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We consider a class of degenerate equations satisfying a parabolicH\"ormander condition, with coefficients that are measurable in time andH\"older continuous in the space variables. By utilizing a generalized notionof strong solution, we establish the existence of a fundamental solution andits optimal H\"older regularity, as well as Gaussian estimates. These resultsare key to study the backward Kolmogorov equations associated to a class ofLangevin-type diffusions.

Optimal regularity for degenerate Kolmogorov equations with rough coefficients