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

Flavia Colonna

Open Mathematics, Tome 11 (2013), p. 55-73 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2013-01-01

Zbl 1279.47041

EUDML-ID : urn:eudml:doc:269568

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