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Bloch-to-Hardy composition operators

100%

Doubtsov E., Petrov A.

Open Mathematics

2013

tom 11

nr 6

985-1003

Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.

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

88%

Colonna F.

Open Mathematics

2013

tom 11

nr 1

55-73

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.

Ograniczanie wyników

2 Open Mathematics

1 Colonna F.

1 Doubtsov E.

1 Petrov A.

2 2013

Wyniki wyszukiwania

Bloch-to-Hardy composition operators

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