Entire $s$-harmonic functions are affine

Mouhamed Moustapha Fall

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arXiv · 1407.5934

Entire $s$-harmonic functions are affine

Mouhamed Moustapha Fall

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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 will allow us to prove uniqueness of the Riesz potential $|x|^{2s-N}$ in Lebesgue spaces.

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Mouhamed Moustapha Fall. 2014-07-22. Entire $s$-harmonic functions are affine. https://arxiv.org/abs/1407.5934

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