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Let $M_G$ denotes the centered Hardy-Littlewood maximal function associatedto the Carnot-Carath\'eodory distance or to the pseudo-distance associated tothe fundamental solution of the Grushin operator on $\R_x^n \times \R_u$,$\Delta_G = \sum_{i = 1}^n \frac{\partial^2}{\partial x_i^2} + (\sum_{i = 1}^nx_i^2) \frac{\partial^2}{\partial u^2}$. We get $L^p$ ($p > 1$) dimension freeestimates for $M_G$. We prove also that there exists a constant $A > 0$ suchthat $\| M_G \|_{L^1 \longrightarrow L^{1, \infty}} \leq A n$, $\forall n$.

Fonctions maximales centr\'ees de Hardy-Littlewood pour les op\'erateurs de Grushin