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HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES

Part of: Linear function spaces and their duals Measures, integration, derivative, holomorphy Nonlinear operators and their properties

Published online by Cambridge University Press:  01 April 2014

CHRISTOPHER BOYD  and
PILAR RUEDA
CHRISTOPHER BOYD*
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
PILAR RUEDA
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, 46100 Burjasot, Valencia, Spain email Pilar.Rueda@uv.es
*
✉Christopher.Boyd@ucd.ie
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Abstract

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We prove that for a large class of Banach function spaces continuity and holomorphy of superposition operators are equivalent and that bounded superposition operators are continuous. We also use techniques from infinite dimensional holomorphy to establish the boundedness of certain superposition operators. Finally, we apply our results to the study of superposition operators on weighted spaces of holomorphic functions and the $F(p, \alpha , \beta )$ spaces of Zhao. Some independent properties on these spaces are also obtained.

Keywords

superposition operatorsweighted spaces of holomorphic functionscontinuity

MSC classification

Secondary: 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) 46G20: Infinite-dimensional holomorphy 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 96 , Issue 2 , April 2014 , pp. 186 - 197
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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