Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition - Pu Zhang; Daiqing Zhang (The Scientific World Journal)
Let T be a singular integral operator with its kernel satisfying |K(x-y)-∑k=1ℓ‍Bk(x)ϕk(y)|≤C|y|γ/|x-y|n+γ, |x|>2|y|>0, where Bk and ϕk  (k=1,…,ℓ) are appropriate functions and γ and C are positive constants. For b→=(b1,…,bm) with bj∈BMO(ℝn), the multilinear commutator Tb→ generated by T and b→ is formally defined by Tb→f(x)=∫ℝn∏j=1m‍(bj(x)-bj(y))K(x,y)f(y)dy. In this paper, the weighted Lp-boundedness and the weighted weak type Llog⁡L estimate for the multilinear commutator Tb→ are established.