Resumen de Superposition operators and functions of bounded p-variation

Gérard Bourdaud, M. Lanza de Cristoforis, Winfried Sickel

• We characterize the set of all functions f of R to itself such that the associated superposition operator Tf: g ? f º g maps the class BVp1(R) into itself. Here BVp1(R), 1 = p < 8, denotes the set of primitives of functions of bounded p-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 Bp,qs are discussed.