# Hardy-Hodge Decomposition of Vector Fields in $Rn$

Abstract : We prove that a $IR n+1$-valued vector field on $IR n$ is the sum of the traces of two harmonic gradients, one in each component of $IR n+1 \ IR n$ , and of a $IR n$-valued divergence free vector field. We apply this to the description of vanishing potentials in divergence form. The results are stated in terms of Clifford Hardy spaces, the structure of which is important for our study.
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Cited literature [20 references]

https://hal.inria.fr/hal-01462960
Contributor : Laurent Baratchart <>
Submitted on : Tuesday, February 14, 2017 - 12:49:27 PM
Last modification on : Thursday, January 17, 2019 - 1:42:02 PM
Long-term archiving on: : Monday, May 15, 2017 - 12:22:55 PM

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BDQ2016_submitted.pdf
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### Identifiers

• HAL Id : hal-01462960, version 1
• ARXIV : 1702.04233

### Citation

Laurent Baratchart, Pei Dang, Tao Qian. Hardy-Hodge Decomposition of Vector Fields in $Rn$. 2017. ⟨hal-01462960⟩

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