I'm reading the proof of the regularity condition for Navier-Stokes, $L^\infty\Rightarrow C^\infty$. I'm confused by the estimate \begin{align*} \|\int_0^t\mathbb P\nabla\cdot(u\otimes u)ds\|_{B_{\infty,\infty}^{(k+1)/2}}\leq C\|u\|_{L^\infty((T_0,T_2),B_{\infty,\infty}^{k/2})}^2\int_{T_0}^t\max\{(t-s)^{-3/4},1\}ds \end{align*} with $\mathbb P$ the Leray projection, $B_{p,q}^s$ a Besov space, $u\in L^\infty((T_0,T_2),B_{\infty,\infty}^{k/2})^d$.
I know that $B_{\infty,\infty}^{k/2}$ is an algebra with pointwise multiplication so $u\otimes u(t)\in(B_{\infty,\infty}^{k/2})^{d\times d}$, but I feel like taking $\mathbb P\nabla\cdot u$ should make it lose a whole derivative, not $1/2$. I also don't see where the $\max\{(t-s)^{-3/4},1\}$ comes from.