This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T_(Σb)~*and T_(Πb)~*,which are generalized by a weighted BMO function 6 and a multilinear singular integral operator T,respectively.As applications,some commutator theorems are established.
In this note, the author prove that maximal Bocher-Riesz commutator Bbδ , generated by operator Bδ , and function b ∈ BMO(ω) is a bounded operator from Lp(μ) into Lp (ν), where ω∈ (μν-1 )1 p , μ , ν∈ Ap for 1 < p < ∞. The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator Bbδ, .
