Quasianalytic wave front sets for solutions of linear partial differential operators

In the present paper, we introduce and study Beurling and Roumieu quasianalytic (and nonquasianalytic) wave front sets, $WF_*$, of classical distributions. In particular, we have the following inclusion $$ WF_\ast (u)\subset WF_\ast(Pu)\cup \Sigma, \quad u\in\D^\prime(\Omega), $$ where $\Omega$ is an open subset of $\R^n$, $P$ is a linear partial differential operator with coefficients in a suitable ultradifferentiable class, and $\Sigma$ is the characteristic set of $P$. Some applications are also investigated.