设函数b=(b1,b2,…,bm)和广义分数次积分L-a/2(0〈α〈n),它们生成多线性算子定义如下 Lb -a/2 f = [bm …, [b2[b1, L-a/2]],…, ]f,其中m ∈ Z+ , bi ∈ Lipβi (0 〈βi 〈 1),其中(1≤i≤m).将讨论Lb -1a/2。从Mp^q(Rn)到Lip(α+β-n/ q) ( Rn )和q^q ( Rn )到BMO(Rn)的有界性.
In this paper, the authors established the ( Mq^q ( Rn ), Lip(α+β-n/ q) ( Rn ) )-boundedness and ( Mq^q ( Rn )) , BMO ( Rn ) )-boundedness of the multilinear commutator L b -a /2, which generated by a finite family of locally integral functions b = (b1, b2, …, bm) and the generalized fractional integral L-a/2 for 0 〈 a 〈 n, is defined by Lb -a/2 f = [bm …, [b2[b1, L-a/2]],…, ]f, where m ∈ Z+ and bi ∈ Lipβi (0 〈βi 〈 1) for (1 ≤i ≤ m).