In this paper the Sobolev regularity properties are investigated of the commutators of fractional maximal functions, both in the global and local case. Some new bounds for the derivatives of the above commutators will be established. As several applications, the boundedness for these operators in Sobolev spaces as well as the bounds of these operators on the Sobolev spaces with zero boundary values in the local setting are obtained.

中文翻译：

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分数极大函数的交换子的 Sobolev 正则性

在本文中，研究了分数极大函数的交换子在全局和局部情况下的 Sobolev 正则性。将建立上述交换子的导数的一些新边界。作为几个应用，获得了这些算子在 Sobolev 空间中的有界性以及这些算子在局部设置中具有零边界值的 Sobolev 空间上的边界。