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/lp/de-gruyter/weighted-composition-operators-on-bergman-and-dirichlet-spaces-EwIcG9MpXP
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- Publisher
- de Gruyter
- Copyright
- © 1997 Plenum Publishing Corporation
- ISSN
- 1072-947X
- eISSN
- 1072-9176
- DOI
- 10.1515/GMJ.1997.373
- Publisher site
- See Article on Publisher Site
Abstract
Let 𝐻(Ω) denote a functional Hilbert space of analytic functions on a domain Ω. Let 𝑤 : Ω → 𝐂 and φ : Ω → Ω be such that 𝑤 𝑓 ○ φ is in 𝐻(Ω) for every 𝑓 in 𝐻(Ω). The operator 𝑤𝐶 φ Given by 𝑓 → 𝑤 𝑓 ○ φ is called a weighted composition operator on 𝐻(Ω). In this paper we characterize such operators and those for which (𝑤𝐶 φ )* is a composition operator. Compact weighted composition operators on some functional Hilbert spaces are also characterized. We give sufficient conditions for the compactness of such operators on weighted Dirichlet spaces.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Aug 1, 1997
Keywords: Weighted composition operator; compact; functional Hilbert space; Carleson measure; angular derivative; Dirichlet space