Compact and weakly compact composition operators from the Bloch space into Möbius invariant spaces
نویسندگان
چکیده
منابع مشابه
Compact Composition Operators on Bloch Type Spaces
In this paper we characterize continuity and compactness of composition operators Cφ mapping the α-Bloch space into the μ-Bloch space, where μ is a weight defined on the unit disk D, in term of certain expression that involve the n-power of the symbol φ.
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We give a new and simple compactness criterion for composition operators Cφ on BMOA and the Bloch space in terms of the norms of φ in the respective spaces.
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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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Suppose that ϕ(z) is an analytic self-map of the unit disk ∆. We consider the boundedness of the composition operator C ϕ from Bloch space Ꮾ into the spaces Q T (Q T ,0) defined by a nonnegative, nondecreasing function T (r) on 0 ≤ r < ∞. 1. Introduction. Let ∆ = {z : |z| < 1} be the unit disk of complex plane C and let H(∆) be the space of all analytic functions in ∆. For a ∈ ∆, Green's functi...
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Abstract. Let φ and ψ be holomorphic self-maps of the unit polydisc U in the n-dimensional complex space, and denote by Cφ and Cψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators Cφ − Cψ from Bloch space to bounded holomorphic function space in the unit polydisc. Moreover the compactness of the difference...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2014.02.005