Abstract and Applied Analysis

Weighted Composition Operators from H to the Bloch Space on the Polydisc

Songxiao Li and Stevo Stević

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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 ) .

Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 48478, 13 pages.

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1183666881

Digital Object Identifier
doi:10.1155/2007/48478

Mathematical Reviews number (MathSciNet)
MR2320803

Zentralblatt MATH identifier
1152.47016

Citation

Li, Songxiao; Stević, Stevo. Weighted Composition Operators from $H^{\infty}$ to the Bloch Space on the Polydisc. Abstr. Appl. Anal. 2007 (2007), Article ID 48478, 13 pages. doi:10.1155/2007/48478. https://projecteuclid.org/euclid.aaa/1183666881


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