Superposition operators and functions of bounded <I>p</I>-variation

  • Gérard Bourdaud

    Université Pierre et Marie Curie, Paris, France
  • Massimo Lanza de Cristoforis

    Università di Padova, Italy
  • Winfried Sickel

    Friedrich-Schiller-Universität Jena, Germany


We characterize the set of all functions ff of R\mathbb R to itself such that the associated superposition operator Tf:gfgT_f: g \to f \circ g maps the class BVp1(R)BV^1_p (\mathbb R) into itself. Here BVp1(R)BV^1_p (\mathbb R), 1p<1 \le p < \infty, denotes the set of primitives of functions of bounded pp-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(Rn)B^s_{p,q}({\mathbb R}^n) 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. 455–487

DOI 10.4171/RMI/463