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Commuting dual Toeplitz operators on the harmonic Bergman space

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Abstract

We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic φ and ψ, S φ S ψ = S ψ S φ on (L 2 h )⊥ if and only if φ and ψ satisfy one of the following conditions: (1) Both φ and ψ are analytic on D. (2) Both φ and ψ are anti-analytic on D. (3) There exist complex constants α and β, not both 0, such that φ = αψ + β. Furthermore, we give the necessary and sufficient conditions for S φ S ψ = S φψ .

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    JingYu Yang & YuFeng Lu

  2. School of Mathematics and Statistics, Chifeng University, Chifeng, 024000, China

    JingYu Yang

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  1. JingYu Yang
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  2. YuFeng Lu
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Correspondence to YuFeng Lu.

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Yang, J., Lu, Y. Commuting dual Toeplitz operators on the harmonic Bergman space. Sci. China Math. 58, 1461–1472 (2015). https://doi.org/10.1007/s11425-014-4940-x

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  • DOI: https://doi.org/10.1007/s11425-014-4940-x

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