Entire $s$-harmonic functions are affine

In this paper, we prove that solutions to the equation $(-Δ)^s u=0$ 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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