Abstract
Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for , is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).
Highlights
We show that the essential norm of composition operator Cφ mapping from the weighted Bloch space to μ-Bloch space Bμ is comparable to lim sup|a| → 1− ‖σa ∘ φ‖Bμ, where for a ∈ D, σa is a certain special function in the weighted Bloch space
As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003)
The weighted Bloch space appears in the literature when we study properties of certain operators acting on certain spaces of analytic functions on the unit disk D of the complex plane C
Summary
A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into μ-Bloch Spaces. Let μ be any weight function defined on the unit disk D and let φ be an analytic self-map of D. We show that the essential norm of composition operator Cφ mapping from the weighted Bloch space to μ-Bloch space Bμ is comparable to lim sup|a| → 1− ‖σa ∘ φ‖Bμ , where for a ∈ D, σa is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003)
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