Weighted Composition Operators from α-Bloch Space to H∞on the Polydisc
- 13 August 2007
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 28 (7-8) , 911-925
Abstract
Let n be the unit polydisc of ℂn, ϕ(z) = (ϕ1(z),…, ϕn(z)) be a holomorphic self-map of n, and ψ(z) a holomorphic function on n. Let H∞(n) be the space of all bounded holomorphic functions on n and ℬα(n) the α-Bloch space. Necessary and sufficient conditions for the weighted composition operator ψCϕ induced by ϕ(z) and ψ(z) to be bounded and compact from ℬα(n) to H∞(n) are given in this paper. One of our results corrects and extends Theorem 1 in the paper by S. Ohno, Weighted composition operators between H∞ and the Bloch space, Taiwanese J. Math. 2001; 5:555–563.Keywords
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