Univalent interpolation on Besov spaces and superposition into Bergman spaces

Buckley, Stephen M. and Vukotić, Dragan (2008) Univalent interpolation on Besov spaces and superposition into Bergman spaces. Potential Analysis , 29 (1). pp. 1-16. ISSN 1572-929X

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We characterize the superposition operators from an analytic Besov space or the little Bloch space into a Bergman space in terms of the order and type of the symbol. We also determine when these operators are continuous or bounded. Along the way, we prove new non-centered Trudinger-Moser inequalities and solve the problem of interpolation by univalent functions in analytic Besov spaces.

Item Type: Article
Keywords: Superposition operator; Trudinger–Moser inequalities; Analytic Besov spaces; Bergman spaces; Little Bloch space; Montel compactness; Univalent interpolation; Entire functions.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1575
Identification Number: 10.1007/s11118-008-9081-9
Depositing User: Prof. Stephen Buckley
Date Deposited: 13 Oct 2009 10:09
Journal or Publication Title: Potential Analysis
Publisher: Springer Netherlands
Refereed: No

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