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Compact generalized weighted composition operators on the Bergman space

Hu O., Zhu X.

Opuscula Mathematica

2017

Vol. 37, no. 2

303--312

We characterize the compactness of the generalized weighted composition operators acting on the Bergman space.

Generalized weighted composition operators on the Bergman space

Sharma A. K.

Demonstratio Mathematica

2011

Vol. 44, nr 2

359--372

Let φ and ψ be holomorphic maps on the open unit disk D such that φ (D) ⊂ D and H (D) be the space of holomorphic functions on D. For a non-negative integer n, define a linear operator (…), f ∈ H (D). In this paper, we characterize boundedness and compactness of (…) on the Bergman space A². We also compute the upper and lower bounds of essential norm of this operator on the Bergman space.