Displaying similar documents to “Riemann–Stieltjes operators between Bergman-type spaces and α -Bloch spaces.”

On Volterra composition operators from Bergman-type space to Bloch-type space

Zhi Jie Jiang (2011)

Czechoslovak Mathematical Journal

Similarity:

Let ϕ be an analytic self-mapping of 𝔻 and g an analytic function on 𝔻 . In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the Bloch-type space. We also obtain an asymptotical expression of the essential norm of these operators in terms of the symbols g and ϕ .

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

Flavia Colonna (2013)

Open Mathematics

Similarity:

Let ψ and φ be analytic functions on the open unit disk 𝔻 with φ( 𝔻 ) ⊆ 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 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...

Boundary vs. interior conditions associated with weighted composition operators

Kei Izuchi, Yuko Izuchi, Shûichi Ohno (2014)

Open Mathematics

Similarity:

Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk 𝔻 , we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior 𝔻 and on the boundary ∂ 𝔻 respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators. ...