Weighted estimates with general weights for multilinear Calderón-Zygmund operators

In this paper, some weighted estimates with general weights are established for the m-linear Calderón-Zygmund operator and the corresponding maximal operator. It is proved that, if p1,…,pm∈[1,∞] and , then for any weight w, integer ℓ with 1 ≤ ℓ ≤ m, these operators are bounded from Lp1(ℝn,MBw)×…×Lpl(ℝn,MBw)×Lpl+1(ℝn,Mw)×…×Lpm(ℝn,Mw) toLp,∞(ℝn,w) orLp(ℝn,w), where B is a Young function and MB is the maximal operator associated with B.