We characterize the set of all functions of to itself such that the associated superposition operator maps the class into itself. Here , , denotes the set of primitives of functions of bounded -variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces are discussed.
Cite this article
Gérard Bourdaud, Massimo Lanza de Cristoforis, Winfried Sickel, Superposition operators and functions of bounded <I>p</I>-variation. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 455–487DOI 10.4171/RMI/463