Entire 𝑠-harmonic functions are affine

Fall, Mouhamed

doi:10.1090/proc/13021

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.

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