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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

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.

Weighted composition operators between a weighted-type space and the Hardy space on the unit ball

80%

Zhou Z.-H. , Liang Y.-X. , Dong X.-T.

Annales Polonici Mathematici

2012

tom 104

nr 3

309-319

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.

Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball

80%

Liang Y.-X. , Wang C.-J. , Zhou Z.-H.

Annales Polonici Mathematici

2015

tom 114

nr 2

101-114

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.