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https://dx.doi.org/10.1155/200...
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Weighted Composition Operators fromH∞to the Bloch Space on the Polydisc

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2007 English Publisher:WileyJournal:Abstract and Applied Analysis, volume 2,007, pages 1-13 (issn: 1085-3375, eissn: 1687-0409, Copyright policy )
Authors: Songxiao Li; Stevo Stevic;

doi: 10.1155/2007/48478

Weighted Composition Operators fromH∞to the Bloch Space on the Polydisc

Abstract

LetDnbe the unit polydisc ofℂn,ϕ(z)=(ϕ1(z),…,ϕn(z))be a holomorphic self-map ofDn, andψ(z)a holomorphic function onDn. LetH(Dn)denote the space of all holomorphic functions with domainDn,H∞(Dn)the space of all bounded holomorphic functions onDn, andB(Dn)the Bloch space, that is,B(Dn)={f∈H(Dn)|‖f‖B=|f(0)|+supz∈Dn∑k=1n|(∂f/∂zk)(z)|(1−|zk|2)<+∞}. We give necessary and sufficient conditions for the weighted composition operatorψCϕinduced byϕ(z)andψ(z)to be bounded and compact fromH∞(Dn)to the Bloch spaceB(Dn).

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Keywords

QA1-939, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
48
Top 10%
Top 10%
Top 1%
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