2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129251We consider a class of possibly degenerate second order elliptic operators $\cal A$ on $\R^n$. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving ${\cal A}$. The Hölder function spaces are defined with respect to a non-euclidean metric related to the operator $\cal A$.Analysis of PDEs35K65, 35J70, 47D07, 35B65text