On , endowed with the Laguerre probability measure 渭伪, we define a Hodge–Laguerre operator L伪=未未鈦?/sup>+未鈦?/sup>未 acting on differential forms. Here 未 is the Laguerre exterior differentiation operator, defined as the classical exterior differential, except that the partial derivatives ∂xi are replaced by the ‘‘Laguerre derivatives’’ , and 未鈦?/sup> is the adjoint of 未 with respect to inner product on forms defined by the Euclidean structure and the Laguerre measure 渭伪. We prove dimension-free bounds on Lp, 1<p<∞, for the Riesz transforms and . As applications we prove the strong Hodge–de Rahm–Kodaira decomposition for forms in Lp and deduce existence and regularity results for the solutions of the Hodge and de Rham equations in Lp. We also prove that for suitable functions m the operator m(L伪) is bounded on Lp, 1<p<∞.