Weighted Composition Operators from H∞ to the Bloch Space of a Bounded Homogeneous Domain

Let D be a bounded homogeneous domain in ℂ n . In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space H ∞ ( D ) into the Bloch space of D . We characterize the bounded weighted composition operators, provide operator norm estimates, and give suffic...

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Bibliographic Details
Published in:Integral equations and operator theory 2010, Vol.66 (1), p.21-40
Main Authors: Allen, Robert F., Colonna, Flavia
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:Let D be a bounded homogeneous domain in ℂ n . In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space H ∞ ( D ) into the Bloch space of D . We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions for compactness. We prove that these conditions are necessary in the case of the unit ball and the polydisk. We then show that if D is a bounded symmetric domain, the bounded multiplication operators from H ∞ ( D ) to the Bloch space of D are the operators whose symbol is bounded.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-009-1736-4