Compact Composition Operators on Bloch type 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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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 X and Y be complete metric spaces of analytic functions over the unit disk in the complex plane. A linear operator T : X → Y is a bounded operator with respect to metric balls if T takes every metric ball in X into a metric ball in Y . We also say that T is metrically compact if it takes every metric ball in X into a relatively compact subset in Y . In this paper we will consider these prop...
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Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2012
ISSN: 0716-0917
DOI: 10.4067/s0716-09172012000100001