JournalsrmiVol. 28, No. 1pp. 239–272

Composition operators on Besov algebras

  • Madani Moussai

    Université de M'sila, Algeria
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We study the composition operator Tf(g):=fgT_f(g):= f\circ g on Besov spaces Bp,qs(R)B_{p,q}^{s}(\mathbb{R}) . In the case 1<p<+1 < p< +\infty, pq+p\le q \le +\infty and s>1+(1/p)s>1+ (1/p) we will prove that the operator TfT_f takes Bp,qs(R)B_{p,q}^{s}(\mathbb{R}) into itself if and only if f(0)=0f(0)=0 and ff belongs locally to Bp,qs(R)B_{p,q}^{s}(\mathbb{R}) .

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Madani Moussai, Composition operators on Besov algebras. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 239–272

DOI 10.4171/RMI/676