An estinatiion for the essential norm of Compositiion operators acting on Bloch-type spaces

2013/01/13 by Ramos-Fernández, Julio C.
#30D45 #32A30 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1301.2740

Abstract

Let μbe any weight function defined on the unit disk \Bbb D and let ϕ be an analytic self-map of \Bbb D. In the present paper we show that the essential norm of composition operator C_ϕ mapping from the α-Bloch space, with α>0, to μ-Bloch space B^μ is comparable to \limsup_{|a|→ 1^-}‖σ_a∘ϕ‖_B^μ, where, for a∈\Bbb D, σ_a is a certain special function in α-Bloch space.

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