Weighted Campanato Estimates for Commutators of Marcinkiewicz Integrals with Variable Kernel

Functionbin commutator is extended from the weighted Lipschitz space to the weighted Campanato space. By use of the sharp maximal function, it is proved that the Marcinkiewicz integral operatorμΩwith viariable kernel and the commu- tatorμbΩgenerated by a weighted Campanato space functionb, are a bounded operator fromLp(ω) to Lq(ω1-q) by use of Sharp maximal function. Thus,the range of use is made still wider.