Asymptotic average solutions for second order hypoelliptic PDEs

Following an analogous procedure with that used in \cite{kogoj_lanconelli_pizzetti}, in turn inspired by a 1909 paper by Pizzetti \cite{pizzetti}, we introduce the notion of {\it asymptotic average solutions} for hypoelliptic linear partial differential operators with non-negative characteristic form. This notion makes every Poisson equation $\text{elle}u(x)=-f(x)$ with continuous data $f$ pointwise solvable.