Revista Matemática Iberoamericana


Full-Text PDF (414 KB) | Metadata | Table of Contents | RMI summary
Volume 28, Issue 1, 2012, pp. 239–272
DOI: 10.4171/RMI/676

Published online: 2012-01-20

Composition operators on Besov algebras

Madani Moussai[1]

(1) Université de M'sila, Algeria

We study the composition operator $T_f(g):= f\circ g$ on Besov spaces $B_{p,q}^{s}(\mathbb{R}) $. In the case $1 < p< +\infty$, $p\le q \le +\infty$ and $s>1+ (1/p)$ we will prove that the operator $T_f$ takes $B_{p,q}^{s}(\mathbb{R}) $ into itself if and only if $f(0)=0$ and $f$ belongs locally to $B_{p,q}^{s}(\mathbb{R}) $.

Keywords: Littlewood–Paley decomposition, Besov spaces, composition operator, functions of bounded p-variation

Moussai Madani: Composition operators on Besov algebras. Rev. Mat. Iberoamericana 28 (2012), 239-272. doi: 10.4171/RMI/676