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Superposition operators on Dirichlet type spaces

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. 41-61. ISSN 1457-8905

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Official URL: http://www.math.jyu.fi/research/reports/rep83c.pdf

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 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.

Item Type: Article
Keywords: Superposition operators; Dirichlet type spaces; Trudingertype inequalities; Function spaces; Conformal geometry; Riemann maps. between di erent 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 speci c case in question. The Dirichlet-type spaces Dp consist of functions whose
Subjects: Science & Engineering > Mathematics
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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