Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations

We present global Schauder type estimates in all variables and unique solvability results in kinetic Hölder spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations. The leading coefficients are Hölder continuous in the $x,v$ variables and are merely measurable in the temporal variable. Our proof is inspired by Campanato’s approach to Schauder estimates and does not rely on the estimates of the fundamental solution of the KFP operator.