Buckley, Stephen M. and Fernández, José L. and Vukotić, Dragan
(2001)
Superposition operators on Dirichlet type spaces.
Report University of Jyväskylä Department of Mathematics and Statistics, 83.
pp. 4161.
ISSN 14578905
Abstract
We characterize the entire functions ℓfor which the induced nonlinear superposition operator f →ℓof one Besov space Bp into another Bq, where B∞ can be taken to be any of the following natural spaces: VMOA, BMOA, B0, and
B. We do the same for the superpositions from one unweighted Dirichlettype space Dp into another, and from Bp into the weighted space Dqά. The admissible functions
are typically polynomials whose degree depends on p and q, or entire functions whose order and type are determined by those exponents. We prove some new Trudingertype
inequalities for analytic functions along the way.
Item Type: 
Article

Keywords: 
Superposition operators; Dirichlet type spaces; Trudingertype inequalities; Function spaces; Conformal
geometry; Riemann maps.
between dierent Besovtype spaces, including the \endpoint spaces" VMOA,
BMOA, little Bloch B0, and Bloch B. The operator S' acts from any one of these
spaces into another of them if and only if ' is either a linear function or a constant,
depending on the specic case in question.
The Dirichlettype spaces Dp consist of functions whose 
Academic Unit: 
Faculty of Science and Engineering > Mathematics and Statistics 
Item ID: 
1609 
Depositing User: 
Prof. Stephen Buckley

Date Deposited: 
21 Oct 2009 09:16 
Journal or Publication Title: 
Report University of Jyväskylä Department of Mathematics and Statistics 
Publisher: 
Jyväskylä Yliopisto, Matematiikan ja Tilastotieteen Laitos 
Refereed: 
Yes 
URI: 

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