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Journal Articles Transactions of the American Mathematical Society Year : 2018

Hardy-Hodge Decomposition of Vector Fields in R$^{n}$

Abstract

We prove that a R^(n+1)-valued vector field on R^n is the sum of the traces of two harmonic gradients, one in each component of R^(n+1) \ R^n , and of a R^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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Dates and versions

hal-01462960 , version 1 (14-02-2017)

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Cite

Laurent Baratchart, Pei Dang, Tao Qian. Hardy-Hodge Decomposition of Vector Fields in R$^{n}$. Transactions of the American Mathematical Society, 2018, 370 (3), pp.2005 - 2022. ⟨10.1090/tran/7202⟩. ⟨hal-01462960⟩
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