Displaying similar documents to “Weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type space”

On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator ψ C ϕ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions

Wolf, Elke (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 47B33, 47B38. Let f be an analytic self-map of the open unit disk D in the complex plane and y be an analytic map on D. Such maps induce a weighted composition operator followed by differentiation DCf, y acting between weighted Banach spaces of holomorphic functions. We characterize boundedness and compactness of such operators in terms of the involved weights as well as the functions f and y.

Embeddings of doubling weighted Besov spaces

Dorothee D. Haroske, Philipp Skandera (2014)

Banach Center Publications

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We study continuous embeddings of Besov spaces of type B p , q s ( ℝ ⁿ , w ) , where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.

On the Banach-Stone problem

Jyh-Shyang Jeang, Ngai-Ching Wong (2003)

Studia Mathematica

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Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of ℓ ₂ ∞ then T can be written as a weighted...

Weighted composition operators on weighted Lorentz spaces

İlker Eryilmaz (2012)

Colloquium Mathematicae

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The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p,q,wdμ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.

Weighted Fréchet spaces of holomorphic functions

Elke Wolf (2006)

Studia Mathematica

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This article deals with weighted Fréchet spaces of holomorphic functions which are defined as countable intersections of weighted Banach spaces of type H ∞ . We characterize when these Fréchet spaces are Schwartz, Montel or reflexive. The quasinormability is also analyzed. In the latter case more restrictive assumptions are needed to obtain a full characterization.

A generalization of the Aleksandrov operator and adjoints of weighted composition operators

Eva A. Gallardo-Gutiérrez, Jonathan R. Partington (2013)

Annales de l’institut Fourier

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A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on ℋ 2 by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generalization of Aleksandrov–Clark measures which corresponds to the unweighted case, that is, to the...

Disc formulas for the weighted Siciak-Zahariuta extremal function

Benedikt Steinar Magnússon, Ragnar Sigurdsson (2007)

Annales Polonici Mathematici

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We prove a disc formula for the weighted Siciak-Zahariuta extremal function V X , q for an upper semicontinuous function q on an open connected subset X in ℂⁿ. This function is also known as the weighted Green function with logarithmic pole at infinity and weighted global extremal function.

On the boundedness of the differentiation operator between weighted spaces of holomorphic functions

Anahit Harutyunyan, Wolfgang Lusky (2008)

Studia Mathematica

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We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.