Potential theory results for a class of PDOs admitting a global fundamental solution (Q2417875)

The author considers a class $\mathcal{L}$ of linear partial parabolic operators of the second order in divergence form. First the author assumes only the assumption of hypolellipticity and proves a non-invariant homogeneous Harnack inequality. Then the author assumes global doubling, Poincaré inequality and other geometrical assumptions to prove an invariant, non-homogeneous Harnack inequality. Finally the author assumes that $\mathcal{L}$ is equipped with a global fundamental solution $\Gamma$ to prove further Potential Theory resuls such as the Strong Maximum principle. Lastly the existence of $\Gamma$ is discussed. For the entire collection see [Zbl 1409.35008].