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
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.
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