Commutators for Approximation Spaces and Marcinkiewicz-Type Multipliers Original Research Article

It is proved that, under some conditions, weaker than those of the Marcinkiewicz multiplier theorem, the multiplier operator Tμ(∑k ckeikt)=∑k μkckeikt satisfies on the Besov space Bσ, qp the commutator theorem‖[T, Tμ]‖Bσ, qp, Bσ, qp⩽c ‖T‖, where ‖T‖=max(‖T‖Bσ0, q0p, Bσ0, q0p, ‖T‖Bσ1, q1p, Bσ1, q1p and σ0>σ>σ1>0.