Abstract
The boundedness and compactness of the product of differentiation and composition operators from Bloch spaces intoQKspaces are discussed in this paper.
Highlights
Introduction and MotivationLet Δ be the open unit disk in the complex plane and let H(Δ) be the class of all analytic functions on Δ
The Bloch space B on Δ is the space of all analytic functions f on Δ such that sup
Let B0 denote the subspace of B consisting of those f ∈ B for which (1 − |z|2)f|z| → 0 as |z| → 1
Summary
Let Δ be the open unit disk in the complex plane and let H(Δ) be the class of all analytic functions on Δ. The Bloch space B on Δ is the space of all analytic functions f on Δ such that. Let B0 denote the subspace of B consisting of those f ∈ B for which (1 − |z|2)f|z| → 0 as |z| → 1 This space is called the little Bloch space. Let φ denote a nonconstant analytic self-map of Δ. The problem of characterizing the boundedness and compactness of composition operators on many Banach spaces of analytic functions has attracted lots of attention recently, for example, [2] and the reference therein. For f ∈ H(Δ), the products of differentiation and composition operators DCφ and CφD are defined by DCφ (f) = (f ∘ φ) = f (φ) φ, CφD (f) = f (φ) ,. Some sufficient and necessary conditions for the boundedness and compactness of this operator are given
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