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Potential Analysis

, Volume 29, Issue 1, pp 1–16 | Cite as

Univalent Interpolation in Besov Spaces and Superposition into Bergman Spaces

  • Stephen M. Buckley
  • Dragan VukotićEmail author
Article

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 and discuss their Montel compactness. 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 

Mathematics Subject Classifications (2000)

47H30 31C25 30H05 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsNational University of IrelandMaynoothIreland
  2. 2.Departamento de Matemáticas, C-XVUniversidad Autónoma de MadridMadridSpain

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