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In this work, we study a class of operators coming from the linearization of some kinetic equations such as Boltzmann equations and Vlasov-Fokker-Planck equations. Since it is not a standard class of pseudodifferential operators, we obtain hypoelliptic estimates in some weight functions space and show the regularity of weak solutions for linear and semilinear equations.doi:10.1215/kjm/1250281072 fatcat:bnr4zrappfa5hlczzgvm3be4m4