Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Hardy-Hodge decomposition of vector fields in $ \mathbb{R}^n$


Authors: Laurent Baratchart, Pei Dang and Tao Qian
Journal: Trans. Amer. Math. Soc. 370 (2018), 2005-2022
MSC (2010): Primary 42B30
DOI: https://doi.org/10.1090/tran/7202
Published electronically: September 15, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that an $ \mathbb{R}^{n+1}$-valued vector field on $ \mathbb{R}^n$ is the sum of the traces of two harmonic gradients, one in each component of $ \mathbb{R}^{n+1}\setminus \mathbb{R}^n$, and of an $ \mathbb{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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 42B30

Retrieve articles in all journals with MSC (2010): 42B30


Additional Information

Laurent Baratchart
Affiliation: INRIA, 2004 route de Lucioles, 06902 Sophia-Antipolis Cedex, France
Email: Laurent.Baratchart@inria.fr

Pei Dang
Affiliation: Faculty of Information Technology, Macau University of Science and Technology, Macao, China
Email: pdang@must.edu.mo

Tao Qian
Affiliation: Department of Mathematics, University of Macau, Macao, China
Email: fsttq@umac.mo

DOI: https://doi.org/10.1090/tran/7202
Received by editor(s): July 9, 2016
Published electronically: September 15, 2017
Additional Notes: This work was supported by the Macao Science and Technology Development Fund: FDCT 045/2015/A2 and FDCT 098/2012, the Chinese National Natural Science Funds for Young Scholars: 11701597, and the University of Macau Multi-Year Research Grant MYRG116 (Y1-L3)-FST13-QT. The third author is the corresponding author.
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society