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Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

100%
Dong X.-T., Zhou Z.-H.
Studia Mathematica
|
2013
|
tom 219
|
nr 2
163-175
EN
We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators $T_{f}T_{g}$ on the harmonic Bergman space is equal to a Toeplitz operator $T_{h}$, then the product $T_{g}T_{f}$ is also the Toeplitz operator $T_{h}$, and hence $T_{f}$ commutes with $T_{g}$. From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.
2
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Dynamics of differentiation operators on generalized weighted Bergman spaces

100%
Zhang L., Zhou Z.-H.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous. Motivated by those, we investigate conditions to ensure that finite many powers of differentiation operators are disjoint hypercyclic on generalized weighted Bergman spaces of entire functions.
3
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Weighted composition operators between a weighted-type space and the Hardy space on the unit ball

81%
Zhou Z.-H., Liang Y.-X., Dong X.-T.
Annales Polonici Mathematici
|
2012
|
tom 104
|
nr 3
309-319
EN
This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.
4
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Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball

81%
Liang Y.-X., Wang C.-J., Zhou Z.-H.
Annales Polonici Mathematici
|
2015
|
tom 114
|
nr 2
101-114
EN
Let H(𝔹) denote the space of all holomorphic functions on the unit ball 𝔹⊂ ℂⁿ. Let φ be a holomorphic self-map of 𝔹 and u∈ H(𝔹). The weighted composition operator $uC_φ$ on H(𝔹) is defined by $uC_φf(z) = u(z)f(φ(z))$. We investigate the boundedness and compactness of $uC_φ$ induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.
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