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Boundary vs. interior conditions associated with weighted composition operators

100%
Izuchi K., Izuchi Y., Ohno S.
Open Mathematics
|
2014
|
tom 12
|
nr 5
761-777
EN
Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$\mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$\mathbb{D}$$ and on the boundary $$\partial \mathbb{D}$$ 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.
2
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New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

64%
Colonna F.
Open Mathematics
|
2013
|
tom 11
|
nr 1
55-73
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.
3
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Multipliers of sequence spaces

64%
Cheng R., Mashreghi J., Ross W. T.
Concrete Operators
|
2017
|
tom 4
|
nr 1
76-108
EN
This paper is selective survey on the space lAp and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality
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