分数次积分的多线性换位子

设L是L2(Rn)上解析半群的无穷小生成算子,其积分核具有高斯界,L-α/2表示L的分数次积分算子,其中0＜α＜n.对自然数m,若bi(i=1,2,…,m)表示Rn上有界平均振荡函数,则由分数次积分L-α/2与bi(i=1,2,…,m)生成多线性交换子是从Lp(Rn)到Lq(Rn)是有界的,其中1＜p＜α/n,1/q=1/p-α/n.

Multilinear Commutators of Fractional Integrals

Let L be the infinitesimal generator of an analytic semigroup on L~2(R~n) with Gaussian kernel bounds, and let L~(-α/2) be the fractional integrals of L for 0 < a < n. Let m be a natural number, and b_i be BMO functions on R~n for i = 1,2,… ,m, we obtain that multilinear commutators generated by fractional integrals and b_i for i = 1,2,…, m are bounded from L~p (R~n) to L~q(R~n), for 1 < p