Appell, J. and Jesús, Z. and Mejía, O.:
Some Remarks on Nonlinear Composition Operators in Spaces of Differentiable Functions
Bollettino dell'Unione Matematica Italiana Serie 9 4 (2011), fasc. n.3, p. 321-336, (English)
pdf (306 Kb), djvu (157 Kb). | MR 2906764 | Zbl 1229.47086
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In this note we study the nonlinear composition operator $f \mapsto g \circ f$ in various spaces of differentiable functions over an interval. It turns out that this operator is always bounded in the corresponding norm, whenever it maps such a space into itself, but continuous only in exceptional cases.
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