Buckley, Stephen M. and Fernández, José L. and Vukotić, Dragan
Superposition operators on Dirichlet type spaces.
Report University of Jyväskylä Department of Mathematics and Statistics, 83.
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 Dirichlet-type 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.
||Superposition operators; Dirichlet type spaces; Trudingertype inequalities; Function spaces; Conformal
geometry; Riemann maps.
between dierent Besov-type 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 Dirichlet-type spaces Dp consist of functions whose
||Faculty of Science and Engineering > Mathematics and Statistics
Prof. Stephen Buckley
||21 Oct 2009 09:16
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||Report University of Jyväskylä Department of Mathematics and Statistics
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