Entire $s$-harmonic functions are affine
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- by Mouhamed Moustapha Fall
- Proc. Amer. Math. Soc. 144 (2016), 2587-2592
- DOI: https://doi.org/10.1090/proc/13021
- Published electronically: January 27, 2016
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Abstract:
In this paper, we prove that solutions to the equation $(-\Delta )^s u=0$ in $\mathbb {R}^N$, for $s\in (0,1)$, are affine. This allows us to prove the uniqueness of the Riesz potential $|x|^{2s-N}$ in Lebesgue spaces.References
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Bibliographic Information
- Mouhamed Moustapha Fall
- Affiliation: African Institute for Mathematical Sciences in Senegal, KM 2, Route de Joal, B.P. 14 18. Mbour, Sénégal
- MR Author ID: 856519
- Email: mouhamed.m.fall@aims-senegal.org, mouhamed.m.fall@gmail.com
- Received by editor(s): July 24, 2014
- Received by editor(s) in revised form: April 9, 2015, and August 1, 2015
- Published electronically: January 27, 2016
- Additional Notes: This work was supported by the Alexander von Humboldt foundation and the author would like to thank Tobias Weth and Krzysztof Bogdan for useful discussions. This work was completed while the author was visiting the Goethe-Universität Frankfurt am Main and the Technische Universität Chemnitz. The author is also very grateful to the referee for the detailed comments. The variety of substantial suggestions helped the author to improve the earlier versions of this manuscript
- Communicated by: Mark M. Meerschaert
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2587-2592
- MSC (2010): Primary 35R11, 42B37
- DOI: https://doi.org/10.1090/proc/13021
- MathSciNet review: 3477075