Let $s\in(0,1)$, $p>1$ and $N\geq 1$. We define the fractional p Laplace operator $(-\Delta)_p^{s}$ by $$ (-\Delta)_p^{s}u(x):=\lim_{r\to 0}\int_{\mathbb{R}^N\setminus B_r(x)}\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+ps}}\,dy. $$ Can somebody please help me under what condition on the function $u$ the above operator is well defined?
Thanking you.