Abstract:

 By the atomic decompositions of Herz-type Hardy spaces and the definition of Herz spaces, using the (q,q) boundedness of the commutator of the Marcinkiewicz integral satisfying the logarithmic Lipschitz condition, the boundedness of the commutator of this class of Marcinkiewicz integral on Herz-type Hardy spaces is obtained. This resultd improves the theory of Marcinkiewicz integral operators.

Key words: Marcinkiewicz integral; commutator; Herz space; Hardy space; boundedness