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In continuation of a former work by the first author with F. Nier (2009) andof a more recent work by the second author on the torus (2019), we consider theKramers-Fokker-Planck operator (KFP) with an external electromagnetic field onR d. We show a maximal type estimate on this operator using a nilpotentapproach for vector field polynomial operators and induced representations of anilpotent graded Lie algebra. This estimate leads to an optimalcharacterization of the domain of the closure of the KFP operator and acriterion for the compactness of the resolvent.

Maximal estimates for the Kramers-Fokker-Planck operator with electromagnetic field