COMMUTATORS OF MULTIPLIERS ON HARDY SPACES

Let T be the multiplier operator associated to a multiplier m, and [b, T] be the commutator generated by T and a BMO function b. In this paper, the authors have proved that [b,T] is bounded from the Hardy space H1(Rn) into the weak L1(Rn) space and from certain atomic Hardy space H1(Rn) into the Lebesgue space L1(Rn), when the multiplier m satisfies the conditions of Hormander type.