Superposition operators and functions of bounded p-variation

• Autores: Gérard Bourdaud, M. Lanza de Cristoforis, Winfried Sickel
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 22, Nº 2, 2006, págs. 455-488
• Idioma: inglés
• DOI: 10.4171/rmi/463
• Títulos paralelos:
  • Operadores de superposición y funciones de p-variación acotada
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• Resumen

  • 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.