To which space $u$ should belong to have that both $u$ and $(-\Delta)^s u$ are bounded?

The condition $u\in W^{2, \infty}(\mathbb R^n)$ guarantees that $u$, its first and second derivatives, are bounded. In particular, the $(-\Delta)u$ happens to be bounded as well.

Take $s\in (0, 1)$. Which is the corresponding condition which ensure that $u$ and $(-\Delta)^s u$ are bounded in $\mathbb R^n$?

I have searched online but I have not found any relevant answer.

Anyone could provide any reference?