Abstract In this paper we introduce and study the commutators of the local multilinear fractional maximal operators and a vector-valued function b⃗ = (b1, …, bm). Under the condition that each bi belongs to the first order Sobolev spaces, the bounds for the above commutators are established on the first order Sobolev spaces.

中文翻译：

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局部多重线性分数极大算子的交换子的正则性

摘要 本文介绍并研究了局部多重线性分数极大值算子的交换子和向量值函数b⃗ = (b1, …, bm)。在每个bi都属于一阶Sobolev空间的条件下，上述交换子的边界建立在一阶Sobolev空间上。