多线性分数次积分与Lipschitz函数生成的交换子的有界性

Commutators Generated by Multilinear Fractional Integrals and Lipschitz Functions

设m∈N,b=(b_1,…,b_m)是一个局部可积函数族,且f=(f_1…,f_m),其中f_1,…,f_m∈L_c~∞(R^n).设x suppf_i,则由多线性分数次积分与函数族b=(b_1,…,b_m)生成的交换子定义为I_(α,m)~b(f)(x)=∫_((R^n)~m) K(x,y_1,…,y_m)(b_i(x)-b_i(y_i))f_i(y_i)dy_1…dy_m.当b_j∈_β_j(R^n)(1≤j≤m)时,作者考虑I_(α,m)~b在乘积Lebeasgue空间,Triebel-Lizorkin空间和Lipschitz函数空间的有界性.

Let m∈ N, b = （b1,..., bm） whose components are of locally integrable functions, and f=（f1,…, fm） where f1,…, fm ∈ Lc∞（Rn）. Let A suppfi, then the commutatorgenerated by the multilinear fractional integral is given by