Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces

Motivated by the recent paper [X. Zhu, Products of differentiation composition and multiplication from Bergman type spaces to Bers spaces, Integral Transform. Spec. Funct. 18 (3) (2007) 223–231], we study the boundedness and compactness of the weighted differentiation composition operator D φ , u n...

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Veröffentlicht in:Applied mathematics and computation Jg. 211; H. 1; S. 222 - 233
1. Verfasser: STEVIC, Stevo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Inc 01.05.2009
Elsevier
Schlagworte:
Boundedness
Compactness
Essential norm
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Mixed-norm space
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Several complex variables and analytic spaces
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Weighted differentiation composition operator
Weighted-type space
Essential norm
Weighted-type space
Weighted differentiation composition operator
Compactness
Mixed-norm space
Boundedness
Multiplication
Weighted differentiation composition
Numerical analysis
Applied mathematics
Holomorphic mapping
Integral transformation
operator
ISSN:0096-3003, 1873-5649
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Beschreibung
Zusammenfassung:Motivated by the recent paper [X. Zhu, Products of differentiation composition and multiplication from Bergman type spaces to Bers spaces, Integral Transform. Spec. Funct. 18 (3) (2007) 223–231], we study the boundedness and compactness of the weighted differentiation composition operator D φ , u n ( f ) ( z ) = u ( z ) f ( n ) ( φ ( z ) ) , where u is a holomorphic function on the unit disk D , φ is a holomorphic self-map of D and n ∈ N 0 , from the mixed-norm space H( p, q, ϕ), where p, q > 0 and ϕ is normal, to the weighted-type space H μ ∞ or the little weighted-type space H μ , 0 ∞ . For the case of the weighted Bergman space A α p , p > 1, some bounds for the essential norm of the operator are also given.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2009.01.061