A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into μ-Bloch Spaces

الملخص EN

Let μ be any weight function defined on the unit disk ? and let ϕ be an analytic self-map of ?.

In the present paper, 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∈?, 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).