1. HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES.
- Author
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BOYD, CHRISTOPHER and RUEDA, PILAR
- Subjects
- *
HOLOMORPHIC functions , *BANACH spaces , *DOMAINS of holomorphy , *INFINITE dimensional Lie algebras , *SUPERPOSITION principle (Physics) - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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