Application of a Riesz-type formula to weighted Bergman spaces
نویسندگان
چکیده
منابع مشابه
Weighted Composition Operators between Bergman-type Spaces
In this paper, we characterize the boundedness and compactness of weighted composition operators ψCφf = ψfoφ acting between Bergman-type spaces.
متن کاملWeighted Composition Operators from Generalized Weighted Bergman Spaces to Weighted-Type Spaces
Let ϕ be a holomorphic self-map and let ψ be a holomorphic function on the unit ball B. The boundedness and compactness of the weighted composition operator ψC ϕ from the generalized weighted Bergman space into a class of weighted-type spaces are studied in this paper.
متن کاملWeighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane
and Applied Analysis 3 Let β > 0. The weighted-type space or growth space on the upper half-planeA∞ β Π consists of all f ∈ H Π such that ∥ ∥f ∥ ∥ A∞ β Π sup z∈Π Iz β ∣ ∣f z ∣ ∣ < ∞. 1.7 It is easy to check thatA∞ β Π is a Banach space with the norm defined above. For weightedtype spaces on the unit disk, polydisk, or the unit ball see, for example, papers 10, 32, 33 and the references therein....
متن کاملWeighted composition operators from Bergman-type spaces into Bloch spaces
Let D be the open unit disk in the complex plane C. Denote by H(D) the class of all functions analytic on D. An analytic self-map φ : D → D induces the composition operator Cφ on H(D), defined by Cφ ( f ) = f (φ(z)) for f analytic on D. It is a well-known consequence of Littlewood’s subordination principle that the composition operator Cφ is bounded on the classical Hardy and Bergman spaces (se...
متن کاملGeneralized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06491-2