Weighted vector-valued estimates for a non-standard Calderón-Zygmund operator

In this paper, the author considers the weighted vector-valued estimates for the operator defined by TAf(x)=p.v.∫RnΩ(x−y)|x−y|n+1(A(x)−A(y)−∇A(y))f(y)dy,and the associated maximal singular integral operator TA∗, where Ω is homogeneous of degree zero, has vanishing moment of order one, A is a function in Rn such that ∇A∈BMO(Rn). By pointwise estimates for ‖{TAfk(x)}‖lq and ‖{TA∗fk(x)}‖lq, the author obtains some quantitative weighted vector-valued bounds for TA and TA∗.