线性交换子的加权估计

Weighted estimate for commutators of multilinear operators

摘要: 多线性交换子Tb(f)(x)=∫Rn∏i=1m(bi(x)-bi(y))k(x,y)f(y)dy在Lp(Rn)(1p∞)上是有界的,而K是一个标准的Calderón-Zygmund核.主要研究交换子Mf(x)=supx∈Q∫Q|f(y)|dy,其中f∈Lloc(Rn),x∈Rn,Q是任何包含x的方体,并用Sharp极大估计得到了该多线性交换子在Herz空间的一个加权有界性.

Abstract: The multilinear commuators defined as Tb(f)(x)=∫Rn∏i=1m(bi(x)-bi(y))k(x,y)f(y)dy is bounded in Lp(Rn)(1p∞),where K is a standard Calderón-Zygmund kenerl.The commutator operator Mf(x)=supx∈Q∫Q|f(y)|dy,where f∈Lloc(Rn),x∈Rn,let Q be any cube which contains x,and associatedto multilinear singular intergals in BMO(Rn),it is obtained that a weighted norm inequalities,the weighted boundedness forthe commutators of multilinear operators are proved.