Pseudo-differential operators in vector-valued spaces and applications

Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential abstract parabolic equation are established. Particularly, it is proven that the operators generated by these pseudo-differential equations are positive and aso are generators of analytic semigroups. As an application, the anisotropic parameter dependent pseudo-differential equations and the system of pseudo-differential equations are studied