Weighted variation inequalities for differential operators and singular integrals

We prove weighted strong q-variation inequalities with 2 < q < infinity for differential and singular integral operators. For the first family of operators the weights used can be either Sawyer's one-sided A(p)(+) weights or Muckenhoupt's A(p) weights according to whether the differential operators in consideration are one-sided or symmetric. We use only Muckenhoupt's A(p) weights for the second family. All these inequalities hold equally in the vector-valued case, that is, for functions with values in l(p) for 1 < p < infinity. As application, we show variation inequalities for mean bounded positive invertible operators on L-p with positive inverses. (C) 2014 Elsevier Inc. All rights reserved.