Superposition operators between weighted Banach spaces of analytic functions of controlled growth
type: Item
instance of: scholarly article
title: Superposition operators between weighted Banach spaces of analytic functions of controlled growth
zbMATH Open document ID: 1278.47056
author: José Bonet
author: Dragan Vukotić
published in: Monatshefte für Mathematik
publication date: 2013-06-17T00:00:00Z
full work available at URL: http://hdl.handle.net/10251/40646
review text: For a weight \(\nu \), let \(H_{\nu}^{\infty}=H_{\nu}^{\infty}(\mathbb{D})\) denote the weighted Banach space of holomorphic functions on the unit disc \(\mathbb{D}\) on the complex plane equipped with the norm \(\| f\|_{\nu}:=\sup_{z\in\mathbb{D}}\nu(z) | f(z)|\). The paper is concerned with conditions on the entire function \(h\) which guarantee that the corresponding Nemytskij superposition operator \(S_{\varphi}(f) :=\varphi \circ f\) maps \(H_{\mu}^{\infty}\) into \(H_{\nu}^{\infty}\). The authors also show that all superposition operators generated by such entire functions are bounded and continuous. Moreover, they give some results for concrete weights (polynomial weights, exponential weights and logarithmic weights).
reviewed by: Małgorzata Wróbel
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 6176421
zbMATH Keywords: superposition operators
zbMATH Keywords: weighted Banach spaces
zbMATH Keywords: entire functions
MaRDI profile type: Publication
OpenAlex ID: W1999720050
cites work: Superposition operators between the Bloch space and Bergman spaces
cites work: Q4040886
cites work: Remarks on the superposition operator problem in various function spaces
cites work: Weighted spaces of holomorphic functions on balanced domains
cites work: Q4376702
cites work: Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions
cites work: Q4389859
cites work: HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES
cites work: Superposition operators between weighted spaces of analytic functions
cites work: Q4548117
cites work: Univalent interpolation in Besov spaces and superposition into Bergman spaces
cites work: Q4855889
cites work: Q4304761
cites work: Bounded superposition operators between Bloch-Orlicz and \(\alpha \)-Bloch spaces
cites work: Q3943468
cites work: Superposition operators between \(Q_p\) spaces and Hardy spaces
cites work: A weak criterion for vector-valued holomorphy
cites work: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions
cites work: Q4355953
cites work: On Weighted Spaces of Harmonic and Holomorphic Functions
cites work: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions
cites work: Q4000499
cites work: Bounded superposition operators between weighted Banach spaces of analytic functions
cites work: Q5634458
cites work: Superposition operators between Qp spaces and Bloch-type spaces
cites work: Superposition operators on Bloch-type spaces
cites work: Q3447431
DOI: 10.1007/S00605-012-0441-6
description: scientific article; zbMATH DE number 6176421