Optimal regularity for degenerate Kolmogorov equations with rough coefficients

We consider a class of degenerate equations satisfying a parabolic H"ormander condition, with coefficients that are measurable in time and H"older continuous in the space variables. By utilizing a generalized notion of strong solution, we establish the existence of a fundamental solution and its optimal H"older regularity, as well as Gaussian estimates. These results are key to study the backward Kolmogorov equations associated to a class of Langevin-type diffusions.