In this note we will show a Calderón–Zygmund decomposition associated with a function \(f\in L^{1}(\mathbb {T}^{\omega })\). The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting of locally compact groups. Some related results about differentiation of integrals on the infinite-dimensional torus are also discussed.

中文翻译：

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Calderón-Zygmund类型的分解以及对无限维环上积分微分的一些观察

在本注释中，我们将显示与函数\（f \ in L ^ {1}（\ mathbb {T} ^ {\ omega}）\）相关联的Calderón–Zygmund分解。这个想法依赖于JL Rubio de Francia对本地紧凑型团体的更普遍结果的改编。还讨论了有关无穷维环上积分微分的一些相关结果。