# Superposition operators and functions of bounded p-variation.

Gérard Bourdaud; Massimo Lanza de Cristoforis; Winfried Sickel

Revista Matemática Iberoamericana (2006)

- Volume: 22, Issue: 2, page 455-487
- ISSN: 0213-2230

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topBourdaud, 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 < ∞, 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 < ∞, 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 -

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