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2013 | 11 | 1 | 55-73
Tytuł artykułu

New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

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EN
Abstrakty
EN
Let ψ and φ be analytic functions on the open unit disk $\mathbb{D}$ with φ($\mathbb{D}$) ⊆ $\mathbb{D}$. We give new characterizations of the bounded and compact weighted composition operators W ψ,ϕ from the Hardy spaces H p, 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A αp, α > − 1,1 ≤ p < ∞, and the Dirichlet space $\mathcal{D}$ to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W ψ,ϕ f for suitable collections of functions f in the respective spaces. We also obtain characterizations of boundedness for H 1 as well as of compactness for H p, 1 ≤ p < ∞, and $\mathcal{D}$ purely in terms of the symbols ψ and φ.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
1
Strony
55-73
Opis fizyczny
Daty
wydano
2013-01-01
online
2012-10-24
Twórcy
Bibliografia
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  • [15] Wulan H., Zheng D., Zhu K., Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc., 2009, 137(11), 3861–3868 http://dx.doi.org/10.1090/S0002-9939-09-09961-4
  • [16] Zhu K.H., Operator Theory in Function Spaces, Monogr. Textbooks Pure Appl. Math., 139, Marcel Dekker, New York, 1990
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0097-4
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