In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new \({{\mathrm{CMO}}({\mathbb {R}}^{n})}\) characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

中文翻译：

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关于换向器的振动紧凑性和变化

在本文中，我们首先建立了奇异积分算子截短换向器的振动和变化的加权紧致性结果。此外，我们通过加权Lebesgue空间上交换子的振动性和变异性的紧凑性，建立了一个新的\（{{\ mathrm {CMO}}（{\ mathbb {R}} ^ {n}）} \）刻画。