Variation operators for commutators of rough singular integrals on weighted morrey spaces

In this paper, we establish the boundedness and compactness the variation operators of commutators of singular integrals with rough kennels omega is an element of ??(S ?-1) for some ?is an element of(1,infinity] on the weighted Lebesgue and Morrey spaces. Our main results represent significant improvements as well as natural extensions of what was known previously.