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Products of Toeplitz operators on the harmonic Bergman space. (English) Zbl 1195.47014
The authors study Toeplitz operators with quasihomogeneous symbols acting on the harmonic Bergman space over the unit disk. The main result of the paper states that, given $$l_1,l_2 > 0$$ and $$k_1, k_2 \in \mathbb{Z}$$, the product $$T_{e^{ik_1\theta}r^{l_1}}T_{e^{ik_2\theta}r^{l_2}}$$, where $$r =|z|$$, is a Toeplitz operator if and only if $$k_1=k_2=0$$, and in this case
$T_{r^{l_1}}T_{r^{l_2}}= \begin{cases}\frac{l_1}{l_1-l_2}T_{r^{l_1}} - \frac{l_2}{l_1-l_2}T_{r^{l_2}} &\text{if }l_1 \neq l_2,\\ T_{r^{l_1}}T_{r^{l_2}}=T_{r^{l_1}(1+ l_1\log r)}&\text{otherwise.}\end{cases}$

##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B38 Linear operators on function spaces (general)
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##### References:
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