Let $s\in (0,1)$ and $u\in D^{s, 2} (\mathbb R^N)$, $\phi\in H^s_{0}(B).$ Here $B$ is a unit ball in $\mathbb R^N$ and 
$$H^s_{0}(B)=\{ u\in H^{s} (\mathbb R^N): u=0 \text{ in } \mathbb R^N- B\}$$ and 
$$D^{s, 2} (\mathbb R^N)= \bigg\{u\in L^{\frac{2N}{N-2s}}(\mathbb R^N): \int_{\mathbb R^{2N}}\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dx dy<+\infty\bigg\}.$$


Is integration by parts valid for  

$$\int_{B} (-\Delta)^s u \phi dx= \int_{\mathbb R^{N}} (-\Delta)^{s/2} u (-\Delta)^{s/2} \phi dx.$$

References are welcome.