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

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

References are welcome.