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

Songxiao Li and Stevo Stević

Abstract and Applied Analysis, 2007, vol. 2007, issue 1

Abstract: Let Dn be the unit polydisc of ℂn, ϕ(z) = (ϕ1(z), …, ϕn(z)) be a holomorphic self‐map of Dn, and ψ(z) a holomorphic function on Dn. Let H(Dn) denote the space of all holomorphic functions with domain Dn, H∞(Dn) the space of all bounded holomorphic functions on Dn, and B(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)

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2007:y:2007:i:1:n:048478

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