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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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Abstract

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.

Keywords:Superposition operator; Trudinger–Moser inequalities; Analytic Besov spaces; Bergman spaces; Little Bloch space; Montel compactness; Univalent interpolation; Entire functions.
Subjects:Science & Engineering > Mathematics
ID Code:1575
Deposited By:Prof. Stephen Buckley
Deposited On:13 Oct 2009 11:09
Journal or Publication Title:Potential Analysis
Publisher:Springer Netherlands
Refereed:No
URL:http://www.springerlink.com/content/100331/?p=9e5244fe171e442889a9d344cc03b81e&pi=84

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