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2007 Weighted Composition Operators from H to the Bloch Space on the Polydisc
Songxiao Li, Stevo Stević
Abstr. Appl. Anal. 2007: 1-13 (2007). DOI: 10.1155/2007/48478

Abstract

Let D n be the unit polydisc of n , ϕ ( z ) = ( ϕ 1 ( z ) , , ϕ n ( z ) ) be a holomorphic self-map of D n , and ψ ( z ) a holomorphic function on D n . Let H ( D n ) denote the space of all holomorphic functions with domain D n , H ( D n ) the space of all bounded holomorphic functions on D n , and B ( D n ) the Bloch space, that is, B ( D n ) = { f H ( D n ) | f B = | f ( 0 ) | + sup z D n k = 1 n | ( f / z k ) ( z ) | ( 1 | z k | 2 ) < + } . We give necessary and sufficient conditions for the weighted composition operator ψ C ϕ induced by ϕ ( z ) and ψ ( z ) to be bounded and compact from H ( D n ) to the Bloch space B ( D n ) .

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Songxiao Li. Stevo Stević. "Weighted Composition Operators from H to the Bloch Space on the Polydisc." Abstr. Appl. Anal. 2007 1 - 13, 2007. https://doi.org/10.1155/2007/48478

Information

Published: 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1152.47016
MathSciNet: MR2320803
Digital Object Identifier: 10.1155/2007/48478

Rights: Copyright © 2007 Hindawi

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