polynomials or when f is a finite linear combination of reproducing kernels and g is a polynomial. We also determine the boundedness of Hankel products on the Fock–Sobolev space for some symbol classes.

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Acknowledgements

This work was completed with the support of National Natural Science Foundation of China (Grant nos. 12031002, 11871131, 11971086).

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, China

    Junmei Fan, Liu Liu & Yufeng Lu

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  1. Junmei Fan
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  2. Liu Liu
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  3. Yufeng Lu
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Correspondence to Junmei Fan.

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Communicated by Yuri Karlovich.

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Fan, J., Liu, L. & Lu, Y. Commuting Toeplitz operators on the Fock–Sobolev space. Adv. Oper. Theory 7, 28 (2022). https://doi.org/10.1007/s43036-022-00192-3

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  • DOI: https://doi.org/10.1007/s43036-022-00192-3

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