Let $T\in(0,\infty)$ and $\Omega\subset\mathbb R^n$ be a smooth domain. In terms of maximal regularity it can be very beneficial to know for which $s_i,p,n$ the following holds true

$W^{s_1,p}(0,T;L^p(\Omega))\cap L^p(0,T;W^{s_2,p}(\Omega))\cdot W^{s_3,p}(0,T;L^p(\Omega))\cap L^p(W^{s_4,p}(\Omega))\subset $

$\qquad\qquad\qquad\qquad\qquad W^{t_1,p}(0,T;L^p(\Omega))\cap L^p(W^{t_2,p}(\Omega)),\quad t_1,t_2\in(0,1)$

In this respect I'm interested in sharp choices of $s,p,n\in\mathbb R_+^4\times(1,\infty)\times \mathbb N$. However due to very complicated Sobolev-Slobodeckii norms the calculations are quite involved, so I was wondering if anybody is aware of a reference in the literature for this problem.