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Commuting dual Toeplitz operators on the harmonic Dirichlet space

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Abstract

In this paper, we characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ, ψ ∈ W 1,∞, S φ S ψ = S ψ S φ on (D h )⊥ if and only if φ and ψ satisfy one of the following conditions: (1) Both φ and ψ are harmonic functions; (2) There exist complex constants α and β, not both 0, such that φ = αψ+β.

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Authors and Affiliations

  1. School of Mathematical Statistics, Chifeng University, Chifeng, 024000, P. R. China

    Jing Yu Yang

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P. R. China

    Yin Yin Hu, Yu Feng Lu & Tao Yu

Authors
  1. Jing Yu Yang
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  2. Yin Yin Hu
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  3. Yu Feng Lu
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  4. Tao Yu
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Correspondence to Yin Yin Hu.

Additional information

Supported by NSFC (Grant Nos. 11271059, 11271332, 11431011, 11301047), NSF of Zhejiang Province (Grant Nos. LY14A010013, LY14A010021), Higher School Foundation of Inner Mongolia of China (Grant No. NJZY 13298)

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Yang, J.Y., Hu, Y.Y., Lu, Y.F. et al. Commuting dual Toeplitz operators on the harmonic Dirichlet space. Acta. Math. Sin.-English Ser. 32, 1099–1105 (2016). https://doi.org/10.1007/s10114-016-5663-4

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  • DOI: https://doi.org/10.1007/s10114-016-5663-4

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