Variation and oscillation for the multilinear singular integrals satisfying Hörmander type conditions

摘要

Suppose that the kernel K satisfies a certain Hörmander type condition. Let b be a function satisfying D^αb ∈ BMO(ℝⁿ) for |α| = m, and let Tb={Tϵb}ϵ>0 be a family of multilinear singular integral operators, i.e., Tϵbf(x)=∫|x−y|>ϵRm+1(b;x,y)|x−y|mK(x,y)f(y)dy. The main purpose of this paper is to establish the weighted L^p-boundedness of the variation operator and the oscillation operator for T^b.