  In this article we prove the BMO-$L_{\infty}$ estimate $$
\|(-\Delta)^{\gamma/2} u\|_{BMO(\mathbf{R}^{d+1})}\leq N
\|\frac{\partial}{\partial t}u-A(t)u\|_{L_{\infty}(\mathbf{R}^{d+1})}, \quad
\forall\, u\in C^{\infty}_c(\mathbf{R}^{d+1}) $$ for a wide class of
pseudo-differential operators $A(t)$ of order $\gamma\in (0,\infty)$. The
coefficients of $A(t)$ are assumed to be merely measurable in time variable. As
an application to the equation $$ \frac{\partial}{\partial t}u=A(t)u+f,\quad
t\in \mathbf{R} $$ we prove that for any $u\in C^{\infty}_c(\mathbf{R}^{d+1})$
$$
\|u_t\|_{L_p(\mathbf{R}^{d+1})}+\|(-\Delta)^{\gamma/2}u\|_{L_p(\mathbf{R}^{d+1})}\leq
N\|u_t-A(t)u\|_{L_p(\mathbf{R}^{d+1})}, $$ where $p\ in (1,\infty)$ and the
constant $N$ is independent of $u$.
