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Science China Mathematics

, Volume 58, Issue 7, pp 1461–1472 | Cite as

Commuting dual Toeplitz operators on the harmonic Bergman space

  • JingYu Yang
  • YuFeng Lu
Articles

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 h 2 ) 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 .

Keywords

dual Toeplitz operator harmonic Bergman space Bergman space 

MSC(2010)

47B35 47B38 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina
  2. 2.School of Mathematics and StatisticsChifeng UniversityChifengChina

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