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

By Robert F. Allen, Flavia Colonna. 2010

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Let D be a bounded homogeneous domain in ℂn. 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.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/083b5f6ee42bc6b98378c0c3813f3d27f4bd446a