Essential norms of composition operators between Bloch type spaces
نویسندگان
چکیده
منابع مشابه
The Essential Norms of Composition Operators between Generalized Bloch Spaces in the Polydisc and Their Applications
Let Un be the unit polydisc of Cn and φ = (φ1, . . . ,φn) a holomorphic self-map of Un. p(Un), p 0 (U n), and p 0∗(U n) denote the p-Bloch space, little p-Bloch space, and little star p-Bloch space in the unit polydisc Un, respectively, where p,q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between p(Un) ( p 0 (U n) or p 0∗(U n)) an...
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Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators uCφ from Bloch type spaces to Zygmund type spaces in D in terms of u,φ, their derivatives and the n-th power φ of φ. Moreover, we obtain some similar estimates for their essential norms. From which...
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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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-10-10285-8