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1
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Some Hilbert spaces related with the Dirichlet space

100%
Arcozzi N., Mozolyako P., Perfekt K.-M., Richter S., Sarfatti G.
Concrete Operators
|
2016
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tom 3
|
nr 1
94-101
EN
We study the reproducing kernel Hilbert space with kernel kd , where d is a positive integer and k is the reproducing kernel of the analytic Dirichlet space.
2
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A remark on the multipliers on spaces of Weak Products of functions

100%
Richter S., Wick B. D.
Concrete Operators
|
2016
|
tom 3
|
nr 1
25-28
EN
If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by [...] We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.
3
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On some radius results for normalized analytic functions

100%
Kim Y., Kwon E.
Annales Polonici Mathematici
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1998
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tom 68
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nr 1
51-60
EN
We investigate some radius results for various geometric properties concerning some subclasses of the class 𝓢 of univalent functions.
4
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New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

88%
Colonna F.
Open Mathematics
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2013
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tom 11
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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.
5
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Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

75%
Gu C., Luo S., Xiao J.
Complex Manifolds
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2017
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tom 4
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nr 1
84-119
EN
This paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].
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