2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167315The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here, we show that these differential operators generate analytic semigroup.26 pagesFunctional Analysis42B15, 46E40, 34G10text