Isometric and Closed-Range Composition Operators between Bloch-Type Spaces
نویسندگان
چکیده
منابع مشابه
Isometric and Closed-Range Composition Operators between Bloch-Type Spaces
We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Blo...
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and Applied Analysis 3 The following lemma is the crucial criterion for the compactness of Cφ, whose proof is an easy modification of the proof of Proposition 3.11 in 1 . Lemma 2.4. Assume that φ is a holomorphic self-map of D. Then Cφ : Bp → Bq is compact if and only if Cφ is bounded and for any bounded sequence {fm}m∈N in Bp which converges to zero uniformly on compact subsets of D, we have ∥...
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Let φ and ψ be analytic self-maps of the open unit disk D . Using pseudo-hyperbolic distance ρ(φ ,ψ) , we characterize the boundedness and compactness of the differences of generalized composition operators (C φ −Ch ψ ) f (z) = ∫ z 0 [ f ′(φ(ξ ))g(ξ )− f ′(ψ(ξ ))h(ξ )]dξ , z ∈ D between two Bloch-type spaces on D . The results generalize the corresponding results on the single generalized compo...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2011
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2011/132541