An optimal symbolic calculus on Besov algebras

Abstract

In this paper we consider Besov algebras on R, that is Besov spaces Bp,qs(R) for s>1/p. For s>1+(1/p), p>4/3, and q≥p we prove that the above algebras have a maximal symbolic calculus in the following sense: for any function f belonging locally to Bp,qs(R) and such that f(0)=0, the associated superposition operator Tf(g):=f○g takes Bp,qs(R) to itself.