Pointwise multiplication in the realized homogeneous Besov and Triebel–Lizorkin spaces

For either homogeneous Besov spaces $\dot B_{p,q}^s(\mathbb{R}^n)$ or homogeneous Triebel–Lizorkin spaces $\dot F_{p,q}^s(\mathbb{R}^n)$, with the conditions either $s < n/p$, or $s = n/p$ and $q \le 1$ in the $\dot B_{p,q}^s$-case, $p \le 1$ in the $\dot F_{p,q}^s$-case, we prove some pointwise multiplication assertions in their realized spaces.