On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball
TLDR
In this article, an integral-type operator on the space H (B ) of all holomorphic functions on the unit ball B ⊂ C n P φ g ( f ) ( z ) = ∫ 0 1 f ( φ ( t z ) ) g ( t t, z ∈ B, where g ∈ H ( B ), g ( 0 ) = 0 and φ is a holomorphic self-map of B.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2009-06-15 and is currently open access. It has received 126 citations till now. The article focuses on the topics: Bloch space & Bergman space.read more
Citations
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Weighted differentiation composition operators from H∞ and Bloch spaces to nth weighted-type spaces on the unit disk
TL;DR: The boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions, the Bloch space and the little Blochspace to nth weighted-type spaces on the unit disk are characterized.
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Products of multiplication composition and differentiation operators on weighted Bergman spaces
TL;DR: This work considers linear operators induced by products of these operators on weighted Bergman spaces on D, establishing boundedness by using Carleson-type measures.
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On an integral-type operator from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces
TL;DR: In this paper, the boundedness and compactness of the integral-type operator P φ g f (z ) = ∫ 0 1 f ( φ ( t z ) ) g (t z ) d t t, z ∈ B, where φ is a holomorphic self-map of the unit ball B in C n and g is a function on B such that g ( 0 ) = 0, from logarithmic Bloch-type and mixed-norm spaces to Bloch type spaces.
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Composition followed by differentiation from H∞ and the Bloch space to nth weighted-type spaces on the unit disk
TL;DR: The boundedness and compactness of the product of the differentiation and composition operator from the space of bounded analytic functions, the Bloch space and the little Blochspace to nth weighted-type spaces on the unit disk are characterized.
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Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces
TL;DR: An asymptotic expression is found for the essential norm of products of these operators on weighted Bergman spaces on the unit disk about holomorphic function ψ on the open unit disk.
References
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Book
Function Theory in the Unit Ball of ℂn
TL;DR: In this paper, the boundary behavior of Cauchy integral functions is investigated and the results of the Schwarz Lemma are discussed, as well as the Zeros of Nevanlinna functions.
Book
Composition Operators on Spaces of Analytic Functions
TL;DR: In this paper, Wogen's Theorem Spectral Properties Spectral properties of Compact Composition Operators Spectra: Boundary Fixed Point, Boundary fixed point, boundary fixed point.
Book
Spaces of Holomorphic Functions in the Unit Ball
TL;DR: In this article, Bergman Spaces, Bloch Spaces, Hardy Spaces, Besov Spaces, Lipschitz Spaces, and Hardy Spaces have been investigated for functions of bounded mean oscillation.
Journal ArticleDOI
Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation
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Integration operators on Bergman spaces
TL;DR: In this article, the authors considered conditions on a positive integrable function such that the operator T_g$ is bounded on a Banach space of analytic functions, and showed that the condition is necessary and sufficient.
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