Abstract
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.
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Fernández, E., Roncal, L. A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus. Potential Anal 53, 1449–1465 (2020). https://doi.org/10.1007/s11118-019-09813-8
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DOI: https://doi.org/10.1007/s11118-019-09813-8
Keywords
- Infinite dimensional torus
- Calderón–Zygmund decomposition
- Differentiation of integrals
- Differentiation basis
- Locally compact groups