Commutators for Fourier multipliers on Besov Spaces Original Research Article

If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and 0<σ1<σ<σ0), it is proved that the commutator [T,Tμ]=TTμ−TμT is bounded on Bpσ,q(Rn), if Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas.