After some thinking, I have a terrible headache caused by the following problem. Imagine we have a function $u \colon \mathbb{R}^n \to \mathbb{R}$ such that $u \in L^2(\mathbb{R}^n)$ and$$\int_{\mathbb{R}^n \times \mathbb{R}^n} \frac{|u(x)-u(y)|^2}{|x-y|^{n+2s}}dx\, dy < +\infty$$ where $0
I can't even guess if the answer is positive (as in the case of truncation for $W^{1,p}$ functions) or negative.