非双倍测度下多线性奇异积分算子及其交换子在Morrey空间上的有界性

摘要

Many mathematicians have paid their attentions to the boundedness problem of multilinear singular integral operators since it was put forward at the end of last century. Assume that μ is a non-doubling measure. By the equivalent characterization of RBMO functions and the properties of the kernel of multilinear singular integral operators, it is proven that T and its commutators with RBMO functions are bounded form Mqlpl(μ)×… × Mqmpm(μ) to Mqp(μ) provided that the multilinear singular operator T is bounded from L1 (μ) ×… ×L1(μ) to Lm/1,∞(μ).%非齐型空间上多线性奇异积分算子的有界性问题,自20世纪末由Tolsa等人提出后,广为人们所关注.设μ是非双倍测度,借助RBMO函数的等价刻划,以及多线性奇异积分算予的核满足的条件,证明如果多线性奇异积分算子T从L1(μ)×…×L1(μ)到L(1/m),∞(μ)有界,则T以及它与有界平均振荡函数生成的交换子是从Mq1p1(μ)×…×Mqmpm(μ)到Mqp(μ)有界的算子.