Superposition operators and functions of bounded p-variation.

Bourdaud, Gérard, Lanza de Cristoforis, Massimo, and Sickel, Winfried. "Superposition operators and functions of bounded p-variation.." Revista Matemática Iberoamericana 22.2 (2006): 455-487. <http://eudml.org/doc/41980>.

@article{Bourdaud2006,
abstract = {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 &lt; ∞, 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.},
author = {Bourdaud, Gérard, Lanza de Cristoforis, Massimo, Sickel, Winfried},
journal = {Revista Matemática Iberoamericana},
keywords = {Operador no lineal; Operadores acotados; Funciones de variación acotada; Espacios de Besov; functions of bounded -variation; homogeneous and inhomogeneous Besov spaces; Peetre's embedding theorem; boundedness of superposition operators},
language = {eng},
number = {2},
pages = {455-487},
title = {Superposition operators and functions of bounded p-variation.},
url = {http://eudml.org/doc/41980},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Bourdaud, Gérard
AU - Lanza de Cristoforis, Massimo
AU - Sickel, Winfried
TI - Superposition operators and functions of bounded p-variation.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 2
SP - 455
EP - 487
AB - 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 &lt; ∞, 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.
LA - eng
KW - Operador no lineal; Operadores acotados; Funciones de variación acotada; Espacios de Besov; functions of bounded -variation; homogeneous and inhomogeneous Besov spaces; Peetre's embedding theorem; boundedness of superposition operators
UR - http://eudml.org/doc/41980
ER -