摘要
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 ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.
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, SφSψ= SψSφ on（L2h）⊥if and only if φ and ψ satisfy one of the following conditions：（1） Both φ and ψ are analytic on D.（2） Both Ф 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 SφSψ= S■ψ.
基金
supported by National Natural Science Foundation of China(Grant Nos.10971020 and 1127059)
Research Fund for the Doctoral Program of Higher Education of China
